%   ORIGINAL: h4/res__quan/RES__SELECT__UNIV
% 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/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/RES__SELECT__DEF: h4/bool/RES__SELECT = (\p m. h4/min/_40 (\x. h4/bool/IN x p /\ m x))
% Assm: h4/bool/EXISTS__DEF: $exists = (\P. P (h4/min/_40 P))
% Assm: h4/res__quan/RES__SELECT: !f P. h4/bool/RES__SELECT P f = h4/min/_40 (\x. h4/bool/IN x P /\ f x)
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/SELECT__UNIQUE: !x P. (!y. P y <=> y = x) ==> h4/min/_40 P = x
% Assm: h4/bool/SELECT__ELIM__THM: !Q P. (?x. P x) /\ (!x. P x ==> Q x) ==> Q (h4/min/_40 P)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/RES__SELECT__THM: !f P. h4/bool/RES__SELECT P f = h4/min/_40 (\x. h4/bool/IN x P /\ f x)
% Assm: h4/res__quan/RES__SELECT__EMPTY: !p. h4/bool/RES__SELECT h4/pred__set/EMPTY p = h4/min/_40 (\x. F)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/res__quan/RES__EXISTS__ALT: !p m. h4/bool/RES__EXISTS p m <=> h4/bool/IN (h4/bool/RES__SELECT p m) p /\ m (h4/bool/RES__SELECT p m)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/res__quan/RES__EXISTS: !f P. h4/bool/RES__EXISTS P f <=> (?x. h4/bool/IN x P /\ f x)
% Assm: h4/pred__set/SPECIFICATION: !x P. h4/bool/IN x P <=> P x
% Assm: h4/option/some__def: !P. h4/option/some P = h4/bool/COND (?x. P x) (h4/option/SOME (h4/min/_40 (\x. P x))) h4/option/NONE
% Assm: h4/list/SET__TO__LIST__primitive: h4/list/SET__TO__LIST = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> R (h4/pred__set/REST s) s))) (\SET__TO__LIST s. h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND (s = h4/pred__set/EMPTY) h4/list/NIL (h4/list/CONS (h4/pred__set/CHOICE s) (SET__TO__LIST (h4/pred__set/REST s)))) h4/bool/ARB))
% Assm: h4/pred__set/ITSET__tupled__primitive__def: !f. h4/pred__set/ITSET__tupled f = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!b s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> R (h4/pair/_2C (h4/pred__set/REST s) (f (h4/pred__set/CHOICE s) b)) (h4/pair/_2C s b)))) (\ITSET__tupled a. h4/pair/pair__CASE a (\s b. h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND (s = h4/pred__set/EMPTY) b (ITSET__tupled (h4/pair/_2C (h4/pred__set/REST s) (f (h4/pred__set/CHOICE s) b)))) h4/bool/ARB)))
% Assm: h4/relation/the__fun__def: !x R M. h4/relation/the__fun R M x = h4/min/_40 (\f. h4/relation/approx R M x f)
% Assm: h4/bool/SELECT__REFL: !x. h4/min/_40 (\y. y = x) = x
% Assm: h4/bool/SELECT__THM: !P. P (h4/min/_40 (\x. P x)) <=> (?x. P x)
% Assm: h4/numpair/invtri0__tupled__primitive__def: h4/numpair/invtri0__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!a n. ~h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> R (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a)))) (\invtri0__tupled a_27. h4/pair/pair__CASE a_27 (\n a. h4/combin/I (h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (invtri0__tupled (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))
% Assm: h4/ind__type/ZBOT0: h4/ind__type/ZBOT = h4/ind__type/INJP (h4/ind__type/INJN h4/num/0) (h4/min/_40 (\z. T))
% Assm: h4/bool/SELECT__REFL__2: !x. h4/min/_40 (\y. x = y) = x
% Assm: h4/prim__rec/PRE__DEF: !m. h4/prim__rec/PRE m = h4/bool/COND (m = h4/num/0) h4/num/0 (h4/min/_40 (\n. m = h4/num/SUC n))
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/pred__set/IN__UNIV: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm: h4/numpair/nlistrec__tupled__primitive__def: h4/numpair/nlistrec__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!f n l. ~(l = h4/num/0) ==> R (h4/pair/_2C n (h4/pair/_2C f (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))) (h4/pair/_2C n (h4/pair/_2C f l))))) (\nlistrec__tupled a. h4/pair/pair__CASE a (\n v1. h4/pair/pair__CASE v1 (\f l. h4/combin/I (h4/bool/COND (l = h4/num/0) n (f (h4/numpair/nfst (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (nlistrec__tupled (h4/pair/_2C n (h4/pair/_2C f (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))))))))
% Assm: h4/bool/COND__DEF: h4/bool/COND = (\t t1 t2. h4/min/_40 (\x. ((t <=> T) ==> x = t1) /\ ((t <=> F) ==> x = t2)))
% Assm: h4/one/one__DEF: h4/one/one0 = h4/min/_40 (\x. T)
% Assm: h4/list/MAP2__tupled__primitive__def: h4/list/MAP2__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!h2 h1 t2 t1 f. R (h4/pair/_2C f (h4/pair/_2C t1 t2)) (h4/pair/_2C f (h4/pair/_2C (h4/list/CONS h1 t1) (h4/list/CONS h2 t2)))))) (\MAP2__tupled a. h4/pair/pair__CASE a (\f v1. h4/pair/pair__CASE v1 (\v2 v3. h4/list/list__CASE v2 (h4/combin/I h4/list/NIL) (\h1 t1. h4/list/list__CASE v3 (h4/combin/I h4/list/NIL) (\h2 t2. h4/combin/I (h4/list/CONS (f h1 h2) (MAP2__tupled (h4/pair/_2C f (h4/pair/_2C t1 t2)))))))))
