%   ORIGINAL: h4/fcp/bit1__induction
% 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/fcp/BIT1C0: h4/fcp/BIT1C = h4/fcp/_20_40ind__typefcp6
% Assm: h4/fcp/BIT1B0: h4/fcp/BIT1B = h4/fcp/_20_40ind__typefcp5
% Assm: h4/fcp/BIT1A0: h4/fcp/BIT1A = h4/fcp/_20_40ind__typefcp4
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/fcp/hidden____20__40ind____typefcp4____def: h4/fcp/_20_40ind__typefcp4 = (\a. h4/fcp/_20_40ind__typefcp7 ((\a0. h4/ind__type/CONSTR h4/num/0 a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/fcp/hidden____20__40ind____typefcp5____def: h4/fcp/_20_40ind__typefcp5 = (\a. h4/fcp/_20_40ind__typefcp7 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/fcp/bit1__repfns_c1: !r. (\a0. !_27bit1_27. (!a00. (?a. a00 = (\a1. h4/ind__type/CONSTR h4/num/0 a1 (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (\n. h4/ind__type/BOTTOM)) a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM) ==> _27bit1_27 a00) ==> _27bit1_27 a0) r <=> h4/fcp/_20_40ind__typefcp8 (h4/fcp/_20_40ind__typefcp7 r) = r
% Assm: h4/fcp/hidden____20__40ind____typefcp6____def: h4/fcp/_20_40ind__typefcp6 = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/fcp/bit1__case__cong: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a. M_27 = h4/fcp/BIT1A a ==> f a = f_27 a) /\ (!a. M_27 = h4/fcp/BIT1B a ==> f1 a = f1_27 a) /\ (M_27 = h4/fcp/BIT1C ==> v = v_27) ==> h4/fcp/bit1__CASE M f f1 v = h4/fcp/bit1__CASE M_27 f_27 f1_27 v_27
% Assm: h4/fcp/bit1__nchotomy: !bb. (?a. bb = h4/fcp/BIT1A a) \/ (?a. bb = h4/fcp/BIT1B a) \/ bb = h4/fcp/BIT1C
% Assm: h4/bool/TRUTH: T
% Assm: h4/fcp/bit1__repfns_c0: !a. h4/fcp/_20_40ind__typefcp7 (h4/fcp/_20_40ind__typefcp8 a) = a
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/fcp/bit1__Axiom: !f2 f1 f0. ?fn. (!a. fn (h4/fcp/BIT1A a) = f0 a) /\ (!a. fn (h4/fcp/BIT1B a) = f1 a) /\ fn h4/fcp/BIT1C = f2
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/fcp/datatype__bit1: !bit1. h4/bool/DATATYPE (bit1 h4/fcp/BIT1A h4/fcp/BIT1B h4/fcp/BIT1C)
% Assm: h4/fcp/bit1__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0. !_27bit1_27. (!a00. (?a. a00 = (\a1. h4/ind__type/CONSTR h4/num/0 a1 (\n. h4/ind__type/BOTTOM)) a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (\n. h4/ind__type/BOTTOM)) a) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (\n. h4/ind__type/BOTTOM) ==> _27bit1_27 a00) ==> _27bit1_27 a0) rep
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/fcp/bit1__distinct_c0: !a_27 a. ~(h4/fcp/BIT1A a = h4/fcp/BIT1B a_27)
% Assm: h4/fcp/bit1__distinct_c1: !a. ~(h4/fcp/BIT1A a = h4/fcp/BIT1C)
% Assm: h4/fcp/bit1__distinct_c2: !a. ~(h4/fcp/BIT1B a = h4/fcp/BIT1C)
% Assm: h4/fcp/bit1__case__def_c2: !v f1 f. h4/fcp/bit1__CASE h4/fcp/BIT1C f f1 v = v
% Assm: h4/fcp/bit1__case__def_c1: !v f1 f a. h4/fcp/bit1__CASE (h4/fcp/BIT1B a) f f1 v = f1 a
% Assm: h4/fcp/bit1__case__def_c0: !v f1 f a. h4/fcp/bit1__CASE (h4/fcp/BIT1A a) f f1 v = f a
% Assm: h4/fcp/bit1__11_c1: !a_27 a. h4/fcp/BIT1B a = h4/fcp/BIT1B a_27 <=> a = a_27
% Assm: h4/fcp/bit1__11_c0: !a_27 a. h4/fcp/BIT1A a = h4/fcp/BIT1A a_27 <=> a = a_27
% Assm: h4/fcp/bit1__size__def_c0: !f a. h4/fcp/bit1__size f (h4/fcp/BIT1A a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (f a)
% Assm: h4/fcp/bit1__size__def_c1: !f a. h4/fcp/bit1__size f (h4/fcp/BIT1B a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (f a)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/fcp/bit1__size__def_c2: !f. h4/fcp/bit1__size f h4/fcp/BIT1C = h4/num/0
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/pred__set/IN__BIGINTER: !x B. h4/bool/IN x (h4/pred__set/BIGINTER B) <=> (!P. h4/bool/IN P B ==> h4/bool/IN x P)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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/pred__set/BIGINTER0: !P. h4/pred__set/BIGINTER P = h4/pred__set/GSPEC (\x. h4/pair/_2C x (!s. h4/bool/IN s P ==> h4/bool/IN x s))
% 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/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/list/FOLDR__CONS: !ls f a. h4/list/FOLDR (\x y. h4/list/CONS (f x) y) a ls = h4/list/APPEND (h4/list/MAP f ls) a
