%   ORIGINAL: h4/rich__list/SPLITP__compute
% 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/rich__list/SPLITP__AUX__def_c1: !t h acc P. h4/rich__list/SPLITP__AUX acc P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/pair/_2C acc (h4/list/CONS h t)) (h4/rich__list/SPLITP__AUX (h4/list/APPEND acc (h4/list/CONS h h4/list/NIL)) P t)
% Assm: h4/rich__list/SPLITP__AUX__def_c0: !acc P. h4/rich__list/SPLITP__AUX acc P h4/list/NIL = h4/pair/_2C acc h4/list/NIL
% Assm: h4/rich__list/SPLITP0_c1: !x l P. h4/rich__list/SPLITP P (h4/list/CONS x l) = h4/bool/COND (P x) (h4/pair/_2C h4/list/NIL (h4/list/CONS x l)) (h4/pair/_2C (h4/list/CONS x (h4/pair/FST (h4/rich__list/SPLITP P l))) (h4/pair/SND (h4/rich__list/SPLITP P l)))
% Assm: h4/rich__list/SPLITP0_c0: !P. h4/rich__list/SPLITP P h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/rich__list/SPLITP__EVERY: !l P. h4/list/EVERY (\x. ~P x) l ==> h4/rich__list/SPLITP P l = h4/pair/_2C l h4/list/NIL
% Assm: h4/rich__list/PREFIX__DEF: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (h4/rich__list/SPLITP (h4/combin/o $not P) l)
% Assm: h4/rich__list/SPLITL__def: !P. h4/rich__list/SPLITL P = h4/rich__list/SPLITP (h4/combin/o $not P)
% Assm: h4/rich__list/SPLITR__def: !l P. h4/rich__list/SPLITR P l = h4/bool/LET (h4/pair/UNCURRY (\a b. h4/pair/_2C (h4/list/REVERSE b) (h4/list/REVERSE a))) (h4/rich__list/SPLITP (h4/combin/o $not P) (h4/list/REVERSE l))
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> 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/pair/CLOSED__PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/list/list__induction: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/EVERY__DEF_c1: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> P h /\ h4/list/EVERY P t
% Assm: h4/list/EVERY__DEF_c0: !P. h4/list/EVERY P h4/list/NIL <=> T
% 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/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/list/UNZIP0_c0: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/list/ZIP0_c0: h4/list/ZIP (h4/pair/_2C h4/list/NIL h4/list/NIL) = h4/list/NIL
% 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/UNZIP__THM_c0: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% 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/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% 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/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/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/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/list/ZIP__UNZIP: !l. h4/list/ZIP (h4/list/UNZIP l) = l
% 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/ZIP0_c1: !x2 x1 l2 l1. h4/list/ZIP (h4/pair/_2C (h4/list/CONS x1 l1) (h4/list/CONS x2 l2)) = h4/list/CONS (h4/pair/_2C x1 x2) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm: h4/list/LIST__REL__EVERY__ZIP: !l2 l1 R. h4/list/LIST__REL R l1 l2 <=> h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ h4/list/EVERY (h4/pair/UNCURRY R) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/list/LENGTH__ZIP: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l1 /\ h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l2
% 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/list/UNZIP0_c1: !x l. h4/list/UNZIP (h4/list/CONS x l) = h4/pair/_2C (h4/list/CONS (h4/pair/FST x) (h4/pair/FST (h4/list/UNZIP l))) (h4/list/CONS (h4/pair/SND x) (h4/pair/SND (h4/list/UNZIP l)))
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/rich__list/UNZIP__FST__DEF: !l. h4/rich__list/UNZIP__FST l = h4/pair/FST (h4/list/UNZIP l)
% Assm: h4/prim__rec/INV__SUC__EQ: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/list/FOLDL__UNION__BIGUNION__paired: !s ls f. h4/list/FOLDL (\s0. h4/pair/UNCURRY (\x y. h4/pred__set/UNION s0 (f x y))) s ls = h4/pred__set/UNION s (h4/pred__set/BIGUNION (h4/pred__set/IMAGE (h4/pair/UNCURRY f) (h4/list/LIST__TO__SET ls)))
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/list/LENGTH__NIL__SYM: !l. h4/num/0 = h4/list/LENGTH l <=> l = h4/list/NIL
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/rich__list/ZIP__APPEND: !d c b a. h4/list/LENGTH a = h4/list/LENGTH b /\ h4/list/LENGTH c = h4/list/LENGTH d ==> h4/list/APPEND (h4/list/ZIP (h4/pair/_2C a b)) (h4/list/ZIP (h4/pair/_2C c d)) = h4/list/ZIP (h4/pair/_2C (h4/list/APPEND a c) (h4/list/APPEND b d))
