%   ORIGINAL: h4/enumeral/bt__to__list__thm
% 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/enumeral/bt__to__list0_c1: !x r l. h4/enumeral/bt__to__list (h4/enumeral/node l x r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__list l) (h4/list/CONS x h4/list/NIL)) (h4/enumeral/bt__to__list r)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/enumeral/bt__repfns_c0: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral1____def: h4/enumeral/_20_40ind__typeenumeral1 = (\a0 a1 a2. h4/enumeral/_20_40ind__typeenumeral2 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) (h4/enumeral/_20_40ind__typeenumeral3 a0) a1 (h4/enumeral/_20_40ind__typeenumeral3 a2)))
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/enumeral/bt__to__list__ac0_c1: !x r m l. h4/enumeral/bt__to__list__ac (h4/enumeral/node l x r) m = h4/enumeral/bt__to__list__ac l (h4/list/CONS x (h4/enumeral/bt__to__list__ac r m))
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral0____def: h4/enumeral/_20_40ind__typeenumeral0 = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/enumeral/node0: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm: h4/enumeral/nt0: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm: h4/enumeral/bt__repfns_c1: !r. (\a0_27. !_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 /\ _27bt_27 a0 /\ _27bt_27 a2) ==> _27bt_27 a0_270) ==> _27bt_27 a0_27) r <=> h4/enumeral/_20_40ind__typeenumeral3 (h4/enumeral/_20_40ind__typeenumeral2 r) = r
% Assm: h4/enumeral/bt__to__list0_c0: h4/enumeral/bt__to__list h4/enumeral/nt = h4/list/NIL
% Assm: h4/enumeral/bt__to__list__ac0_c0: !m. h4/enumeral/bt__to__list__ac h4/enumeral/nt m = m
% 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/enumeral/bl__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 a2 /\ _27bl_27 a2) ==> _27bl_27 a0_270) ==> _27bl_27 a0_27) rep
% Assm: h4/enumeral/bl__repfns_c1: !r. (\a0_27. !_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 a2 /\ _27bl_27 a2) ==> _27bl_27 a0_270) ==> _27bl_27 a0_27) r <=> h4/enumeral/_20_40ind__typeenumeral8 (h4/enumeral/_20_40ind__typeenumeral7 r) = r
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral6____def: h4/enumeral/_20_40ind__typeenumeral6 = (\a0 a1 a2. h4/enumeral/_20_40ind__typeenumeral7 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 (h4/enumeral/_20_40ind__typeenumeral8 a2)))
% Assm: h4/enumeral/bt__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 /\ _27bt_27 a0 /\ _27bt_27 a2) ==> _27bt_27 a0_270) ==> _27bt_27 a0_27) rep
% Assm: h4/enumeral/bl__repfns_c0: !a. h4/enumeral/_20_40ind__typeenumeral7 (h4/enumeral/_20_40ind__typeenumeral8 a) = a
% Assm: h4/enumeral/onebl0: h4/enumeral/onebl = h4/enumeral/_20_40ind__typeenumeral6
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral4____def: h4/enumeral/_20_40ind__typeenumeral4 = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM))
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral5____def: h4/enumeral/_20_40ind__typeenumeral5 = (\a. h4/enumeral/_20_40ind__typeenumeral7 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/enumeral/_20_40ind__typeenumeral8 a)))
% Assm: h4/enumeral/zerbl0: h4/enumeral/zerbl = h4/enumeral/_20_40ind__typeenumeral5