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/list/hidden____20__40ind____typelist1____def: h4/list/_20_40ind__typelist1 = (\a0 a1. h4/list/_20_40ind__typelist2 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 (h4/list/_20_40ind__typelist3 a1)))
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/FOLDR0_c1: !x l f e. h4/list/FOLDR f e (h4/list/CONS x l) = f x (h4/list/FOLDR f e l)
% Assm: h4/list/FOLDR0_c0: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm: h4/list/LAST__APPEND__CONS: !l2 l1 h. h4/list/LAST (h4/list/APPEND l1 (h4/list/CONS h l2)) = h4/list/LAST (h4/list/CONS h l2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/list/LAST__CONS__cond: !t h. h4/list/LAST (h4/list/CONS h t) = h4/bool/COND (t = h4/list/NIL) h (h4/list/LAST t)
% Assm: h4/list/APPEND__eq__NIL_c0: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm: h4/bool/AND__CLAUSES_c3: !t. t /\ F <=> F
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/list/APPEND__SNOC: !x l2 l1. h4/list/APPEND l1 (h4/list/SNOC x l2) = h4/list/SNOC x (h4/list/APPEND l1 l2)
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/SNOC0_c1: !x_27 x l. h4/list/SNOC x (h4/list/CONS x_27 l) = h4/list/CONS x_27 (h4/list/SNOC x l)
% Assm: h4/ind__type/CONSTR0: !r i c. h4/ind__type/CONSTR c i r = h4/ind__type/mk__rec (h4/ind__type/ZCONSTR c i (\n. h4/ind__type/dest__rec (r n)))
% Assm: h4/list/FILTER__COND__REWRITE_c1: !l h P. P h ==> h4/list/FILTER P (h4/list/CONS h l) = h4/list/CONS h (h4/list/FILTER P l)
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/list/FILTER0_c1: !t h P. h4/list/FILTER P (h4/list/CONS h t) = h4/bool/COND (P h) (h4/list/CONS h (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm: h4/list/FILTER0_c0: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/list/FOLDL2__tupled__primitive__def: h4/list/FOLDL2__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!cs bs c b a f. R (h4/pair/_2C f (h4/pair/_2C (f a b c) (h4/pair/_2C bs cs))) (h4/pair/_2C f (h4/pair/_2C a (h4/pair/_2C (h4/list/CONS b bs) (h4/list/CONS c cs))))))) (\FOLDL2__tupled a_27. h4/pair/pair__CASE a_27 (\f v1. h4/pair/pair__CASE v1 (\a v3. h4/pair/pair__CASE v3 (\v4 v5. h4/list/list__CASE v4 (h4/combin/I a) (\b bs. h4/list/list__CASE v5 (h4/combin/I a) (\c cs. h4/combin/I (FOLDL2__tupled (h4/pair/_2C f (h4/pair/_2C (f a b c) (h4/pair/_2C bs cs))))))))))
% Assm: h4/list/EXISTS__LIST__EQ__MAP: !ls f. h4/list/EVERY (\x. ?y. x = f y) ls ==> (?l. ls = h4/list/MAP f l)
% Assm: h4/list/EVERY__DEF_c1: !t h P. h4/list/EVERY P (h4/list/CONS h t) <=> P h /\ h4/list/EVERY P t
% Assm: h4/list/EVERY__DEF_c0: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/relation/TC__lifts__monotonicities: !f R. (!x y. R x y ==> R (f x) (f y)) ==> (!x y. h4/relation/TC R x y ==> h4/relation/TC R (f x) (f y))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/FORALL__AND__THM: !Q P. (!x. P x /\ Q x) <=> (!x. P x) /\ (!x. Q x)
% Assm: h4/bool/RIGHT__AND__FORALL__THM: !Q P. P /\ (!x. Q x) <=> (!x. P /\ Q x)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/relation/TC__RULES_c1: !z y x R. h4/relation/TC R x y /\ h4/relation/TC R y z ==> h4/relation/TC R x z
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/relation/TC__RULES_c0: !y x R. R x y ==> h4/relation/TC R x y
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/relation/TC__INDUCT: !R P. (!x y. R x y ==> P x y) /\ (!x y z. P x y /\ P y z ==> P x z) ==> (!u v. h4/relation/TC R u v ==> P u v)
% Assm: h4/ind__type/ZCONSTR__ZBOT: !r i c. ~(h4/ind__type/ZCONSTR c i r = h4/ind__type/ZBOT)
% 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/ind__type/INJP__INJ: !f2_27 f2 f1_27 f1. h4/ind__type/INJP f1 f2 = h4/ind__type/INJP f1_27 f2_27 <=> f1 = f1_27 /\ f2 = f2_27
% Assm: h4/ind__type/ZCONSTR0: !r i c. h4/ind__type/ZCONSTR c i r = h4/ind__type/INJP (h4/ind__type/INJN (h4/num/SUC c)) (h4/ind__type/INJP (h4/ind__type/INJA i) (h4/ind__type/INJF r))
% Assm: h4/ind__type/INJN__INJ: !n2 n1. h4/ind__type/INJN n1 = h4/ind__type/INJN n2 <=> n1 = n2
% Assm: h4/num/NOT__SUC: !n. ~(h4/num/SUC n = h4/num/0)
% Assm: h4/list/LUPDATE__def_c1: !x l e. h4/list/LUPDATE e h4/num/0 (h4/list/CONS x l) = h4/list/CONS e l