% Assm: h4/list/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/pred__set/EXTENSION: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm: h4/pred__set/EQ__UNIV: !s. (!x. h4/bool/IN x s) <=> s = h4/pred__set/UNIV
% Assm: h4/pred__set/UNION__UNIV_c1: !s. h4/pred__set/UNION s h4/pred__set/UNIV = h4/pred__set/UNIV
% Assm: h4/pred__set/INTER__UNIV_c1: !s. h4/pred__set/INTER s h4/pred__set/UNIV = s
% Assm: h4/pred__set/UNION__UNIV_c0: !s. h4/pred__set/UNION h4/pred__set/UNIV s = h4/pred__set/UNIV
% Assm: h4/pred__set/NOT__IN__FINITE: ~h4/pred__set/FINITE h4/pred__set/UNIV <=> (!s. h4/pred__set/FINITE s ==> (?x. ~h4/bool/IN x s))
% Assm: h4/pred__set/infinite__num__inj: !s. ~h4/pred__set/FINITE s <=> (?f. h4/pred__set/INJ f h4/pred__set/UNIV s)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/pred__set/IN__UNION: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c1: !t. t \/ T <=> T
% Assm: h4/pred__set/IN__INTER: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/NOT__IMP: !B A. ~(A ==> B) <=> A /\ ~B
% Assm: h4/pred__set/chooser__def_c1: !s n. h4/pred__set/chooser s (h4/num/SUC n) = h4/pred__set/chooser (h4/pred__set/REST s) n
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/pred__set/chooser__def_c0: !s. h4/pred__set/chooser s h4/num/0 = h4/pred__set/CHOICE s
% Assm: h4/pred__set/INFINITE__INHAB: !P. ~h4/pred__set/FINITE P ==> (?x. h4/bool/IN x P)
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/pred__set/INJ__DEF: !t s f. h4/pred__set/INJ f s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN (f x) t) /\ (!x y. h4/bool/IN x s /\ h4/bool/IN y s ==> f x = f y ==> x = y)
% Assm: h4/pred__set/REST__SUBSET: !s. h4/pred__set/SUBSET (h4/pred__set/REST s) s
% Assm: h4/pred__set/REST__DEF: !s. h4/pred__set/REST s = h4/pred__set/DELETE s (h4/pred__set/CHOICE s)
% Assm: h4/pred__set/infinite__rest: !s. ~h4/pred__set/FINITE s ==> ~h4/pred__set/FINITE (h4/pred__set/REST s)
% Assm: h4/pred__set/CHOICE__DEF: !s. ~(s = h4/pred__set/EMPTY) ==> h4/bool/IN (h4/pred__set/CHOICE s) s
% Assm: h4/pred__set/IN__DELETE: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm: h4/pred__set/INSERT__DEF: !x s. h4/pred__set/INSERT x s = h4/pred__set/GSPEC (\y. h4/pair/_2C y (y = x \/ h4/bool/IN y s))
% Assm: h4/pred__set/FINITE__INDUCT: !P. P h4/pred__set/EMPTY /\ (!s. h4/pred__set/FINITE s /\ P s ==> (!e. ~h4/bool/IN e s ==> P (h4/pred__set/INSERT e s))) ==> (!s. h4/pred__set/FINITE s ==> P s)
% Assm: h4/pred__set/FINITE__DELETE: !x s. h4/pred__set/FINITE (h4/pred__set/DELETE s x) <=> h4/pred__set/FINITE s
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/pred__set/UNIV__NOT__EMPTY: ~(h4/pred__set/UNIV = h4/pred__set/EMPTY)
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/pred__set/SUBSET__DEF: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm: h4/pred__set/SUBSET__REFL: !s. h4/pred__set/SUBSET s s
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/pred__set/GSPECIFICATION: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = f x)
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__add_c2: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/arithmetic/num__CASES: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/bool/LEFT__FORALL__OR__THM: !Q P. (!x. P x \/ Q) <=> (!x. P x) \/ Q
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/arithmetic/NOT__NUM__EQ: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/LESS__EQ: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/numeral/numeral__distrib_c2: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm: h4/prim__rec/INV__SUC__EQ: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm: h4/pair/PAIR__EQ: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm: h4/num/INDUCTION: !P. P h4/num/0 /\ (!n. P n ==> P (h4/num/SUC n)) ==> (!n. P n)
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/LEFT__OR__OVER__AND: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__DISJ__THM: !B A. A ==> B <=> ~A \/ B
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/numeral/numeral__add_c0: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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)
% Goal: !p. h4/bool/RES__SELECT h4/pred__set/UNIV p = h4/min/_40 p
%   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_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_RESu_u_SELECTu_u_DEF]: !_0. (!x x' x. happ (happ (happ _0 x) x') x <=> h4/bool/IN x x /\ happ x' x) ==> (!x x'. h4/bool/RES__SELECT x x' = h4/min/_40 (happ (happ _0 x) x'))