% Assm: h4/enumeral/nbl0: h4/enumeral/nbl = h4/enumeral/_20_40ind__typeenumeral4
% Assm: h4/enumeral/bt__distinct0: !a2 a1 a0. ~(h4/enumeral/nt = h4/enumeral/node a0 a1 a2)
% Assm: h4/enumeral/BL__ACCUM0_c1: !bl ac a. h4/enumeral/BL__ACCUM a ac (h4/enumeral/zerbl bl) = h4/enumeral/onebl a ac bl
% Assm: h4/enumeral/bt__size__def_c1: !f a2 a1 a0. h4/enumeral/bt__size f (h4/enumeral/node a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (f a1) (h4/enumeral/bt__size f a2)))
% Assm: h4/enumeral/bl__distinct_c1: !a2 a1 a0. ~(h4/enumeral/nbl = h4/enumeral/onebl a0 a1 a2)
% Assm: h4/enumeral/bl__distinct_c2: !a2 a1 a0 a. ~(h4/enumeral/zerbl a = h4/enumeral/onebl a0 a1 a2)
% Assm: h4/enumeral/bt__distinct: !a2 a1 a0. ~(h4/enumeral/nt = h4/enumeral/node a0 a1 a2)
% Assm: h4/enumeral/BL__ACCUM0_c0: !ac a. h4/enumeral/BL__ACCUM a ac h4/enumeral/nbl = h4/enumeral/onebl a ac h4/enumeral/nbl
% Assm: h4/enumeral/bl__size__def_c2: !f a2 a1 a0. h4/enumeral/bl__size f (h4/enumeral/onebl a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/arithmetic/_2B (h4/enumeral/bt__size f a1) (h4/enumeral/bl__size f a2)))
% Assm: h4/enumeral/bt__nchotomy: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = h4/enumeral/node b a b0)
% Assm: h4/enumeral/bl__nchotomy: !bb. bb = h4/enumeral/nbl \/ (?b. bb = h4/enumeral/zerbl b) \/ (?a b0 b. bb = h4/enumeral/onebl a b0 b)
% Assm: h4/enumeral/bl__11_c1: !a2_27 a2 a1_27 a1 a0_27 a0. h4/enumeral/onebl a0 a1 a2 = h4/enumeral/onebl a0_27 a1_27 a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm: h4/enumeral/BL__ACCUM0_c2: !rft r bl ac a. h4/enumeral/BL__ACCUM a ac (h4/enumeral/onebl r rft bl) = h4/enumeral/zerbl (h4/enumeral/BL__ACCUM a (h4/enumeral/node ac r rft) bl)
% Assm: h4/enumeral/bt__case__cong: !v_27 v f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nt ==> v = v_27) /\ (!a0 a1 a2. M_27 = h4/enumeral/node a0 a1 a2 ==> f a0 a1 a2 = f_27 a0 a1 a2) ==> h4/enumeral/bt__CASE M v f = h4/enumeral/bt__CASE M_27 v_27 f_27
% Assm: h4/enumeral/bt__110: !a2_27 a2 a1_27 a1 a0_27 a0. h4/enumeral/node a0 a1 a2 = h4/enumeral/node a0_27 a1_27 a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm: h4/enumeral/bt__11: !a2_27 a2 a1_27 a1 a0_27 a0. h4/enumeral/node a0 a1 a2 = h4/enumeral/node a0_27 a1_27 a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm: h4/enumeral/bl__case__cong: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nbl ==> v = v_27) /\ (!a. M_27 = h4/enumeral/zerbl a ==> f a = f_27 a) /\ (!a0 a1 a2. M_27 = h4/enumeral/onebl a0 a1 a2 ==> f1 a0 a1 a2 = f1_27 a0 a1 a2) ==> h4/enumeral/bl__CASE M v f f1 = h4/enumeral/bl__CASE M_27 v_27 f_27 f1_27
% Assm: h4/enumeral/bl__induction: !P. P h4/enumeral/nbl /\ (!b. P b ==> P (h4/enumeral/zerbl b)) /\ (!b. P b ==> (!b0 a. P (h4/enumeral/onebl a b0 b))) ==> (!b. P b)
% Assm: h4/enumeral/bt__induction: !P. P h4/enumeral/nt /\ (!b b0. P b /\ P b0 ==> (!a. P (h4/enumeral/node b a b0))) ==> (!b. P b)
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/enumeral/bt__case__def0_c1: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = f a0 a1 a2
% Assm: h4/enumeral/bt__case__def0_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/enumeral/bl__case__def_c1: !v f1 f a. h4/enumeral/bl__CASE (h4/enumeral/zerbl a) v f f1 = f a