% Assm: h4/list/LIST__REL__NIL_c0: !x R. h4/list/LIST__REL R h4/list/NIL x <=> x = h4/list/NIL
% Assm: h4/list/LIST__REL__CONS1: !xs t h R. h4/list/LIST__REL R (h4/list/CONS h t) xs <=> (?h_27 t_27. xs = h4/list/CONS h_27 t_27 /\ R h h_27 /\ h4/list/LIST__REL R t t_27)
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/bool/EQ__IMP__THM: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm: h4/arithmetic/SUC__NOT: !n. ~(h4/num/0 = h4/num/SUC n)
% Assm: h4/list/FOLDL2__tupled__primitive__def: h4/list/FOLDL2__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!cs bs c b a f. R (h4/pair/_2C f (h4/pair/_2C (f a b c) (h4/pair/_2C bs cs))) (h4/pair/_2C f (h4/pair/_2C a (h4/pair/_2C (h4/list/CONS b bs) (h4/list/CONS c cs))))))) (\FOLDL2__tupled a_27. h4/pair/pair__CASE a_27 (\f v1. h4/pair/pair__CASE v1 (\a v3. h4/pair/pair__CASE v3 (\v4 v5. h4/list/list__CASE v4 (h4/combin/I a) (\b bs. h4/list/list__CASE v5 (h4/combin/I a) (\c cs. h4/combin/I (FOLDL2__tupled (h4/pair/_2C f (h4/pair/_2C (f a b c) (h4/pair/_2C bs cs))))))))))
% Assm: h4/list/MAP2__MAP: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f. h4/list/MAP2 f l1 l2 = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C l1 l2)))
% Assm: h4/list/FOLDL0_c1: !x l f e. h4/list/FOLDL f e (h4/list/CONS x l) = h4/list/FOLDL f (f e x) l
% Assm: h4/list/LIST__TO__SET0_c1: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm: h4/list/FOLDL0_c0: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm: h4/list/LIST__TO__SET0_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/pred__set/BIGUNION__EMPTY: h4/pred__set/BIGUNION h4/pred__set/EMPTY = h4/pred__set/EMPTY
% Assm: h4/pred__set/IMAGE__EMPTY: !f. h4/pred__set/IMAGE f h4/pred__set/EMPTY = h4/pred__set/EMPTY
% Assm: h4/pred__set/IMAGE__INSERT: !x s f. h4/pred__set/IMAGE f (h4/pred__set/INSERT x s) = h4/pred__set/INSERT (f x) (h4/pred__set/IMAGE f s)
% Assm: h4/pred__set/UNION__EMPTY_c1: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm: h4/pred__set/UNION__ASSOC: !u t s. h4/pred__set/UNION s (h4/pred__set/UNION t u) = h4/pred__set/UNION (h4/pred__set/UNION s t) u
% Assm: h4/pred__set/BIGUNION__INSERT: !s P. h4/pred__set/BIGUNION (h4/pred__set/INSERT s P) = h4/pred__set/UNION s (h4/pred__set/BIGUNION P)
% Assm: h4/pair/ABS__PAIR__THM: !x. ?q r. x = h4/pair/_2C q r
% Assm: h4/rich__list/REVERSE__ZIP: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/REVERSE (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/ZIP (h4/pair/_2C (h4/list/REVERSE l1) (h4/list/REVERSE l2))
% Assm: h4/list/APPEND__NIL: !l. h4/list/APPEND l h4/list/NIL = l
% 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/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/list/LENGTH__NIL: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/list/list__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/list/MAP__ZIP__SAME: !ls f. h4/list/MAP f (h4/list/ZIP (h4/pair/_2C ls ls)) = h4/list/MAP (\x. f (h4/pair/_2C x x)) ls
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/MAP20_c1: !t2 t1 h2 h1 f. h4/list/MAP2 f (h4/list/CONS h1 t1) (h4/list/CONS h2 t2) = h4/list/CONS (f h1 h2) (h4/list/MAP2 f t1 t2)
% Assm: h4/list/MAP20_c0: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm: h4/list/REVERSE__APPEND: !l2 l1. h4/list/REVERSE (h4/list/APPEND l1 l2) = h4/list/APPEND (h4/list/REVERSE l2) (h4/list/REVERSE l1)
% 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/LENGTH__REVERSE: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm: h4/list/REVERSE__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/APPEND__11_c0: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/list/list__nchotomy: !l. l = h4/list/NIL \/ (?h t. l = h4/list/CONS h t)
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: h4/rich__list/SPLITP = h4/rich__list/SPLITP__AUX h4/list/NIL
%   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_richu_u_lists_SPLITPu_u_AUXu_u_defu_c1]: !t h acc P. happ (happ (h4/rich__list/SPLITP__AUX acc) P) (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (h4/pair/_2C acc (happ (happ h4/list/CONS h) t)) (happ (happ (h4/rich__list/SPLITP__AUX (h4/list/APPEND acc (happ (happ h4/list/CONS h) h4/list/NIL))) P) t)
% Assm [h4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c0]: !acc P. happ (happ (h4/rich__list/SPLITP__AUX acc) P) h4/list/NIL = h4/pair/_2C acc h4/list/NIL