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = 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/SUC__ONE__ADD: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/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/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% 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__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
% Goal: !P. (!a. P (h4/fcp/BIT1A a)) /\ (!a. P (h4/fcp/BIT1B a)) /\ P h4/fcp/BIT1C ==> (!b. P b)
%   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_fcps_BIT1C0]: h4/fcp/BIT1C = h4/fcp/_20_40ind__typefcp6
% Assm [h4s_fcps_BIT1B0]: h4/fcp/BIT1B = h4/fcp/_20_40ind__typefcp5
% Assm [h4s_fcps_BIT1A0]: h4/fcp/BIT1A = h4/fcp/_20_40ind__typefcp4
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/fcp/_20_40ind__typefcp4 x = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR h4/num/0 x _0))
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/fcp/_20_40ind__typefcp5 x = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x _0))
% Assm [h4s_fcps_bit1u_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bit1_27. (!a00. (?a. a00 = h4/ind__type/CONSTR h4/num/0 a _0) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a _0) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0 ==> happ _27bit1_27 a00) ==> happ _27bit1_27 r) <=> h4/fcp/_20_40ind__typefcp8 (h4/fcp/_20_40ind__typefcp7 r) = r)
% Assm [h4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/fcp/_20_40ind__typefcp6 = h4/fcp/_20_40ind__typefcp7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _0)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_fcps_bit1u_u_caseu_u_cong]: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (!a. M_27 = happ h4/fcp/BIT1A a ==> happ f a = happ f_27 a) /\ (!a. M_27 = happ h4/fcp/BIT1B a ==> happ f1 a = happ f1_27 a) /\ (M_27 = h4/fcp/BIT1C ==> v = v_27) ==> h4/fcp/bit1__CASE M f f1 v = h4/fcp/bit1__CASE M_27 f_27 f1_27 v_27
% Assm [h4s_fcps_bit1u_u_nchotomy]: !bb. (?a. bb = happ h4/fcp/BIT1A a) \/ (?a. bb = happ h4/fcp/BIT1B a) \/ bb = h4/fcp/BIT1C
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_fcps_bit1u_u_repfnsu_c0]: !a. h4/fcp/_20_40ind__typefcp7 (h4/fcp/_20_40ind__typefcp8 a) = a
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_fcps_bit1u_u_Axiom]: !f2 f1 f0. ?fn. (!a. happ fn (happ h4/fcp/BIT1A a) = happ f0 a) /\ (!a. happ fn (happ h4/fcp/BIT1B a) = happ f1 a) /\ happ fn h4/fcp/BIT1C = f2
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_fcps_datatypeu_u_bit1]: !bit1. h4/bool/DATATYPE (happ (happ (happ bit1 h4/fcp/BIT1A) h4/fcp/BIT1B) h4/fcp/BIT1C)
% Assm [h4s_fcps_bit1u_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0. happ _0 a0 <=> (!_27bit1_27. (!a00. (?a. a00 = h4/ind__type/CONSTR h4/num/0 a _1) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a _1) \/ a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB _1 ==> happ _27bit1_27 a00) ==> happ _27bit1_27 a0)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_fcps_bit1u_u_distinctu_c0]: !a_27 a. ~(happ h4/fcp/BIT1A a = happ h4/fcp/BIT1B a_27)
% Assm [h4s_fcps_bit1u_u_distinctu_c1]: !a. ~(happ h4/fcp/BIT1A a = h4/fcp/BIT1C)
% Assm [h4s_fcps_bit1u_u_distinctu_c2]: !a. ~(happ h4/fcp/BIT1B a = h4/fcp/BIT1C)
% Assm [h4s_fcps_bit1u_u_caseu_u_defu_c2]: !v f1 f. h4/fcp/bit1__CASE h4/fcp/BIT1C f f1 v = v
% Assm [h4s_fcps_bit1u_u_caseu_u_defu_c1]: !v f1 f a. h4/fcp/bit1__CASE (happ h4/fcp/BIT1B a) f f1 v = happ f1 a
% Assm [h4s_fcps_bit1u_u_caseu_u_defu_c0]: !v f1 f a. h4/fcp/bit1__CASE (happ h4/fcp/BIT1A a) f f1 v = happ f a
% Assm [h4s_fcps_bit1u_u_11u_c1]: !a_27 a. happ h4/fcp/BIT1B a = happ h4/fcp/BIT1B a_27 <=> a = a_27
% Assm [h4s_fcps_bit1u_u_11u_c0]: !a_27 a. happ h4/fcp/BIT1A a = happ h4/fcp/BIT1A a_27 <=> a = a_27
% Assm [h4s_fcps_bit1u_u_sizeu_u_defu_c0]: !f a. h4/fcp/bit1__size f (happ h4/fcp/BIT1A a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (happ f a)
% Assm [h4s_fcps_bit1u_u_sizeu_u_defu_c1]: !f a. h4/fcp/bit1__size f (happ h4/fcp/BIT1B a) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (happ f a)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_fcps_bit1u_u_sizeu_u_defu_c2]: !f. h4/fcp/bit1__size f h4/fcp/BIT1C = h4/num/0