% Assm: h4/enumeral/bl__case__def_c2: !v f1 f a2 a1 a0. h4/enumeral/bl__CASE (h4/enumeral/onebl a0 a1 a2) v f f1 = f1 a0 a1 a2
% Assm: h4/enumeral/bl__case__def_c0: !v f1 f. h4/enumeral/bl__CASE h4/enumeral/nbl v f f1 = v
% Assm: h4/enumeral/bl__Axiom: !f2 f1 f0. ?fn. fn h4/enumeral/nbl = f0 /\ (!a. fn (h4/enumeral/zerbl a) = f1 a (fn a)) /\ (!a0 a1 a2. fn (h4/enumeral/onebl a0 a1 a2) = f2 a0 a1 a2 (fn a2))
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/enumeral/BL__CONS0: !bl a. h4/enumeral/BL__CONS a bl = h4/enumeral/BL__ACCUM a h4/enumeral/nt bl
% Assm: h4/enumeral/bt__case__def_c1: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = f a0 a1 a2
% Assm: h4/enumeral/bt__case__def_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/enumeral/bt__Axiom: !f1 f0. ?fn. fn h4/enumeral/nt = f0 /\ (!a0 a1 a2. fn (h4/enumeral/node a0 a1 a2) = f1 a1 a0 a2 (fn a0) (fn a2))
% Assm: h4/enumeral/bt__size__def_c0: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/0
% Assm: h4/enumeral/datatype__bt: !bt. h4/bool/DATATYPE (bt h4/enumeral/nt h4/enumeral/node)
% Assm: h4/enumeral/datatype__bl: !bl. h4/bool/DATATYPE (bl h4/enumeral/nbl h4/enumeral/zerbl h4/enumeral/onebl)
% Assm: h4/list/LAST__EL: !ls. ~(ls = h4/list/NIL) ==> h4/list/LAST ls = h4/list/EL (h4/prim__rec/PRE (h4/list/LENGTH ls)) ls
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/list/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/list__repfns_c1: !r. (\a0_27. !_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM))) a0 a1 /\ _27list_27 a1) ==> _27list_27 a0_270) ==> _27list_27 a0_27) r <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm: h4/list/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/rich__list/PREFIX__FOLDR: !l P. h4/rich__list/PREFIX P l = h4/list/FOLDR (\x l_27. h4/bool/COND (P x) (h4/list/CONS x l_27) h4/list/NIL) h4/list/NIL l
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/LENGTH0_c0: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm: h4/list/LENGTH0_c1: !t h. h4/list/LENGTH (h4/list/CONS h t) = h4/num/SUC (h4/list/LENGTH t)
% Assm: h4/bool/IMP__CLAUSES_c2: !t. F ==> t <=> T
% Assm: h4/list/EL__restricted_c1: !n ls l. h4/list/EL (h4/num/SUC n) (h4/list/CONS l ls) = h4/list/EL n ls
% Assm: h4/list/EL__restricted_c0: h4/list/EL h4/num/0 = h4/list/HD
% Assm: h4/list/LAST__CONS_c0: !x. h4/list/LAST (h4/list/CONS x h4/list/NIL) = x
% Assm: h4/list/LAST__CONS_c1: !z y x. h4/list/LAST (h4/list/CONS x (h4/list/CONS y z)) = h4/list/LAST (h4/list/CONS y z)
% Assm: h4/list/HD0: !t h. h4/list/HD (h4/list/CONS h t) = h
% Assm: h4/prim__rec/PRE0_c1: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/list/NULL__EQ: !l. h4/list/NULL l <=> l = h4/list/NIL
% Assm: h4/rich__list/SPLITP0_c0: !P. h4/rich__list/SPLITP P h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% Assm: h4/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/FOLDR0_c0: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm: h4/rich__list/SPLITP0_c1: !x l P. h4/rich__list/SPLITP P (h4/list/CONS x l) = h4/bool/COND (P x) (h4/pair/_2C h4/list/NIL (h4/list/CONS x l)) (h4/pair/_2C (h4/list/CONS x (h4/pair/FST (h4/rich__list/SPLITP P l))) (h4/pair/SND (h4/rich__list/SPLITP P l)))