% Assm [h4s_richu_u_lists_SPLITP0u_c1]: !x l P. happ (happ h4/rich__list/SPLITP P) (happ (happ h4/list/CONS x) l) = h4/bool/COND (happ P x) (h4/pair/_2C h4/list/NIL (happ (happ h4/list/CONS x) l)) (h4/pair/_2C (happ (happ h4/list/CONS x) (h4/pair/FST (happ (happ h4/rich__list/SPLITP P) l))) (h4/pair/SND (happ (happ h4/rich__list/SPLITP P) l)))
% Assm [h4s_richu_u_lists_SPLITP0u_c0]: !P. happ (happ h4/rich__list/SPLITP P) h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_richu_u_lists_SPLITPu_u_EVERY]: !_0. (!P x. happ (happ _0 P) x <=> ~happ P x) ==> (!l P. h4/list/EVERY (happ _0 P) l ==> happ (happ h4/rich__list/SPLITP P) l = h4/pair/_2C l h4/list/NIL)
% Assm [h4s_richu_u_lists_PREFIXu_u_DEF]: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (happ (happ h4/rich__list/SPLITP (h4/combin/o $not P)) l)
% Assm [h4s_richu_u_lists_SPLITLu_u_def]: !P. h4/rich__list/SPLITL P = happ h4/rich__list/SPLITP (h4/combin/o $not P)
% Assm [h4s_richu_u_lists_SPLITRu_u_def]: !_1. (!a b. happ (happ _1 a) b = h4/pair/_2C (h4/list/REVERSE b) (h4/list/REVERSE a)) ==> (!_0. (!a. happ _0 a = happ _1 a) ==> (!l P. h4/rich__list/SPLITR P l = h4/bool/LET (h4/pair/UNCURRY _0) (happ (happ h4/rich__list/SPLITP (h4/combin/o $not P)) (h4/list/REVERSE l))))
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_pairs_CLOSEDu_u_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. happ (happ h4/list/CONS a0) a1 = happ (happ h4/list/CONS a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% 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_EVERYu_u_DEFu_c1]: !t h P. h4/list/EVERY P (happ (happ h4/list/CONS h) t) <=> happ P h /\ h4/list/EVERY P t
% Assm [h4s_lists_EVERYu_u_DEFu_c0]: !P. h4/list/EVERY P h4/list/NIL <=> T
% 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_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_lists_UNZIP0u_c0]: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_lists_ZIP0u_c0]: h4/list/ZIP (h4/pair/_2C h4/list/NIL h4/list/NIL) = h4/list/NIL
% 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_UNZIPu_u_THMu_c0]: h4/list/UNZIP h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% 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_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% 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_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% 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_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_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_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_lists_ZIPu_u_UNZIP]: !l. h4/list/ZIP (h4/list/UNZIP l) = l
% 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_ZIP0u_c1]: !x2 x1 l2 l1. h4/list/ZIP (h4/pair/_2C (happ (happ h4/list/CONS x1) l1) (happ (happ h4/list/CONS x2) l2)) = happ (happ h4/list/CONS (h4/pair/_2C x1 x2)) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm [h4s_lists_LISTu_u_RELu_u_EVERYu_u_ZIP]: !l2 l1 R. h4/list/LIST__REL R l1 l2 <=> h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ h4/list/EVERY (h4/pair/UNCURRY R) (h4/list/ZIP (h4/pair/_2C l1 l2))
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. happ (h4/pair/UNCURRY f) (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_lists_LENGTHu_u_ZIP]: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l1 /\ h4/list/LENGTH (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/LENGTH l2
% 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_lists_UNZIP0u_c1]: !x l. h4/list/UNZIP (happ (happ h4/list/CONS x) l) = h4/pair/_2C (happ (happ h4/list/CONS (h4/pair/FST x)) (h4/pair/FST (h4/list/UNZIP l))) (happ (happ h4/list/CONS (h4/pair/SND x)) (h4/pair/SND (h4/list/UNZIP l)))
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_richu_u_lists_UNZIPu_u_FSTu_u_DEF]: !l. h4/rich__list/UNZIP__FST l = h4/pair/FST (h4/list/UNZIP l)
% Assm [h4s_primu_u_recs_INVu_u_SUCu_u_EQ]: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (happ (happ h4/list/CONS h) t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_lists_FOLDLu_u_UNIONu_u_BIGUNIONu_u_paired]: !_2. (!s0 f x y. happ (happ (happ (happ _2 s0) f) x) y = h4/pred__set/UNION s0 (happ (happ f x) y)) ==> (!_1. (!s0 f x. happ (happ (happ _1 s0) f) x = happ (happ (happ _2 s0) f) x) ==> (!_0. (!f s0. happ (happ _0 f) s0 = h4/pair/UNCURRY (happ (happ _1 s0) f)) ==> (!s ls f. h4/list/FOLDL (happ _0 f) s ls = h4/pred__set/UNION s (h4/pred__set/BIGUNION (h4/pred__set/IMAGE (h4/pair/UNCURRY f) (h4/list/LIST__TO__SET ls))))))