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_predu_u_sets_INu_u_BIGINTER]: !x B. h4/bool/IN x (h4/pred__set/BIGINTER B) <=> (!P. h4/bool/IN P B ==> h4/bool/IN x P)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% 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_predu_u_sets_BIGINTER0]: !_0. (!P x. ?v. (v <=> (!s. h4/bool/IN s P ==> h4/bool/IN x s)) /\ happ (happ _0 P) x = h4/pair/_2C x v) ==> (!P. h4/pred__set/BIGINTER P = h4/pred__set/GSPEC (happ _0 P))
% 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_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_lists_FOLDRu_u_CONS]: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ h4/list/CONS (happ f x)) y) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!ls f a. h4/list/FOLDR (happ _0 f) a ls = h4/list/APPEND (h4/list/MAP f ls) a))
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/list/_20_40ind__typelist1 x) x = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/list/_20_40ind__typelist3 x) _0)))
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (happ f h)) (h4/list/MAP f t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_FOLDR0u_c1]: !x l f e. h4/list/FOLDR f e (happ (happ h4/list/CONS x) l) = happ (happ f x) (h4/list/FOLDR f e l)
% Assm [h4s_lists_FOLDR0u_c0]: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm [h4s_lists_LASTu_u_APPENDu_u_CONS]: !l2 l1 h. h4/list/LAST (h4/list/APPEND l1 (happ (happ h4/list/CONS h) l2)) = h4/list/LAST (happ (happ h4/list/CONS h) l2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_lists_LASTu_u_CONSu_u_cond]: !t h. ?v. (v <=> t = h4/list/NIL) /\ h4/list/LAST (happ (happ h4/list/CONS h) t) = h4/bool/COND v h (h4/list/LAST t)
% Assm [h4s_lists_APPENDu_u_equ_u_NILu_c0]: !l2 l1. h4/list/NIL = h4/list/APPEND l1 l2 <=> l1 = h4/list/NIL /\ l2 = h4/list/NIL
% Assm [h4s_bools_ANDu_u_CLAUSESu_c3]: !t. t /\ F <=> F
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_lists_APPENDu_u_SNOC]: !x l2 l1. h4/list/APPEND l1 (h4/list/SNOC x l2) = h4/list/SNOC x (h4/list/APPEND l1 l2)
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_lists_SNOC0u_c1]: !x_27 x l. h4/list/SNOC x (happ (happ h4/list/CONS x_27) l) = happ (happ h4/list/CONS x_27) (h4/list/SNOC x l)
% Assm [h4s_indu_u_types_CONSTR0]: !_0. (!r n. happ (happ _0 r) n = h4/ind__type/dest__rec (happ r n)) ==> (!r i c. h4/ind__type/CONSTR c i r = h4/ind__type/mk__rec (h4/ind__type/ZCONSTR c i (happ _0 r)))
% Assm [h4s_lists_FILTERu_u_CONDu_u_REWRITEu_c1]: !l h P. happ P h ==> h4/list/FILTER P (happ (happ h4/list/CONS h) l) = happ (happ h4/list/CONS h) (h4/list/FILTER P l)
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_lists_FILTER0u_c1]: !t h P. h4/list/FILTER P (happ (happ h4/list/CONS h) t) = h4/bool/COND (happ P h) (happ (happ h4/list/CONS h) (h4/list/FILTER P t)) (h4/list/FILTER P t)
% Assm [h4s_lists_FILTER0u_c0]: !P. h4/list/FILTER P h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_lists_FOLDL2u_u_tupledu_u_primitiveu_u_def]: !_12. (!FOLDL2__tupled f a b c bs cs. happ (happ (happ (happ (happ (happ (happ _12 FOLDL2__tupled) f) a) b) c) bs) cs = h4/combin/I (happ FOLDL2__tupled (h4/pair/_2C f (h4/pair/_2C (happ (happ (happ f a) b) c) (h4/pair/_2C bs cs))))) ==> (!_11. (!FOLDL2__tupled f a b bs c. happ (happ (happ (happ (happ (happ _11 FOLDL2__tupled) f) a) b) bs) c = happ (happ (happ (happ (happ (happ _12 FOLDL2__tupled) f) a) b) c) bs) ==> (!_10. (!v5 FOLDL2__tupled f a b bs. happ (happ (happ (happ (happ (happ _10 v5) FOLDL2__tupled) f) a) b) bs = h4/list/list__CASE v5 (h4/combin/I a) (happ (happ (happ (happ (happ _11 FOLDL2__tupled) f) a) b) bs)) ==> (!_9. (!v5 FOLDL2__tupled f a b. happ (happ (happ (happ (happ _9 v5) FOLDL2__tupled) f) a) b = happ (happ (happ (happ (happ _10 v5) FOLDL2__tupled) f) a) b) ==> (!_8. (!v4 FOLDL2__tupled f a v5. happ (happ (happ (happ (happ _8 v4) FOLDL2__tupled) f) a) v5 = h4/list/list__CASE v4 (h4/combin/I a) (happ (happ (happ (happ _9 v5) FOLDL2__tupled) f) a)) ==> (!_7. (!FOLDL2__tupled f a v4. happ (happ (happ (happ _7 FOLDL2__tupled) f) a) v4 = happ (happ (happ (happ _8 v4) FOLDL2__tupled) f) a) ==> (!_6. (!FOLDL2__tupled f a v3. happ (happ (happ (happ _6 FOLDL2__tupled) f) a) v3 = h4/pair/pair__CASE v3 (happ (happ (happ _7 FOLDL2__tupled) f) a)) ==> (!_5. (!FOLDL2__tupled f a. happ (happ (happ _5 FOLDL2__tupled) f) a = happ (happ (happ _6 FOLDL2__tupled) f) a) ==> (!