% Assm: h4/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/combin/o__THM: !x g f. h4/combin/o f g x = f (g x)
% Assm: h4/rich__list/PREFIX__DEF: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (h4/rich__list/SPLITP (h4/combin/o $not P) l)
% Assm: h4/bool/EXCLUDED__MIDDLE: !t. t \/ ~t
% Assm: h4/list/SNOC0_c0: !x. h4/list/SNOC x h4/list/NIL = h4/list/CONS x h4/list/NIL
% Assm: h4/list/NOT__CONS__NIL: !a1 a0. ~(h4/list/CONS a0 a1 = h4/list/NIL)
% Assm: h4/list/NULL0_c0: h4/list/NULL h4/list/NIL
% Assm: h4/list/NULL0_c1: !t h. ~h4/list/NULL (h4/list/CONS h t)
% Assm: h4/list/list__Axiom: !f1 f0. ?fn. fn h4/list/NIL = f0 /\ (!a0 a1. fn (h4/list/CONS a0 a1) = f1 a0 a1 (fn a1))
% Assm: h4/rich__list/DROP__LENGTH__NIL__rwt: !m l. m = h4/list/LENGTH l ==> h4/list/DROP m l = h4/list/NIL
% Assm: h4/rich__list/DROP__LENGTH__NIL: !l. h4/list/DROP (h4/list/LENGTH l) l = h4/list/NIL
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/list/lupdate__append2: !x v l2 l1. h4/list/LUPDATE v (h4/list/LENGTH l1) (h4/list/APPEND (h4/list/APPEND l1 (h4/list/CONS x h4/list/NIL)) l2) = h4/list/APPEND (h4/list/APPEND l1 (h4/list/CONS v h4/list/NIL)) l2
% Assm: h4/string/IMPLODE__def_c0: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm: h4/list/LUPDATE__def_c2: !x n l e. h4/list/LUPDATE e (h4/num/SUC n) (h4/list/CONS x l) = h4/list/CONS x (h4/list/LUPDATE e n l)
% 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/list/APPEND0_c1: !l2 l1 h. h4/list/APPEND (h4/list/CONS h l1) l2 = h4/list/CONS h (h4/list/APPEND l1 l2)
% Assm: h4/list/APPEND0_c0: !l. h4/list/APPEND h4/list/NIL l = l
% Assm: h4/list/MAP20_c0: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm: h4/bool/EQ__EXPAND: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Goal: !t. h4/enumeral/bt__to__list t = h4/enumeral/bt__to__list__ac t h4/list/NIL
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_enumerals_btu_u_tou_u_list0u_c1]: !x r l. h4/enumeral/bt__to__list (happ (happ (happ h4/enumeral/node l) x) r) = h4/list/APPEND (h4/list/APPEND (h4/enumeral/bt__to__list l) (happ (happ h4/list/CONS x) h4/list/NIL)) (h4/enumeral/bt__to__list r)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_enumerals_btu_u_repfnsu_c0]: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x'. happ (happ (happ h4/enumeral/_20_40ind__typeenumeral1 x) x) x' = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral3 x) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral3 x') _0))))
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_enumerals_btu_u_tou_u_listu_u_ac0u_c1]: !x r m l. h4/enumeral/bt__to__list__ac (happ (happ (happ h4/enumeral/node l) x) r) m = h4/enumeral/bt__to__list__ac l (happ (happ h4/list/CONS x) (h4/enumeral/bt__to__list__ac r m))
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/enumeral/_20_40ind__typeenumeral0 = h4/enumeral/_20_40ind__typeenumeral2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_enumerals_node0]: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm [h4s_enumerals_nt0]: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm [h4s_enumerals_btu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a2 _0)) /\ happ _27bt_27 a0 /\ happ _27bt_27 a2) ==> happ _27bt_27 a0_270) ==> happ _27bt_27 r) <=> h4/enumeral/_20_40ind__typeenumeral3 (h4/enumeral/_20_40ind__typeenumeral2 r) = r)