% Assm [h4s_bools_EXISTSu_u_DEF]: !x. $exists x <=> happ x (h4/min/_40 x)
% Assm [h4s_resu_u_quans_RESu_u_SELECT]: !_0. (!P f x. happ (happ (happ _0 P) f) x <=> h4/bool/IN x P /\ happ f x) ==> (!f P. h4/bool/RES__SELECT P f = h4/min/_40 (happ (happ _0 P) f))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_SELECTu_u_UNIQUE]: !x P. (!y. happ P y <=> y = x) ==> h4/min/_40 P = x
% Assm [h4s_bools_SELECTu_u_ELIMu_u_THM]: !Q P. (?x. happ P x) /\ (!x. happ P x ==> happ Q x) ==> happ Q (h4/min/_40 P)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_RESu_u_SELECTu_u_THM]: !_0. (!P f x. happ (happ (happ _0 P) f) x <=> h4/bool/IN x P /\ happ f x) ==> (!f P. h4/bool/RES__SELECT P f = h4/min/_40 (happ (happ _0 P) f))
% Assm [h4s_resu_u_quans_RESu_u_SELECTu_u_EMPTY]: !_0. (!x. happ _0 x <=> F) ==> (!p. h4/bool/RES__SELECT h4/pred__set/EMPTY p = h4/min/_40 _0)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_resu_u_quans_RESu_u_EXISTSu_u_ALT]: !p m. h4/bool/RES__EXISTS p m <=> h4/bool/IN (h4/bool/RES__SELECT p m) p /\ happ m (h4/bool/RES__SELECT p m)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_resu_u_quans_RESu_u_EXISTS]: !f P. h4/bool/RES__EXISTS P f <=> (?x. h4/bool/IN x P /\ happ f x)
% Assm [h4s_predu_u_sets_SPECIFICATION]: !x P. h4/bool/IN x P <=> happ P x
% Assm [h4s_options_someu_u_def]: !_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!P. ?v. (v <=> (?x. happ P x)) /\ h4/option/some P = h4/bool/COND v (h4/option/SOME (h4/min/_40 (happ _0 P))) h4/option/NONE)
% Assm [h4s_lists_SETu_u_TOu_u_LISTu_u_primitive]: !_2. (!SET__TO__LIST s. ?v. (v <=> s = h4/pred__set/EMPTY) /\ happ (happ _2 SET__TO__LIST) s = h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND v h4/list/NIL (h4/list/CONS (h4/pred__set/CHOICE s) (happ SET__TO__LIST (h4/pred__set/REST s)))) h4/bool/ARB)) ==> (!_1. (!SET__TO__LIST. happ _1 SET__TO__LIST = happ _2 SET__TO__LIST) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> happ (happ R (h4/pred__set/REST s)) s)) ==> h4/list/SET__TO__LIST = h4/relation/WFREC (h4/min/_40 _0) _1))
% Assm [h4s_predu_u_sets_ITSETu_u_tupledu_u_primitiveu_u_def]: !_4. (!ITSET__tupled f s b. ?v. (v <=> s = h4/pred__set/EMPTY) /\ happ (happ (happ (happ _4 ITSET__tupled) f) s) b = h4/combin/I (h4/bool/COND (h4/pred__set/FINITE s) (h4/bool/COND v b (happ ITSET__tupled (h4/pair/_2C (h4/pred__set/REST s) (happ (happ f (h4/pred__set/CHOICE s)) b)))) h4/bool/ARB)) ==> (!_3. (!ITSET__tupled f s. happ (happ (happ _3 ITSET__tupled) f) s = happ (happ (happ _4 ITSET__tupled) f) s) ==> (!_2. (!ITSET__tupled f a. happ (happ (happ _2 ITSET__tupled) f) a = h4/pair/pair__CASE a (happ (happ _3 ITSET__tupled) f)) ==> (!_1. (!f ITSET__tupled. happ (happ _1 f) ITSET__tupled = happ (happ _2 ITSET__tupled) f) ==> (!_0. (!f R. happ (happ _0 f) R <=> h4/relation/WF R /\ (!b s. h4/pred__set/FINITE s /\ ~(s = h4/pred__set/EMPTY) ==> happ (happ R (h4/pair/_2C (h4/pred__set/REST s) (happ (happ f (h4/pred__set/CHOICE s)) b))) (h4/pair/_2C s b))) ==> (!f. h4/pred__set/ITSET__tupled f = h4/relation/WFREC (h4/min/_40 (happ _0 f)) (happ _1 f))))))
% Assm [h4s_relations_theu_u_funu_u_def]: !_0. (!R M x f. happ (happ (happ (happ _0 R) M) x) f <=> h4/relation/approx R M x f) ==> (!x R M. h4/relation/the__fun R M x = h4/min/_40 (happ (happ (happ _0 R) M) x))
% Assm [h4s_bools_SELECTu_u_REFL]: !_0. (!x y. happ (happ _0 x) y <=> y = x) ==> (!x. h4/min/_40 (happ _0 x) = x)
% Assm [h4s_bools_SELECTu_u_THM]: !_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!P. happ P (h4/min/_40 (happ _0 P)) <=> (?x. happ P x))
% Assm [h4s_numpairs_invtri0u_u_tupledu_u_primitiveu_u_def]: !_4. (!invtri0__tupled n a. happ (happ (happ _4 invtri0__tupled) n) a = h4/combin/I (h4/bool/COND (h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/pair/_2C n a) (happ invtri0__tupled (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) ==> (!_3. (!invtri0__tupled n. happ (happ _3 invtri0__tupled) n = happ (happ _4 invtri0__tupled) n) ==> (!_2. (!invtri0__tupled a_27. happ (happ _2 invtri0__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 invtri0__tupled)) ==> (!_1. (!invtri0__tupled. happ _1 invtri0__tupled = happ _2 invtri0__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!a n. ~h4/prim__rec/_3C n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))) ==> happ (happ R (h4/pair/_2C (h4/arithmetic/_2D n (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))) (h4/arithmetic/_2B a (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/pair/_2C n a))) ==> h4/numpair/invtri0__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))