_4. (!FOLDL2__tupled f v1. happ (happ (happ _4 FOLDL2__tupled) f) v1 = h4/pair/pair__CASE v1 (happ (happ _5 FOLDL2__tupled) f)) ==> (!_3. (!FOLDL2__tupled f. happ (happ _3 FOLDL2__tupled) f = happ (happ _4 FOLDL2__tupled) f) ==> (!_2. (!FOLDL2__tupled a_27. happ (happ _2 FOLDL2__tupled) a_27 = h4/pair/pair__CASE a_27 (happ _3 FOLDL2__tupled)) ==> (!_1. (!FOLDL2__tupled. happ _1 FOLDL2__tupled = happ _2 FOLDL2__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!cs bs c b a f. happ (happ R (h4/pair/_2C f (h4/pair/_2C (happ (happ (happ f a) b) c) (h4/pair/_2C bs cs)))) (h4/pair/_2C f (h4/pair/_2C a (h4/pair/_2C (happ (happ h4/list/CONS b) bs) (happ (happ h4/list/CONS c) cs)))))) ==> h4/list/FOLDL2__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_lists_EXISTSu_u_LISTu_u_EQu_u_MAP]: !_0. (!f x. happ (happ _0 f) x <=> (?y. x = happ f y)) ==> (!ls f. h4/list/EVERY (happ _0 f) ls ==> (?l. ls = h4/list/MAP f l))
% Assm [h4s_lists_EVERYu_u_DEFu_c1]: !t h P. h4/list/EVERY P (happ (happ h4/list/CONS h) t) <=> happ P h /\ h4/list/EVERY P t
% Assm [h4s_lists_EVERYu_u_DEFu_c0]: !P. h4/list/EVERY P h4/list/NIL <=> T
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_relations_TCu_u_liftsu_u_monotonicities]: !f R. (!x y. happ (happ R x) y ==> happ (happ R (happ f x)) (happ f y)) ==> (!x y. h4/relation/TC R x y ==> h4/relation/TC R (happ f x) (happ f y))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_FORALLu_u_ANDu_u_THM]: !Q P. (!x. happ P x /\ happ Q x) <=> (!x. happ P x) /\ (!x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM]: !Q P. P /\ (!x. happ Q x) <=> (!x. P /\ happ Q x)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% 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_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_relations_TCu_u_RULESu_c1]: !z y x R. h4/relation/TC R x y /\ h4/relation/TC R y z ==> h4/relation/TC R x z
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_relations_TCu_u_RULESu_c0]: !y x R. happ (happ R x) y ==> h4/relation/TC R x y
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_relations_TCu_u_INDUCT]: !R P. (!x y. happ (happ R x) y ==> happ (happ P x) y) /\ (!x y z. happ (happ P x) y /\ happ (happ P y) z ==> happ (happ P x) z) ==> (!u v. h4/relation/TC R u v ==> happ (happ P u) v)
% Assm [h4s_indu_u_types_ZCONSTRu_u_ZBOT]: !r i c. ~(h4/ind__type/ZCONSTR c i r = h4/ind__type/ZBOT)
% 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_indu_u_types_INJPu_u_INJ]: !f2_27 f2 f1_27 f1. h4/ind__type/INJP f1 f2 = h4/ind__type/INJP f1_27 f2_27 <=> f1 = f1_27 /\ f2 = f2_27
% Assm [h4s_indu_u_types_ZCONSTR0]: !r i c. h4/ind__type/ZCONSTR c i r = h4/ind__type/INJP (h4/ind__type/INJN (h4/num/SUC c)) (h4/ind__type/INJP (h4/ind__type/INJA i) (h4/ind__type/INJF r))
% Assm [h4s_indu_u_types_INJNu_u_INJ]: !n2 n1. h4/ind__type/INJN n1 = h4/ind__type/INJN n2 <=> n1 = n2
% Assm [h4s_nums_NOTu_u_SUC]: !n. ~(h4/num/SUC n = h4/num/0)
% Assm [h4s_lists_LUPDATEu_u_defu_c1]: !x l e. h4/list/LUPDATE e h4/num/0 (happ (happ h4/list/CONS x) l) = happ (happ h4/list/CONS e) l
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = 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_SUCu_u_ONEu_u_ADD]: !n. h4/num/SUC n = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_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_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_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
% Goal: !P. (!a. happ P (happ h4/fcp/BIT1A a)) /\ (!a. happ P (happ h4/fcp/BIT1B a)) /\ happ P h4/fcp/BIT1C ==> (!b. happ P b)
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_Q1280697,TV_Q1280693]: ![V_f, V_g]: (![V_x]: s(TV_Q1280693,happ(s(t_fun(TV_Q1280697,TV_Q1280693),V_f),s(TV_Q1280697,V_x))) = s(TV_Q1280693,happ(s(t_fun(TV_Q1280697,TV_Q1280693),V_g),s(TV_Q1280697,V_x))) => s(t_fun(TV_Q1280697,TV_Q1280693),V_f) = s(t_fun(TV_Q1280697,TV_Q1280693),V_g))).
fof(ah4s_fcps_BIT1C0, axiom, ![TV_u_27a]: s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp6)).
fof(ah4s_fcps_BIT1B0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b) = s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp5)).
fof(ah4s_fcps_BIT1A0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a) = s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp4)).