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_lists_LENGTHu_u_NILu_u_SYM]: !l. h4/num/0 = h4/list/LENGTH l <=> l = h4/list/NIL
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_richu_u_lists_ZIPu_u_APPEND]: !d c b a. h4/list/LENGTH a = h4/list/LENGTH b /\ h4/list/LENGTH c = h4/list/LENGTH d ==> h4/list/APPEND (h4/list/ZIP (h4/pair/_2C a b)) (h4/list/ZIP (h4/pair/_2C c d)) = h4/list/ZIP (h4/pair/_2C (h4/list/APPEND a c) (h4/list/APPEND b d))
% Assm [h4s_lists_LISTu_u_RELu_u_NILu_c0]: !x R. h4/list/LIST__REL R h4/list/NIL x <=> x = h4/list/NIL
% Assm [h4s_lists_LISTu_u_RELu_u_CONS1]: !xs t h R. h4/list/LIST__REL R (happ (happ h4/list/CONS h) t) xs <=> (?h_27 t_27. xs = happ (happ h4/list/CONS h_27) t_27 /\ happ (happ R h) h_27 /\ h4/list/LIST__REL R t t_27)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_bools_EQu_u_IMPu_u_THM]: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm [h4s_arithmetics_SUCu_u_NOT]: !n. ~(h4/num/0 = h4/num/SUC n)
% Assm [h4s_lists_FOLDL2u_u_tupledu_u_primitiveu_u_def]: !_12. (!FOLDL2__tupled f a b c bs cs. happ (happ (happ (happ (happ (happ (happ _12 FOLDL2__tupled) f) a) b) c) bs) cs = h4/combin/I (happ FOLDL2__tupled (h4/pair/_2C f (h4/pair/_2C (happ (happ (happ f a) b) c) (h4/pair/_2C bs cs))))) ==> (!_11. (!FOLDL2__tupled f a b bs c. happ (happ (happ (happ (happ (happ _11 FOLDL2__tupled) f) a) b) bs) c = happ (happ (happ (happ (happ (happ _12 FOLDL2__tupled) f) a) b) c) bs) ==> (!_10. (!v5 FOLDL2__tupled f a b bs. happ (happ (happ (happ (happ (happ _10 v5) FOLDL2__tupled) f) a) b) bs = h4/list/list__CASE v5 (h4/combin/I a) (happ (happ (happ (happ (happ _11 FOLDL2__tupled) f) a) b) bs)) ==> (!_9. (!v5 FOLDL2__tupled f a b. happ (happ (happ (happ (happ _9 v5) FOLDL2__tupled) f) a) b = happ (happ (happ (happ (happ _10 v5) FOLDL2__tupled) f) a) b) ==> (!_8. (!v4 FOLDL2__tupled f a v5. happ (happ (happ (happ (happ _8 v4) FOLDL2__tupled) f) a) v5 = h4/list/list__CASE v4 (h4/combin/I a) (happ (happ (happ (happ _9 v5) FOLDL2__tupled) f) a)) ==> (!_7. (!FOLDL2__tupled f a v4. happ (happ (happ (happ _7 FOLDL2__tupled) f) a) v4 = happ (happ (happ (happ _8 v4) FOLDL2__tupled) f) a) ==> (!_6. (!FOLDL2__tupled f a v3. happ (happ (happ (happ _6 FOLDL2__tupled) f) a) v3 = h4/pair/pair__CASE v3 (happ (happ (happ _7 FOLDL2__tupled) f) a)) ==> (!_5. (!FOLDL2__tupled f a. happ (happ (happ _5 FOLDL2__tupled) f) a = happ (happ (happ _6 FOLDL2__tupled) f) a) ==> (!_4. (!FOLDL2__tupled f v1. happ (happ (happ _4 FOLDL2__tupled) f) v1 = h4/pair/pair__CASE v1 (happ (happ _5 FOLDL2__tupled) f)) ==> (!_3. (!FOLDL2__tupled f. happ (happ _3 FOLDL2__tupled) f = happ (happ _4 FOLDL2__tupled) f) ==> (!_2. (!FOLDL2__tupled a_27. happ (happ _2 FOLDL2__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 FOLDL2__tupled)) ==> (!_1. (!FOLDL2__tupled. happ _1 FOLDL2__tupled = happ _2 FOLDL2__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!cs bs c b a f. happ (happ R (h4/pair/_2C f (h4/pair/_2C (happ (happ (happ f a) b) c) (h4/pair/_2C bs cs)))) (h4/pair/_2C f (h4/pair/_2C a (h4/pair/_2C (happ (happ h4/list/CONS b) bs) (happ (happ h4/list/CONS c) cs)))))) ==> h4/list/FOLDL2__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_lists_MAP2u_u_MAP]: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> (!f. h4/list/MAP2 f l1 l2 = h4/list/MAP (h4/pair/UNCURRY f) (h4/list/ZIP (h4/pair/_2C l1 l2)))
% Assm [h4s_lists_FOLDL0u_c1]: !x l f e. h4/list/FOLDL f e (happ (happ h4/list/CONS x) l) = h4/list/FOLDL f (happ (happ f e) x) l
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c1]: !t h. h4/list/LIST__TO__SET (happ (happ h4/list/CONS h) t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_FOLDL0u_c0]: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_BIGUNIONu_u_EMPTY]: h4/pred__set/BIGUNION h4/pred__set/EMPTY = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_IMAGEu_u_EMPTY]: !f. h4/pred__set/IMAGE f h4/pred__set/EMPTY = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_IMAGEu_u_INSERT]: !x s f. h4/pred__set/IMAGE f (h4/pred__set/INSERT x s) = h4/pred__set/INSERT (happ f x) (h4/pred__set/IMAGE f s)
% Assm [h4s_predu_u_sets_UNIONu_u_EMPTYu_c1]: !s. h4/pred__set/UNION s h4/pred__set/EMPTY = s