% Assm [h4s_enumerals_btu_u_tou_u_list0u_c0]: h4/enumeral/bt__to__list h4/enumeral/nt = h4/list/NIL
% Assm [h4s_enumerals_btu_u_tou_u_listu_u_ac0u_c0]: !m. h4/enumeral/bt__to__list__ac h4/enumeral/nt m = m
% 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_enumerals_blu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _1 \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _1) /\ happ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a0 a1) (h4/ind__type/FCONS a2 _1) /\ happ _27bl_27 a2) ==> happ _27bl_27 a0_270) ==> happ _27bl_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_enumerals_blu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0 \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _0) /\ happ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a0 a1) (h4/ind__type/FCONS a2 _0) /\ happ _27bl_27 a2) ==> happ _27bl_27 a0_270) ==> happ _27bl_27 r) <=> h4/enumeral/_20_40ind__typeenumeral8 (h4/enumeral/_20_40ind__typeenumeral7 r) = r)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x. happ (happ (happ h4/enumeral/_20_40ind__typeenumeral6 x) x) x = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C x x) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral8 x) _0)))
% Assm [h4s_enumerals_btu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _1 \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a2 _1)) /\ happ _27bt_27 a0 /\ happ _27bt_27 a2) ==> happ _27bt_27 a0_270) ==> happ _27bt_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_enumerals_blu_u_repfnsu_c0]: !a. h4/enumeral/_20_40ind__typeenumeral7 (h4/enumeral/_20_40ind__typeenumeral8 a) = a
% Assm [h4s_enumerals_onebl0]: h4/enumeral/onebl = h4/enumeral/_20_40ind__typeenumeral6
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/enumeral/_20_40ind__typeenumeral4 = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/enumeral/_20_40ind__typeenumeral5 x = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral8 x) _0)))
% Assm [h4s_enumerals_zerbl0]: h4/enumeral/zerbl = h4/enumeral/_20_40ind__typeenumeral5
% Assm [h4s_enumerals_nbl0]: h4/enumeral/nbl = h4/enumeral/_20_40ind__typeenumeral4
% Assm [h4s_enumerals_btu_u_distinct0]: !a2 a1 a0. ~(h4/enumeral/nt = happ (happ (happ h4/enumeral/node a0) a1) a2)
% Assm [h4s_enumerals_BLu_u_ACCUM0u_c1]: !bl ac a. h4/enumeral/BL__ACCUM a ac (happ h4/enumeral/zerbl bl) = happ (happ (happ h4/enumeral/onebl a) ac) bl
% Assm [h4s_enumerals_btu_u_sizeu_u_defu_c1]: !f a2 a1 a0. h4/enumeral/bt__size f (happ (happ (happ h4/enumeral/node a0) a1) a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (happ f a1) (h4/enumeral/bt__size f a2)))
% Assm [h4s_enumerals_blu_u_distinctu_c1]: !a2 a1 a0. ~(h4/enumeral/nbl = happ (happ (happ h4/enumeral/onebl a0) a1) a2)
% Assm [h4s_enumerals_blu_u_distinctu_c2]: !a2 a1 a0 a. ~(happ h4/enumeral/zerbl a = happ (happ (happ h4/enumeral/onebl a0) a1) a2)
% Assm [h4s_enumerals_btu_u_distinct]: !a2 a1 a0. ~(h4/enumeral/nt = happ (happ (happ h4/enumeral/node a0) a1) a2)