% Assm [h4s_indu_u_types_ZBOT0]: !_0. (!z. happ _0 z <=> T) ==> h4/ind__type/ZBOT = h4/ind__type/INJP (h4/ind__type/INJN h4/num/0) (h4/min/_40 _0)
% Assm [h4s_bools_SELECTu_u_REFLu_u_2]: !_0. (!x y. happ (happ _0 x) y <=> x = y) ==> (!x. h4/min/_40 (happ _0 x) = x)
% Assm [h4s_primu_u_recs_PREu_u_DEF]: !_0. (!m n. happ (happ _0 m) n <=> m = h4/num/SUC n) ==> (!m. ?v. (v <=> m = h4/num/0) /\ h4/prim__rec/PRE m = h4/bool/COND v h4/num/0 (h4/min/_40 (happ _0 m)))
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_predu_u_sets_INu_u_UNIV]: !x. h4/bool/IN x h4/pred__set/UNIV
% Assm [h4s_numpairs_nlistrecu_u_tupledu_u_primitiveu_u_def]: !_6. (!nlistrec__tupled n f l. ?v. (v <=> l = h4/num/0) /\ happ (happ (happ (happ _6 nlistrec__tupled) n) f) l = h4/combin/I (h4/bool/COND v n (happ (happ (happ f (h4/numpair/nfst (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))) (happ nlistrec__tupled (h4/pair/_2C n (h4/pair/_2C f (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)))))))))) ==> (!_5. (!nlistrec__tupled n f. happ (happ (happ _5 nlistrec__tupled) n) f = happ (happ (happ _6 nlistrec__tupled) n) f) ==> (!_4. (!nlistrec__tupled n v1. happ (happ (happ _4 nlistrec__tupled) n) v1 = h4/pair/pair__CASE v1 (happ (happ _5 nlistrec__tupled) n)) ==> (!_3. (!nlistrec__tupled n. happ (happ _3 nlistrec__tupled) n = happ (happ _4 nlistrec__tupled) n) ==> (!_2. (!nlistrec__tupled a. happ (happ _2 nlistrec__tupled) a = h4/pair/pair__CASE a (happ _3 nlistrec__tupled)) ==> (!_1. (!nlistrec__tupled. happ _1 nlistrec__tupled = happ _2 nlistrec__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!f n l. ~(l = h4/num/0) ==> happ (happ R (h4/pair/_2C n (h4/pair/_2C f (h4/numpair/nsnd (h4/arithmetic/_2D l (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))))))) (h4/pair/_2C n (h4/pair/_2C f l)))) ==> h4/numpair/nlistrec__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))
% Assm [h4s_bools_CONDu_u_DEF]: !_0. (!x x x' x''. happ (happ (happ (happ _0 x) x) x') x'' <=> ((x <=> T) ==> x'' = x) /\ ((x <=> F) ==> x'' = x')) ==> (!x x x'. h4/bool/COND x x x' = h4/min/_40 (happ (happ (happ _0 x) x) x'))
% Assm [h4s_ones_oneu_u_DEF]: !_0. (!x. happ _0 x <=> T) ==> h4/one/one0 = h4/min/_40 _0
% 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 (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 (h4/list/CONS h1 t1) (h4/list/CONS h2 t2))))) ==> h4/list/MAP2__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% 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 (h4/list/CONS b bs) (h4/list/CONS c cs)))))) ==> h4/list/FOLDL2__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_predu_u_sets_EXTENSION]: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm [h4s_predu_u_sets_EQu_u_UNIV]: !s. (!x. h4/bool/IN x s) <=> s = h4/pred__set/UNIV
% Assm [h4s_predu_u_sets_UNIONu_u_UNIVu_c1]: !s. h4/pred__set/UNION s h4/pred__set/UNIV = h4/pred__set/UNIV
% Assm [h4s_predu_u_sets_INTERu_u_UNIVu_c1]: !s. h4/pred__set/INTER s h4/pred__set/UNIV = s
% Assm [h4s_predu_u_sets_UNIONu_u_UNIVu_c0]: !s. h4/pred__set/UNION h4/pred__set/UNIV s = h4/pred__set/UNIV
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_FINITE]: ~h4/pred__set/FINITE h4/pred__set/UNIV <=> (!s. h4/pred__set/FINITE s ==> (?x. ~h4/bool/IN x s))
% Assm [h4s_predu_u_sets_infiniteu_u_numu_u_inj]: !s. ~h4/pred__set/FINITE s <=> (?f. h4/pred__set/INJ f h4/pred__set/UNIV s)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_predu_u_sets_INu_u_UNION]: !x t s. h4/bool/IN x (h4/pred__set/UNION s t) <=> h4/bool/IN x s \/ h4/bool/IN x t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c1]: !t. t \/ T <=> T
% Assm [h4s_predu_u_sets_INu_u_INTER]: !x t s. h4/bool/IN x (h4/pred__set/INTER s t) <=> h4/bool/IN x s /\ h4/bool/IN x t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_NOTu_u_IMP]: !B A. ~(A ==> B) <=> A /\ ~B
% Assm [h4s_predu_u_sets_chooseru_u_defu_c1]: !s n. h4/pred__set/chooser s (h4/num/SUC n) = h4/pred__set/chooser (h4/pred__set/REST s) n
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_predu_u_sets_chooseru_u_defu_c0]: !s. h4/pred__set/chooser s h4/num/0 = h4/pred__set/CHOICE s
% Assm [h4s_predu_u_sets_INFINITEu_u_INHAB]: !P. ~h4/pred__set/FINITE P ==> (?x. h4/bool/IN x P)
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_predu_u_sets_INJu_u_DEF]: !t s f. h4/pred__set/INJ f s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN (happ f x) t) /\ (!x y. h4/bool/IN x s /\ h4/bool/IN y s ==> happ f x = happ f y ==> x = y)