% Assm [h4s_predu_u_sets_UNIONu_u_ASSOC]: !u t s. h4/pred__set/UNION s (h4/pred__set/UNION t u) = h4/pred__set/UNION (h4/pred__set/UNION s t) u
% Assm [h4s_predu_u_sets_BIGUNIONu_u_INSERT]: !s P. h4/pred__set/BIGUNION (h4/pred__set/INSERT s P) = h4/pred__set/UNION s (h4/pred__set/BIGUNION P)
% Assm [h4s_pairs_ABSu_u_PAIRu_u_THM]: !x. ?q r. x = h4/pair/_2C q r
% Assm [h4s_richu_u_lists_REVERSEu_u_ZIP]: !l2 l1. h4/list/LENGTH l1 = h4/list/LENGTH l2 ==> h4/list/REVERSE (h4/list/ZIP (h4/pair/_2C l1 l2)) = h4/list/ZIP (h4/pair/_2C (h4/list/REVERSE l1) (h4/list/REVERSE l2))
% Assm [h4s_lists_APPENDu_u_NIL]: !l. h4/list/APPEND l h4/list/NIL = l
% 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_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_lists_LENGTHu_u_NIL]: !l. h4/list/LENGTH l = h4/num/0 <=> l = h4/list/NIL
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_lists_listu_u_11]: !a1_27 a1 a0_27 a0. happ (happ h4/list/CONS a0) a1 = happ (happ h4/list/CONS a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% 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_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_arithmetics_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_lists_MAPu_u_ZIPu_u_SAME]: !_0. (!f x. happ (happ _0 f) x = happ f (h4/pair/_2C x x)) ==> (!ls f. h4/list/MAP f (h4/list/ZIP (h4/pair/_2C ls ls)) = h4/list/MAP (happ _0 f) ls)
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (happ f h)) (h4/list/MAP f t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MAP20u_c1]: !t2 t1 h2 h1 f. h4/list/MAP2 f (happ (happ h4/list/CONS h1) t1) (happ (happ h4/list/CONS h2) t2) = happ (happ h4/list/CONS (happ (happ f h1) h2)) (h4/list/MAP2 f t1 t2)
% Assm [h4s_lists_MAP20u_c0]: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_REVERSEu_u_APPEND]: !l2 l1. h4/list/REVERSE (h4/list/APPEND l1 l2) = h4/list/APPEND (h4/list/REVERSE l2) (h4/list/REVERSE l1)
% 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_LENGTHu_u_REVERSE]: !l. h4/list/LENGTH (h4/list/REVERSE l) = h4/list/LENGTH l
% Assm [h4s_lists_REVERSEu_u_DEFu_c0]: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_APPENDu_u_11u_c0]: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_lists_listu_u_nchotomy]: !l. l = h4/list/NIL \/ (?h t. l = happ (happ h4/list/CONS h) t)
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Goal: h4/rich__list/SPLITP = h4/rich__list/SPLITP__AUX h4/list/NIL
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_Q1253669,TV_Q1253665]: ![V_f, V_g]: (![V_x]: s(TV_Q1253665,happ(s(t_fun(TV_Q1253669,TV_Q1253665),V_f),s(TV_Q1253669,V_x))) = s(TV_Q1253665,happ(s(t_fun(TV_Q1253669,TV_Q1253665),V_g),s(TV_Q1253669,V_x))) => s(t_fun(TV_Q1253669,TV_Q1253665),V_f) = s(t_fun(TV_Q1253669,TV_Q1253665),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_richu_u_lists_SPLITPu_u_AUXu_u_defu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_acc, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),V_acc))),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_pairs_prod(t_h4s_lists_list(TV_u_27a),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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_acc),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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_acc),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))))))),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_richu_u_lists_SPLITPu_u_AUXu_u_defu_c0, axiom, ![TV_u_27a]: ![V_acc, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),V_acc))),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_acc),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_richu_u_lists_SPLITP0u_c1, axiom, ![TV_u_27a]: ![V_x, V_l, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),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_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),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_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(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_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(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_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),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_pairs_snd(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l)))))))))).