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_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp4u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp4),s(TV_u_27a,V_x))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp5u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_u_20u_40indu_u_typefcp5),s(TV_u_27a,V_x))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_fcps_bit1u_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27bit1u_27]: (![V_a00]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp8(s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_fcps_hiddenu_u_u_u_20u_u_40indu_u_u_u_typefcp6u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp6) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_fcps_bit1u_u_caseu_u_cong, axiom, ![TV_u_27a,TV_u_27b]: ![V_vu_27, V_v, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_fcps_bit1(TV_u_27a),V_M) = s(t_h4s_fcps_bit1(TV_u_27a),V_Mu_27) & (![V_a]: (s(t_h4s_fcps_bit1(TV_u_27a),V_Mu_27) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_fu_27),s(TV_u_27a,V_a)))) & (![V_a]: (s(t_h4s_fcps_bit1(TV_u_27a),V_Mu_27) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1u_27),s(TV_u_27a,V_a)))) & (s(t_h4s_fcps_bit1(TV_u_27a),V_Mu_27) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c) => s(TV_u_27b,V_v) = s(TV_u_27b,V_vu_27))))) => s(TV_u_27b,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(TV_u_27a),V_M),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27b,V_v))) = s(TV_u_27b,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(TV_u_27a),V_Mu_27),s(t_fun(TV_u_27a,TV_u_27b),V_fu_27),s(t_fun(TV_u_27a,TV_u_27b),V_f1u_27),s(TV_u_27b,V_vu_27))))).
fof(ah4s_fcps_bit1u_u_nchotomy, axiom, ![TV_u_27a]: ![V_bb]: (?[V_a]: s(t_h4s_fcps_bit1(TV_u_27a),V_bb) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))) | (?[V_a]: s(t_h4s_fcps_bit1(TV_u_27a),V_bb) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))) | s(t_h4s_fcps_bit1(TV_u_27a),V_bb) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c)))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_fcps_bit1u_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp7(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_fcps_u_20u_40indu_u_typefcp8(s(t_h4s_fcps_bit1(TV_u_27a),V_a))))) = s(t_h4s_fcps_bit1(TV_u_27a),V_a)).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_fcps_bit1u_u_Axiom, axiom, ![TV_u_27a,TV_u_27b]: ![V_f2, V_f1, V_f0]: ?[V_fn]: (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f0),s(TV_u_27a,V_a))) & (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a))) & s(TV_u_27b,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c))) = s(TV_u_27b,V_f2)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_fcps_datatypeu_u_bit1, axiom, ![TV_u_27a]: ![V_bit1]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool))),V_bit1),s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a))),s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b))),s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c))))))).
fof(ah4s_fcps_bit1u_u_TYu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) <=> ![V_uu_27bit1u_27]: (![V_a00]: ((?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1))) | s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27bit1u_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_0),s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_h4s_indu_u_types_recspace(TV_u_27a)),V_rep))))))).
fof(ah4s_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_fcps_bit1u_u_distinctu_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: ~ (s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_au_27))))).
fof(ah4s_fcps_bit1u_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a]: ~ (s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c))).
fof(ah4s_fcps_bit1u_u_distinctu_c2, axiom, ![TV_u_27a]: ![V_a]: ~ (s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))) = s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c))).
fof(ah4s_fcps_bit1u_u_caseu_u_defu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f1, V_f]: s(TV_u_27b,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27b,V_v))) = s(TV_u_27b,V_v)).
fof(ah4s_fcps_bit1u_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27b,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27b,V_v))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27a,V_a)))).
fof(ah4s_fcps_bit1u_u_caseu_u_defu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27b,h4s_fcps_bit1u_u_case(s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,TV_u_27b),V_f1),s(TV_u_27b,V_v))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a)))).
fof(ah4s_fcps_bit1u_u_11u_c1, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_au_27))) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_au_27))).
fof(ah4s_fcps_bit1u_u_11u_c0, axiom, ![TV_u_27a]: ![V_au_27, V_a]: (s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))) = s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_au_27))) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_au_27))).
fof(ah4s_fcps_bit1u_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_fcps_bit1u_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a))))) = 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,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a)))))).
fof(ah4s_fcps_bit1u_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a]: s(t_h4s_nums_num,h4s_fcps_bit1u_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a))))) = 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,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a)))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_fcps_bit1u_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_nums_num,h4s_fcps_bit1u_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,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_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,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_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_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_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_predu_u_sets_INu_u_BIGINTER, axiom, ![TV_u_27a]: ![V_x, V_B]: (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_biginter(s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_B)))))) <=> ![V_P]: (p(s(t_bool,h4s_bools_in(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_B)))) => 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_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_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_predu_u_sets_BIGINTER0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: ?[V_v]: ((p(s(t_bool,V_v)) <=> ![V_s]: (p(s(t_bool,h4s_bools_in(s(t_fun(TV_u_27a,t_bool),V_s),s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P)))) => 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_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(t_fun(TV_u_27a,t_bool),t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_h4s_pairs_prod(TV_u_27a,t_bool),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_bool,V_v)))) => ![V_P]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_biginter(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_gspec(s(t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool)),happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_bool),t_bool),t_fun(TV_u_27a,t_h4s_pairs_prod(TV_u_27a,t_bool))),V_uu_0),s(t_fun(t_fun(TV_u_27a,t_bool),t_bool),V_P))))))).