% Assm [h4s_predu_u_sets_RESTu_u_SUBSET]: !s. h4/pred__set/SUBSET (h4/pred__set/REST s) s
% Assm [h4s_predu_u_sets_RESTu_u_DEF]: !s. h4/pred__set/REST s = h4/pred__set/DELETE s (h4/pred__set/CHOICE s)
% Assm [h4s_predu_u_sets_infiniteu_u_rest]: !s. ~h4/pred__set/FINITE s ==> ~h4/pred__set/FINITE (h4/pred__set/REST s)
% Assm [h4s_predu_u_sets_CHOICEu_u_DEF]: !s. ~(s = h4/pred__set/EMPTY) ==> h4/bool/IN (h4/pred__set/CHOICE s) s
% Assm [h4s_predu_u_sets_INu_u_DELETE]: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm [h4s_predu_u_sets_INSERTu_u_DEF]: !_0. (!x s y. ?v. (v <=> y = x \/ h4/bool/IN y s) /\ happ (happ (happ _0 x) s) y = h4/pair/_2C y v) ==> (!x s. h4/pred__set/INSERT x s = h4/pred__set/GSPEC (happ (happ _0 x) s))
% Assm [h4s_predu_u_sets_FINITEu_u_INDUCT]: !P. happ P h4/pred__set/EMPTY /\ (!s. h4/pred__set/FINITE s /\ happ P s ==> (!e. ~h4/bool/IN e s ==> happ P (h4/pred__set/INSERT e s))) ==> (!s. h4/pred__set/FINITE s ==> happ P s)
% Assm [h4s_predu_u_sets_FINITEu_u_DELETE]: !x s. h4/pred__set/FINITE (h4/pred__set/DELETE s x) <=> h4/pred__set/FINITE s
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_predu_u_sets_UNIVu_u_NOTu_u_EMPTY]: ~(h4/pred__set/UNIV = h4/pred__set/EMPTY)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_predu_u_sets_SUBSETu_u_DEF]: !t s. h4/pred__set/SUBSET s t <=> (!x. h4/bool/IN x s ==> h4/bool/IN x t)
% Assm [h4s_predu_u_sets_SUBSETu_u_REFL]: !s. h4/pred__set/SUBSET s s
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_predu_u_sets_GSPECIFICATION]: !v f. h4/bool/IN v (h4/pred__set/GSPEC f) <=> (?x. h4/pair/_2C v T = happ f x)
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_addu_c2]: !n m. h4/numeral/iZ (h4/arithmetic/_2B (h4/arithmetic/BIT1 n) (h4/arithmetic/BIT1 m)) = h4/arithmetic/BIT2 (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_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_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_arithmetics_numu_u_CASES]: !m. m = h4/num/0 \/ (?n. m = h4/num/SUC n)
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM]: !Q P. (!x. happ P x \/ Q) <=> (!x. happ P x) \/ Q
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_arithmetics_NOTu_u_NUMu_u_EQ]: !n m. ~(m = n) <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n \/ h4/arithmetic/_3C_3D (h4/num/SUC n) m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_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_LESSu_u_EQ]: !n m. h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D (h4/num/SUC m) n
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_numerals_numeralu_u_distribu_c2]: !n m. h4/arithmetic/_2B (h4/arithmetic/NUMERAL n) (h4/arithmetic/NUMERAL m) = h4/arithmetic/NUMERAL (h4/numeral/iZ (h4/arithmetic/_2B n m))
% Assm [h4s_primu_u_recs_INVu_u_SUCu_u_EQ]: !n m. h4/num/SUC m = h4/num/SUC n <=> m = n
% Assm [h4s_pairs_PAIRu_u_EQ]: !y x b a. h4/pair/_2C x y = h4/pair/_2C a b <=> x = a /\ y = b
% Assm [h4s_nums_INDUCTION]: !P. happ P h4/num/0 /\ (!n. happ P n ==> happ P (h4/num/SUC n)) ==> (!n. happ P n)
% Assm [h4s_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_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_LEFTu_u_ORu_u_OVERu_u_AND]: !C B A. A \/ B /\ C <=> (A \/ B) /\ (A \/ C)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_DISJu_u_THM]: !B A. A ==> B <=> ~A \/ B
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_numerals_numeralu_u_addu_c0]: !n. h4/numeral/iZ (h4/arithmetic/_2B h4/arithmetic/ZERO n) = n
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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)
% Goal: !p. h4/bool/RES__SELECT h4/pred__set/UNIV p = h4/min/_40 p
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_Q1368362,TV_Q1368358]: ![V_f, V_g]: (![V_x]: s(TV_Q1368358,happ(s(t_fun(TV_Q1368362,TV_Q1368358),V_f),s(TV_Q1368362,V_x))) = s(TV_Q1368358,happ(s(t_fun(TV_Q1368362,TV_Q1368358),V_g),s(TV_Q1368362,V_x))) => s(t_fun(TV_Q1368362,TV_Q1368358),V_f) = s(t_fun(TV_Q1368362,TV_Q1368358),V_g))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_RESu_u_SELECTu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_xi_, V_x0]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_x))),s(t_fun(TV_u_27a,t_bool),V_xi_))),s(TV_u_27a,V_x0)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x0),s(t_fun(TV_u_27a,t_bool),V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_xi_),s(TV_u_27a,V_x0)))))) => ![V_x, V_xi_]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27a,t_bool),V_xi_))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_x))),s(t_fun(TV_u_27a,t_bool),V_xi_))))))).