fof(ah4s_richu_u_lists_SPLITP0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(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_SPLITPu_u_EVERY, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),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,V_x)))))) => ![V_l, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l)))) => s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))))).
fof(ah4s_richu_u_lists_PREFIXu_u_DEF, axiom, ![TV_u_27a]: ![V_l, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_prefix(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_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P))))),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_richu_u_lists_SPLITLu_u_def, axiom, ![TV_u_27a]: ![V_P]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_richu_u_lists_splitl(s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_richu_u_lists_SPLITRu_u_def, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_a, V_b]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_h4s_lists_list(TV_u_27a),V_a))),s(t_h4s_lists_list(TV_u_27a),V_b))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_b))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_a))))) => ![V_uu_0]: (![V_a]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_h4s_lists_list(TV_u_27a),V_a))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_h4s_lists_list(TV_u_27a),V_a))) => ![V_l, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitr(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_bools_let(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_pairs_uncurry(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(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(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp),s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l)))))))))).
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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_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_pairs_CLOSEDu_u_PAIRu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x, V_b, V_a]: (s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(TV_u_27b,V_b))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & s(TV_u_27b,V_y) = s(TV_u_27b,V_b)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_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_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),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),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_a0u_27))),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_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_EVERYu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_every(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_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_EVERYu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
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_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_UNZIP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))).
fof(ah4s_lists_ZIP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(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(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil)).
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_UNZIPu_u_THMu_c0, axiom, ![TV_u_27a,TV_u_27b]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))).
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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_ZIPu_u_UNZIP, axiom, ![TV_u_27a,TV_u_27b]: ![V_l]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)).
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_ZIP0u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_x2, V_x1, V_l2, V_l1]: s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(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_x1))),s(t_h4s_lists_list(TV_u_27a),V_l1))),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_x2))),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),h4s_lists_cons),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(TV_u_27b,V_x2))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))))))).
fof(ah4s_lists_LISTu_u_RELu_u_EVERYu_u_ZIP, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2, V_l1, V_R]: (p(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),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))) <=> (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) & p(s(t_bool,h4s_lists_every(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))))))).
fof(ah4s_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_lists_LENGTHu_u_ZIP, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) & s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2)))))).
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_lists_UNZIP0u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_l]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b))),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)))),h4s_lists_cons),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(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_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))))))),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,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))),s(t_h4s_lists_list(TV_u_27b),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))))))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_richu_u_lists_UNZIPu_u_FSTu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_unzipu_u_fst(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_lists_unzip(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_l)))))).
fof(ah4s_primu_u_recs_INVu_u_SUCu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),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_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_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_nums_NOTu_u_SUC, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_lists_FOLDLu_u_UNIONu_u_BIGUNIONu_u_paired, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_uu_2]: (![V_s0, V_f, V_x, V_y]: s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)))),happ(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))))),V_uu_2),s(t_fun(TV_u_27c,t_bool),V_s0))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))) = s(t_fun(TV_u_27c,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27c,t_bool),V_s0),s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))))) => ![V_uu_1]: (![V_s0, V_f, V_x]: s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)))),happ(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))))),V_uu_1),s(t_fun(TV_u_27c,t_bool),V_s0))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)))),happ(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))))),V_uu_2),s(t_fun(TV_u_27c,t_bool),V_s0))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(TV_u_27a,V_x))) => ![V_uu_0]: (![V_f, V_s0]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool)),happ(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(t_fun(TV_u_27c,t_bool),V_s0))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool)),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool)))),happ(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))))),V_uu_1),s(t_fun(TV_u_27c,t_bool),V_s0))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))))) => ![V_s, V_ls, V_f]: s(t_fun(TV_u_27c,t_bool),h4s_lists_foldl(s(t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),t_fun(t_fun(TV_u_27c,t_bool),t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(t_fun(TV_u_27c,t_bool),V_s),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_ls))) = s(t_fun(TV_u_27c,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27c,t_bool),V_s),s(t_fun(TV_u_27c,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(TV_u_27c,t_bool),t_bool),h4s_predu_u_sets_image(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_fun(TV_u_27c,t_bool)),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_bool))),V_f))),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),V_ls))))))))))))).