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_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_lists_FOLDRu_u_CONS, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f, V_x, V_y]: s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)))),V_uu_1),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27b),V_y))) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(t_h4s_lists_list(TV_u_27b),V_y))) => ![V_uu_0]: (![V_f, V_x]: s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)))),V_uu_1),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))) => ![V_ls, V_f, V_a]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27b),V_a),s(t_h4s_lists_list(TV_u_27a),V_ls))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_append(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_ls))),s(t_h4s_lists_list(TV_u_27b),V_a)))))).
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_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_x0))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_lists_listu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),V_a))))) = s(t_h4s_lists_list(TV_u_27a),V_a)).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_FOLDR0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_FOLDR0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_lists_LASTu_u_APPENDu_u_CONS, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l2))))))) = s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_lists_LASTu_u_CONSu_u_cond, axiom, ![TV_u_27a]: ![V_t, V_h]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_lists_list(TV_u_27a),V_t) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)) & s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27a,V_h),s(TV_u_27a,h4s_lists_last(s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_APPENDu_u_equ_u_NILu_c0, axiom, ![TV_u_27a]: ![V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) <=> (s(t_h4s_lists_list(TV_u_27a),V_l1) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,f))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_lists_APPENDu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_SNOC0u_c1, axiom, ![TV_u_27a]: ![V_xu_27, V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_indu_u_types_CONSTR0, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_r, V_n]: s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_destu_u_rec(s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_r, V_i, V_c]: s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_mku_u_rec(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)))),V_uu_0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))))).
fof(ah4s_lists_FILTERu_u_CONDu_u_REWRITEu_c1, axiom, ![TV_u_27a]: ![V_l, V_h, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_lists_FILTER0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_FILTER0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_filter(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_FOLDL2u_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_uu_12]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_c, V_bs, V_cs]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_lists_list(TV_u_27b),V_bs))),s(t_h4s_lists_list(TV_u_27c),V_cs))) = s(TV_u_27a,h4s_combins_i(s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs),s(t_h4s_lists_list(TV_u_27c),V_cs))))))))))) => ![V_uu_11]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_bs, V_c]: s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))),s(TV_u_27c,V_c))) = s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_12),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_lists_list(TV_u_27b),V_bs))) => ![V_uu_10]: (![V_v5, V_FOLDL2u_u_tupled, V_f, V_a, V_b, V_bs]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))) = s(TV_u_27a,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27c),V_v5),s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_a))),s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))))),V_uu_11),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))))) => ![V_uu_9]: (![V_v5, V_FOLDL2u_u_tupled, V_f, V_a, V_b]: s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_10),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) => ![V_uu_8]: (![V_v4, V_FOLDL2u_u_tupled, V_f, V_a, V_v5]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_8),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27c),V_v5))) = s(TV_u_27a,h4s_lists_listu_u_case(s(t_h4s_lists_list(TV_u_27b),V_v4),s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_a))),s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a))))),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27a)))))),V_uu_9),s(t_h4s_lists_list(TV_u_27c),V_v5))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))))) => ![V_uu_7]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_v4]: s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27b),V_v4))) = s(t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_8),s(t_h4s_lists_list(TV_u_27b),V_v4))),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) => ![V_uu_6]: (![V_FOLDL2u_u_tupled, V_f, V_a, V_v3]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),V_v3))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),V_v3),s(t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a)))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27b),t_fun(t_h4s_lists_list(TV_u_27c),TV_u_27a))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))))) => ![V_uu_5]: (![V_FOLDL2u_u_tupled, V_f, V_a]: s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) = s(t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_6),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(TV_u_27a,V_a))) => ![V_uu_4]: (![V_FOLDL2u_u_tupled, V_f, V_v1]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_v1))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),V_v1),s(t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(TV_u_27a,t_fun(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),TV_u_27a)))),V_uu_5),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))))) => ![V_uu_3]: (![V_FOLDL2u_u_tupled, V_f]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_4),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f))) => ![V_uu_2]: (![V_FOLDL2u_u_tupled, V_au_27]: s(TV_u_27a,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),V_au_27))) = s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),V_au_27),s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),TV_u_27a))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))))) => ![V_uu_1]: (![V_FOLDL2u_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),V_FOLDL2u_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),V_R)))) & ![V_cs, V_bs, V_c, V_b, V_a, V_f]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),V_R),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))),s(TV_u_27c,V_c))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),V_bs),s(t_h4s_lists_list(TV_u_27c),V_cs))))))))),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),V_f),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c))),h4s_pairs_u_2c(s(TV_u_27a,V_a),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs))),s(t_h4s_lists_list(TV_u_27c),happ(s(t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c)),happ(s(t_fun(TV_u_27c,t_fun(t_h4s_lists_list(TV_u_27c),t_h4s_lists_list(TV_u_27c))),h4s_lists_cons),s(TV_u_27c,V_c))),s(t_h4s_lists_list(TV_u_27c),V_cs)))))))))))))) => s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),h4s_lists_foldl2u_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a),t_fun(t_h4s_pairs_prod(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a))),t_h4s_pairs_prod(TV_u_27a,t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27c)))),TV_u_27a)),V_uu_1))))))))))))))))).