fof(ah4s_bools_EXISTSu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_x)))))).
fof(ah4s_resu_u_quans_RESu_u_SELECT, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_f, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x)))))) => ![V_f, V_P]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_fun(TV_u_27a,t_bool),V_f))))))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_SELECTu_u_UNIQUE, axiom, ![TV_u_27a]: ![V_x, V_P]: (![V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_y)))) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x)) => s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P))) = s(TV_u_27a,V_x))).
fof(ah4s_bools_SELECTu_u_ELIMu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![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)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
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_RESu_u_SELECTu_u_THM, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_f, V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_fun(TV_u_27a,t_bool),V_f))),s(TV_u_27a,V_x)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x)))))) => ![V_f, V_P]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),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_fun(TV_u_27a,t_bool),V_f))))))).
fof(ah4s_resu_u_quans_RESu_u_SELECTu_u_EMPTY, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_uu_0),s(TV_u_27a,V_x))) = s(t_bool,f) => ![V_p]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty),s(t_fun(TV_u_27a,t_bool),V_p))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_uu_0))))).
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_resu_u_quans_RESu_u_EXISTSu_u_ALT, axiom, ![TV_u_27a]: ![V_p, V_m]: (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_p),s(t_fun(TV_u_27a,t_bool),V_m)))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_p),s(t_fun(TV_u_27a,t_bool),V_m))),s(t_fun(TV_u_27a,t_bool),V_p)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_m),s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),V_p),s(t_fun(TV_u_27a,t_bool),V_m))))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_resu_u_quans_RESu_u_EXISTS, axiom, ![TV_u_27a]: ![V_f, V_P]: (p(s(t_bool,h4s_bools_resu_u_exists(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_f)))) <=> ?[V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_f),s(TV_u_27a,V_x))))))).
fof(ah4s_predu_u_sets_SPECIFICATION, axiom, ![TV_u_27a]: ![V_x, V_P]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))).
fof(ah4s_options_someu_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: 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))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))) => ![V_P]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) & s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(t_fun(TV_u_27a,t_bool),V_P))) = s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27a),h4s_options_some0(s(TV_u_27a,h4s_mins_u_40(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_options_option(TV_u_27a),h4s_options_none)))))).
fof(ah4s_lists_SETu_u_TOu_u_LISTu_u_primitive, axiom, ![TV_u_27a]: ![V_uu_2]: (![V_SETu_u_TOu_u_LIST, V_s]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) & s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),V_SETu_u_TOu_u_LIST))),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_h4s_lists_list(TV_u_27a),h4s_combins_i(s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),V_SETu_u_TOu_u_LIST),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))))))))),s(t_h4s_lists_list(TV_u_27a),h4s_bools_arb)))))) => ![V_uu_1]: (![V_SETu_u_TOu_u_LIST]: s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a))),V_uu_1),s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),V_SETu_u_TOu_u_LIST))) = s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a))),V_uu_2),s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),V_SETu_u_TOu_u_LIST))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),t_bool),V_uu_0),s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_R)))) & ![V_s]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) => p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),V_R),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))))),s(t_fun(TV_u_27a,t_bool),V_s))))))) => s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),h4s_lists_setu_u_tou_u_list) = s(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_fun(t_fun(TV_u_27a,t_bool),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_bool),t_h4s_lists_list(TV_u_27a))),V_uu_1))))))).
fof(ah4s_predu_u_sets_ITSETu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_4]: (![V_ITSETu_u_tupled, V_f, V_s, V_b]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) & s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_b))) = s(TV_u_27b,h4s_combins_i(s(TV_u_27b,h4s_bools_cond(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27b,V_b),s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,V_b))))))))),s(TV_u_27b,h4s_bools_arb)))))) => ![V_uu_3]: (![V_ITSETu_u_tupled, V_f, V_s]: s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(TV_u_27a,t_bool),V_s))) => ![V_uu_2]: (![V_ITSETu_u_tupled, V_f, V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),V_a))) = s(TV_u_27b,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),V_a),s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27b,TV_u_27b)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))) => ![V_uu_1]: (![V_f, V_ITSETu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),V_ITSETu_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))) => ![V_uu_0]: (![V_f, V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R)))) & ![V_b, V_s]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,V_b))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27b,V_b))))))))) => ![V_f]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),h4s_predu_u_sets_itsetu_u_tupled(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),t_bool)),t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_bool),TV_u_27b),TV_u_27b))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f))))))))))).