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_lists_LENGTHu_u_NILu_u_SYM, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_nums_num,h4s_nums_0) = 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_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_richu_u_lists_ZIPu_u_APPEND, axiom, ![TV_u_27a,TV_u_27b]: ![V_d, V_c, V_b, V_a]: ((s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_a))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_b))) & s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_c))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_d)))) => s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_append(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27b),V_b))))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_c),s(t_h4s_lists_list(TV_u_27b),V_d))))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_a),s(t_h4s_lists_list(TV_u_27a),V_c))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_append(s(t_h4s_lists_list(TV_u_27b),V_b),s(t_h4s_lists_list(TV_u_27b),V_d))))))))).
fof(ah4s_lists_LISTu_u_RELu_u_NILu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_R]: (p(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),V_x)))) <=> s(t_h4s_lists_list(TV_u_27b),V_x) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))).
fof(ah4s_lists_LISTu_u_RELu_u_CONS1, axiom, ![TV_u_27a,TV_u_27b]: ![V_xs, V_t, V_h, V_R]: (p(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),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_27b),V_xs)))) <=> ?[V_hu_27, V_tu_27]: (s(t_h4s_lists_list(TV_u_27b),V_xs) = 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_hu_27))),s(t_h4s_lists_list(TV_u_27b),V_tu_27))) & (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_R),s(TV_u_27a,V_h))),s(TV_u_27b,V_hu_27)))) & p(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),V_t),s(t_h4s_lists_list(TV_u_27b),V_tu_27)))))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & 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,V_a)))))).
fof(ah4s_bools_EQu_u_IMPu_u_THM, 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_t2)) => p(s(t_bool,V_t1)))))).
fof(ah4s_arithmetics_SUCu_u_NOT, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_0) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))).
fof(ah4s_lists_FOLDL2u_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_12]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_c, V_bs, V_cs]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_lists_list(TV_u_27b),V_bs))),s(t_h4s_lists_list(TV_u_27c),V_cs))) = s(TV_u_27a,h4s_combins_i(s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(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(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)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),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_bs),s(t_h4s_lists_list(TV_u_27c),V_cs))))))))))) => ![V_uu_11]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_bs, V_c]: s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),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),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))),s(TV_u_27c,V_c))) = s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_lists_list(TV_u_27b),V_bs))) => ![V_uu_10]: (![V_v5, V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_bs]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))) = s(TV_u_27a,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27c),V_v5),s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_a))),s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),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),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))))) => ![V_uu_9]: (![V_v5, V_FOLDL2u_u_tupled, V_f, V_a, V_b]: s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) => ![V_uu_8]: (![V_v4, V_FOLDL2u_u_tupled, V_f, V_a, V_v5]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_8),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27c),V_v5))) = s(TV_u_27a,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27b),V_v4),s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_a))),s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))))) => ![V_uu_7]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_v4]: s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27b),V_v4))) = s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_8),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_v3]: s(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)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),V_v3))) = s(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_v3),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))))) => ![V_uu_5]: (![V_FOLDL2u_u_tupled, V_f, V_a]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) => ![V_uu_4]: (![V_FOLDL2u_u_tupled, V_f, V_v1]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_v1))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_v1),s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))))) => ![V_uu_3]: (![V_FOLDL2u_u_tupled, V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))) => ![V_uu_2]: (![V_FOLDL2u_u_tupled, V_au_27]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),V_au_27))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),V_au_27),s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))))) => ![V_uu_1]: (![V_FOLDL2u_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_cs, V_bs, V_c, V_b, V_a, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(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(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)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),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_bs),s(t_h4s_lists_list(TV_u_27c),V_cs))))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(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(TV_u_27a,V_a),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_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))),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_c))),s(t_h4s_lists_list(TV_u_27c),V_cs)))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),h4s_lists_foldl2u_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(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_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_1))))))))))))))))).
fof(ah4s_lists_MAP2u_u_MAP, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => ![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),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))) = s(t_h4s_lists_list(TV_u_27c),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),TV_u_27c),h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f))),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))))).