fof(ah4s_lists_EXISTSu_u_LISTu_u_EQu_u_MAP, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![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_27b,TV_u_27a),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27b,TV_u_27a),V_f))),s(TV_u_27a,V_x)))) <=> ?[V_y]: s(TV_u_27a,V_x) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(TV_u_27b,V_y)))) => ![V_ls, V_f]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27b,TV_u_27a),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27b,TV_u_27a),V_f))),s(t_h4s_lists_list(TV_u_27a),V_ls)))) => ?[V_l]: s(t_h4s_lists_list(TV_u_27a),V_ls) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_map(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_lists_list(TV_u_27b),V_l)))))).
fof(ah4s_lists_EVERYu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_t, V_h, V_P]: (p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_h)))) & p(s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t))))))).
fof(ah4s_lists_EVERYu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_bool,h4s_lists_every(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_bools_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_relations_TCu_u_liftsu_u_monotonicities, axiom, ![TV_u_27a]: ![V_f, V_R]: (![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_R),s(TV_u_27a,V_x))),s(TV_u_27a,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_R),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x))))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_y))))))) => ![V_x, V_y]: (p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x),s(TV_u_27a,V_y)))) => p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_x))),s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),V_f),s(TV_u_27a,V_y))))))))).
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_FORALLu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) & ![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ![V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => p(s(t_bool,f))))).
fof(ah4s_sats_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_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_relations_TCu_u_RULESu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x, V_R]: ((p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x),s(TV_u_27a,V_y)))) & p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y),s(TV_u_27a,V_z))))) => p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x),s(TV_u_27a,V_z)))))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_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_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_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_relations_TCu_u_RULESu_c0, axiom, ![TV_u_27a]: ![V_y, V_x, V_R]: (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_R),s(TV_u_27a,V_x))),s(TV_u_27a,V_y)))) => p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x),s(TV_u_27a,V_y)))))).
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_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_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_relations_TCu_u_INDUCT, axiom, ![TV_u_27a]: ![V_R, V_P]: ((![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_R),s(TV_u_27a,V_x))),s(TV_u_27a,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_P),s(TV_u_27a,V_x))),s(TV_u_27a,V_y))))) & ![V_x, V_y, V_z]: ((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_P),s(TV_u_27a,V_x))),s(TV_u_27a,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_P),s(TV_u_27a,V_y))),s(TV_u_27a,V_z))))) => 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_P),s(TV_u_27a,V_x))),s(TV_u_27a,V_z)))))) => ![V_u, V_v]: (p(s(t_bool,h4s_relations_tc(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_u),s(TV_u_27a,V_v)))) => 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_P),s(TV_u_27a,V_u))),s(TV_u_27a,V_v))))))).
fof(ah4s_indu_u_types_ZCONSTRu_u_ZBOT, axiom, ![TV_u_27a]: ![V_r, V_i, V_c]: ~ (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zbot))).
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_indu_u_types_INJPu_u_INJ, axiom, ![TV_u_27a]: ![V_f2u_27, V_f2, V_f1u_27, V_f1]: (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)),V_f1),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2))) = 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)),V_f1u_27),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2u_27))) <=> (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f1u_27) & s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),V_f2u_27)))).
fof(ah4s_indu_u_types_ZCONSTR0, axiom, ![TV_u_27a]: ![V_r, V_i, V_c]: s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_zconstr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r))) = 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_suc(s(t_h4s_nums_num,V_c))))),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_inja(s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool))),V_r)))))))).
fof(ah4s_indu_u_types_INJNu_u_INJ, axiom, ![TV_u_27a]: ![V_n2, V_n1]: (s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,V_n1))) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_bool)),h4s_indu_u_types_injn(s(t_h4s_nums_num,V_n2))) <=> s(t_h4s_nums_num,V_n1) = s(t_h4s_nums_num,V_n2))).
fof(ah4s_nums_NOTu_u_SUC, axiom, ![V_n]: ~ (s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_0))).
fof(ah4s_lists_LUPDATEu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x, V_l, V_e]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_lupdate(s(TV_u_27a,V_e),s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_e))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_numerals_numeralu_u_distribu_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_SUCu_u_ONEu_u_ADD, axiom, ![V_n]: s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_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_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_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_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(ch4s_fcps_bit1u_u_induction, conjecture, ![TV_u_27a]: ![V_P]: ((![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),V_P),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1a),s(TV_u_27a,V_a)))))) & (![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),V_P),s(t_h4s_fcps_bit1(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_fcps_bit1(TV_u_27a)),h4s_fcps_bit1b),s(TV_u_27a,V_a)))))) & p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),V_P),s(t_h4s_fcps_bit1(TV_u_27a),h4s_fcps_bit1c)))))) => ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_fcps_bit1(TV_u_27a),t_bool),V_P),s(t_h4s_fcps_bit1(TV_u_27a),V_b)))))).