fof(ah4s_relations_theu_u_funu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_R, V_M, V_x, V_f]: s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))),s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(t_bool,h4s_relations_approx(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(TV_u_27a,V_x),s(t_fun(TV_u_27a,TV_u_27b),V_f))) => ![V_x, V_R, V_M]: s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_theu_u_fun(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27a,TV_u_27b),h4s_mins_u_40(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),t_fun(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,TV_u_27b),t_bool)))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R))),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_SELECTu_u_REFL, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_uu_0),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x)) => ![V_x]: s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_uu_0),s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x))).
fof(ah4s_bools_SELECTu_u_THM, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: 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))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))) => ![V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(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)))))))) <=> ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_numpairs_invtri0u_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_4]: (![V_invtri0u_u_tupled, V_n, V_a]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_a))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_combins_i(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_bools_cond(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),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_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))) => ![V_uu_3]: (![V_invtri0u_u_tupled, V_n]: s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_nums_num,V_n))) => ![V_uu_2]: (![V_invtri0u_u_tupled, V_au_27]: s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_au_27))) = s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),V_au_27),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))))) => ![V_uu_1]: (![V_invtri0u_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),V_invtri0u_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R)))) & ![V_a, V_n]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a),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_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_a))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_numpairs_invtri0u_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_nums_num))),V_uu_1))))))))).
fof(ah4s_indu_u_types_ZBOT0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_z]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_z))) = s(t_bool,t) => s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zbot) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injp(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,h4s_nums_0))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),t_bool),V_uu_0))))))).
fof(ah4s_bools_SELECTu_u_REFLu_u_2, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_uu_0),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) => ![V_x]: s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_uu_0),s(TV_u_27a,V_x))))) = s(TV_u_27a,V_x))).
fof(ah4s_primu_u_recs_PREu_u_DEF, axiom, ![V_uu_0]: (![V_m, V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))) => ![V_m]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0)) & s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,V_v),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,h4s_mins_u_40(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),V_uu_0),s(t_h4s_nums_num,V_m)))))))))).
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_predu_u_sets_INu_u_UNIV, axiom, ![TV_u_27a]: ![V_x]: p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))))).
fof(ah4s_numpairs_nlistrecu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_6]: (![V_nlistrecu_u_tupled, V_n, V_f, V_l]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_l) = s(t_h4s_nums_num,h4s_nums_0)) & s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f))),s(t_h4s_nums_num,V_l))) = s(TV_u_27a,h4s_combins_i(s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_n),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_nums_num,h4s_numpairs_nfst(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),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(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),h4s_pairs_u_2c(s(TV_u_27a,V_n),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))))))))))))))))))) => ![V_uu_5]: (![V_nlistrecu_u_tupled, V_n, V_f]: s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f))) = s(t_fun(t_h4s_nums_num,TV_u_27a),happ(s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f))) => ![V_uu_4]: (![V_nlistrecu_u_tupled, V_n, V_v1]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),V_v1))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),V_v1),s(t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_fun(t_h4s_nums_num,TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))))) => ![V_uu_3]: (![V_nlistrecu_u_tupled, V_n]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(TV_u_27a,V_n))) => ![V_uu_2]: (![V_nlistrecu_u_tupled, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),V_a))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),V_a),s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))))) => ![V_uu_1]: (![V_nlistrecu_u_tupled]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a)),V_uu_1),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),V_nlistrecu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),V_R)))) & ![V_f, V_n, V_l]: (~ (s(t_h4s_nums_num,V_l) = s(t_h4s_nums_num,h4s_nums_0)) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),V_R),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),h4s_pairs_u_2c(s(TV_u_27a,V_n),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_nums_num,h4s_numpairs_nsnd(s(t_h4s_nums_num,h4s_arithmetics_u_2d(s(t_h4s_nums_num,V_l),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_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),h4s_pairs_u_2c(s(TV_u_27a,V_n),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),V_f),s(t_h4s_nums_num,V_l))))))))))) => s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),h4s_numpairs_nlistrecu_u_tupled) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27a))),t_h4s_nums_num)),TV_u_27a)),V_uu_1))))))))))).
fof(ah4s_bools_CONDu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_x0, V_xi_, V_xi_i_]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x))),s(t_bool,V_x0))),s(TV_u_27a,V_xi_))),s(TV_u_27a,V_xi_i_)))) <=> ((s(t_bool,V_x0) = s(t_bool,t) => s(TV_u_27a,V_xi_i_) = s(TV_u_27a,V_x)) & (s(t_bool,V_x0) = s(t_bool,f) => s(TV_u_27a,V_xi_i_) = s(TV_u_27a,V_xi_)))) => ![V_x, V_x0, V_xi_]: s(TV_u_27a,h4s_bools_cond(s(t_bool,V_x),s(TV_u_27a,V_x0),s(TV_u_27a,V_xi_))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x0))),s(t_bool,V_x))),s(TV_u_27a,V_xi_))))))).
fof(ah4s_ones_oneu_u_DEF, axiom, ![V_uu_0]: (![V_x]: s(t_bool,happ(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0),s(t_h4s_ones_one,V_x))) = s(t_bool,t) => s(t_h4s_ones_one,h4s_ones_one0) = s(t_h4s_ones_one,h4s_mins_u_40(s(t_fun(t_h4s_ones_one,t_bool),V_uu_0))))).