fof(ah4s_lists_FOLDL0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,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,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(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_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_h),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),V_t)))))).
fof(ah4s_lists_FOLDL0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,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_LISTu_u_TOu_u_SET0u_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_predu_u_sets_BIGUNIONu_u_EMPTY, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_predu_u_sets_IMAGEu_u_EMPTY, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_predu_u_sets_IMAGEu_u_INSERT, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_s, V_f]: s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))),s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_image(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_predu_u_sets_UNIONu_u_EMPTYu_c1, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(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_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_predu_u_sets_UNIONu_u_ASSOC, axiom, ![TV_u_27a]: ![V_u, V_t, V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_t),s(t_fun(TV_u_27a,t_bool),V_u))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t))),s(t_fun(TV_u_27a,t_bool),V_u)))).
fof(ah4s_predu_u_sets_BIGUNIONu_u_INSERT, axiom, ![TV_u_27a]: ![V_s, V_P]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),h4s_predu_u_sets_insert(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P))))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_union(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_bigunion(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P)))))).
fof(ah4s_pairs_ABSu_u_PAIRu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: ?[V_q, V_r]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_q),s(TV_u_27b,V_r)))).
fof(ah4s_richu_u_lists_REVERSEu_u_ZIP, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2, V_l1]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) => s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_reverse(s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2))))))) = s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27b)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27b),V_l2))))))))).
fof(ah4s_lists_APPENDu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_LENGTHu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) = 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),h4s_lists_nil))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_lists_listu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, 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),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_a0u_27))),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_numerals_numeralu_u_lteu_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_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_EQu_u_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_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_arithmetics_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_bools_IMPu_u_DISJu_u_THM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) => p(s(t_bool,V_B))) <=> (~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B))))).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_lists_MAPu_u_ZIPu_u_SAME, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27a,V_x))))) => ![V_ls, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f),s(t_h4s_lists_list(t_h4s_pairs_prod(TV_u_27a,TV_u_27a)),h4s_lists_zip(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),V_ls),s(t_h4s_lists_list(TV_u_27a),V_ls))))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27a),TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27a),V_ls))))).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),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_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = 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,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_MAP20u_c1, axiom, ![TV_u_27f,TV_u_27d,TV_u_27e]: ![V_t2, V_t1, V_h2, V_h1, V_f]: s(t_h4s_lists_list(TV_u_27f),h4s_lists_map2(s(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),V_f),s(t_h4s_lists_list(TV_u_27d),happ(s(t_fun(t_h4s_lists_list(TV_u_27d),t_h4s_lists_list(TV_u_27d)),happ(s(t_fun(TV_u_27d,t_fun(t_h4s_lists_list(TV_u_27d),t_h4s_lists_list(TV_u_27d))),h4s_lists_cons),s(TV_u_27d,V_h1))),s(t_h4s_lists_list(TV_u_27d),V_t1))),s(t_h4s_lists_list(TV_u_27e),happ(s(t_fun(t_h4s_lists_list(TV_u_27e),t_h4s_lists_list(TV_u_27e)),happ(s(t_fun(TV_u_27e,t_fun(t_h4s_lists_list(TV_u_27e),t_h4s_lists_list(TV_u_27e))),h4s_lists_cons),s(TV_u_27e,V_h2))),s(t_h4s_lists_list(TV_u_27e),V_t2))))) = s(t_h4s_lists_list(TV_u_27f),happ(s(t_fun(t_h4s_lists_list(TV_u_27f),t_h4s_lists_list(TV_u_27f)),happ(s(t_fun(TV_u_27f,t_fun(t_h4s_lists_list(TV_u_27f),t_h4s_lists_list(TV_u_27f))),h4s_lists_cons),s(TV_u_27f,happ(s(t_fun(TV_u_27e,TV_u_27f),happ(s(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),V_f),s(TV_u_27d,V_h1))),s(TV_u_27e,V_h2))))),s(t_h4s_lists_list(TV_u_27f),h4s_lists_map2(s(t_fun(TV_u_27d,t_fun(TV_u_27e,TV_u_27f)),V_f),s(t_h4s_lists_list(TV_u_27d),V_t1),s(t_h4s_lists_list(TV_u_27e),V_t2)))))).
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_lists_REVERSEu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l1)))))).
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_LENGTHu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))).
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_11u_c0, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l3))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_lists_listu_u_nchotomy, 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) | ?[V_h, V_t]: 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_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))).
fof(ah4s_numerals_numeralu_u_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ch4s_richu_u_lists_SPLITPu_u_compute, conjecture, ![TV_u_27a]: s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitp) = s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),h4s_richu_u_lists_splitpu_u_aux(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