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),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),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),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_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),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),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_predu_u_sets_EXTENSION, axiom, ![TV_u_27a]: ![V_t, V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t) <=> ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ah4s_predu_u_sets_EQu_u_UNIV, axiom, ![TV_u_27a]: ![V_s]: (![V_x]: p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) <=> s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))).
fof(ah4s_predu_u_sets_UNIONu_u_UNIVu_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_univ))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)).
fof(ah4s_predu_u_sets_INTERu_u_UNIVu_c1, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))) = s(t_fun(TV_u_27a,t_bool),V_s)).
fof(ah4s_predu_u_sets_UNIONu_u_UNIVu_c0, 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),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ)).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_FINITE, axiom, ![TV_u_27a]: (~ (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ))))) <=> ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ?[V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))))))).
fof(ah4s_predu_u_sets_infiniteu_u_numu_u_inj, axiom, ![TV_u_27a]: ![V_s]: (~ (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))))) <=> ?[V_f]: p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_fun(t_h4s_nums_num,t_bool),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_predu_u_sets_INu_u_UNION, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),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)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) | p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_predu_u_sets_INu_u_INTER, axiom, ![TV_u_27a]: ![V_x, V_t, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_inter(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
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_NOTu_u_CLAUSESu_c0, axiom, ![V_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_NOTu_u_IMP, 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_predu_u_sets_chooseru_u_defu_c1, axiom, ![TV_u_27a]: ![V_s, V_n]: s(TV_u_27a,h4s_predu_u_sets_chooser(s(t_fun(TV_u_27a,t_bool),V_s),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,h4s_predu_u_sets_chooser(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_predu_u_sets_chooseru_u_defu_c0, axiom, ![TV_u_27a]: ![V_s]: s(TV_u_27a,h4s_predu_u_sets_chooser(s(t_fun(TV_u_27a,t_bool),V_s),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ah4s_predu_u_sets_INFINITEu_u_INHAB, axiom, ![TV_u_27a]: ![V_P]: (~ (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_P))))) => ?[V_x]: p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_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_predu_u_sets_INJu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_s, V_f]: (p(s(t_bool,h4s_predu_u_sets_inj(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27b,t_bool),V_t)))) <=> (![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(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),V_t))))) & ![V_x, V_y]: ((p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s))))) => (s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))))).
fof(ah4s_predu_u_sets_RESTu_u_SUBSET, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_predu_u_sets_RESTu_u_DEF, axiom, ![TV_u_27a]: ![V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_predu_u_sets_infiniteu_u_rest, axiom, ![TV_u_27a]: ![V_s]: (~ (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))))) => ~ (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))))))))).
fof(ah4s_predu_u_sets_CHOICEu_u_DEF, axiom, ![TV_u_27a]: ![V_s]: (~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_predu_u_sets_INu_u_DELETE, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_y)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y))))).
fof(ah4s_predu_u_sets_INSERTu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_x, V_s, V_y]: ?[V_v]: ((p(s(t_bool,V_v)) <=> (s(TV_u_27a,V_y) = s(TV_u_27a,V_x) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))))) & s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27a,V_y))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_y),s(t_bool,V_v)))) => ![V_x, V_s]: 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_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)))),V_uu_0),s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_FINITEu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(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_empty)))) & ![V_s]: ((p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) & p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_s))))) => ![V_e]: (~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),V_s))))) => p(s(t_bool,happ(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_insert(s(TV_u_27a,V_e),s(t_fun(TV_u_27a,t_bool),V_s))))))))) => ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_FINITEu_u_DELETE, axiom, ![TV_u_27a]: ![V_x, V_s]: s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_x))))) = s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_predu_u_sets_UNIVu_u_NOTu_u_EMPTY, axiom, ![TV_u_27a]: ~ (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_predu_u_sets_SUBSETu_u_DEF, axiom, ![TV_u_27a]: ![V_t, V_s]: (p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_t)))) <=> ![V_x]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) => p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))))).
fof(ah4s_predu_u_sets_SUBSETu_u_REFL, axiom, ![TV_u_27a]: ![V_s]: p(s(t_bool,h4s_predu_u_sets_subset(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(TV_u_27a,t_bool),V_s))))).
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_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![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))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![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))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_predu_u_sets_GSPECIFICATION, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_v),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_gspec(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f)))))) <=> ?[V_x]: s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_v),s(t_bool,t))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27b,t_h4s_pairs_prod(TV_u_27a,t_bool)),V_f),s(TV_u_27b,V_x))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_addu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_m))))))) = s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_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_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_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_arithmetics_numu_u_CASES, axiom, ![V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_0) | ?[V_n]: s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_bools_LEFTu_u_FORALLu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,V_Q))) <=> (![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,V_Q))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_NOTu_u_NUMu_u_EQ, axiom, ![V_n, V_m]: (~ (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n)) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))) | p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_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_LESSu_u_EQ, axiom, ![V_n, V_m]: s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ADDu_u_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_numerals_numeralu_u_distribu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))))).
fof(ah4s_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_pairs_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_nums_INDUCTION, axiom, ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_0)))) & ![V_n]: (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n)))))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_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_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_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_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_LEFTu_u_ORu_u_OVERu_u_AND, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) & p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) & (p(s(t_bool,V_A)) | p(s(t_bool,V_C)))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_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_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_numerals_numeralu_u_addu_c0, axiom, ![V_n]: s(t_h4s_nums_num,h4s_numerals_iz(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_zero),s(t_h4s_nums_num,V_n))))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_bools_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(ch4s_resu_u_quans_RESu_u_SELECTu_u_UNIV, conjecture, ![TV_u_27a]: ![V_p]: s(TV_u_27a,h4s_bools_resu_u_select(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_univ),s(t_fun(TV_u_27a,t_bool),V_p))) = s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_p)))).