% Assm [h4s_enumerals_BLu_u_ACCUM0u_c0]: !ac a. h4/enumeral/BL__ACCUM a ac h4/enumeral/nbl = happ (happ (happ h4/enumeral/onebl a) ac) h4/enumeral/nbl
% Assm [h4s_enumerals_blu_u_sizeu_u_defu_c2]: !f a2 a1 a0. h4/enumeral/bl__size f (happ (happ (happ h4/enumeral/onebl a0) a1) a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/arithmetic/_2B (h4/enumeral/bt__size f a1) (h4/enumeral/bl__size f a2)))
% Assm [h4s_enumerals_btu_u_nchotomy]: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = happ (happ (happ h4/enumeral/node b) a) b0)
% Assm [h4s_enumerals_blu_u_nchotomy]: !bb. bb = h4/enumeral/nbl \/ (?b. bb = happ h4/enumeral/zerbl b) \/ (?a b0 b. bb = happ (happ (happ h4/enumeral/onebl a) b0) b)
% Assm [h4s_enumerals_blu_u_11u_c1]: !a2_27 a2 a1_27 a1 a0_27 a0. happ (happ (happ h4/enumeral/onebl a0) a1) a2 = happ (happ (happ h4/enumeral/onebl a0_27) a1_27) a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm [h4s_enumerals_BLu_u_ACCUM0u_c2]: !rft r bl ac a. h4/enumeral/BL__ACCUM a ac (happ (happ (happ h4/enumeral/onebl r) rft) bl) = happ h4/enumeral/zerbl (h4/enumeral/BL__ACCUM a (happ (happ (happ h4/enumeral/node ac) r) rft) bl)
% Assm [h4s_enumerals_btu_u_caseu_u_cong]: !v_27 v f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nt ==> v = v_27) /\ (!a0 a1 a2. M_27 = happ (happ (happ h4/enumeral/node a0) a1) a2 ==> happ (happ (happ f a0) a1) a2 = happ (happ (happ f_27 a0) a1) a2) ==> h4/enumeral/bt__CASE M v f = h4/enumeral/bt__CASE M_27 v_27 f_27
% Assm [h4s_enumerals_btu_u_110]: !a2_27 a2 a1_27 a1 a0_27 a0. happ (happ (happ h4/enumeral/node a0) a1) a2 = happ (happ (happ h4/enumeral/node a0_27) a1_27) a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm [h4s_enumerals_btu_u_11]: !a2_27 a2 a1_27 a1 a0_27 a0. happ (happ (happ h4/enumeral/node a0) a1) a2 = happ (happ (happ h4/enumeral/node a0_27) a1_27) a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm [h4s_enumerals_blu_u_caseu_u_cong]: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nbl ==> v = v_27) /\ (!a. M_27 = happ h4/enumeral/zerbl a ==> happ f a = happ f_27 a) /\ (!a0 a1 a2. M_27 = happ (happ (happ h4/enumeral/onebl a0) a1) a2 ==> happ (happ (happ f1 a0) a1) a2 = happ (happ (happ f1_27 a0) a1) a2) ==> h4/enumeral/bl__CASE M v f f1 = h4/enumeral/bl__CASE M_27 v_27 f_27 f1_27
% Assm [h4s_enumerals_blu_u_induction]: !P. happ P h4/enumeral/nbl /\ (!b. happ P b ==> happ P (happ h4/enumeral/zerbl b)) /\ (!b. happ P b ==> (!b0 a. happ P (happ (happ (happ h4/enumeral/onebl a) b0) b))) ==> (!b. happ P b)
% Assm [h4s_enumerals_btu_u_induction]: !P. happ P h4/enumeral/nt /\ (!b b0. happ P b /\ happ P b0 ==> (!a. happ P (happ (happ (happ h4/enumeral/node b) a) b0))) ==> (!b. happ P b)
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_enumerals_btu_u_caseu_u_def0u_c1]: !v f a2 a1 a0. h4/enumeral/bt__CASE (happ (happ (happ h4/enumeral/node a0) a1) a2) v f = happ (happ (happ f a0) a1) a2
% Assm [h4s_enumerals_btu_u_caseu_u_def0u_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c1]: !v f1 f a. h4/enumeral/bl__CASE (happ h4/enumeral/zerbl a) v f f1 = happ f a
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c2]: !v f1 f a2 a1 a0. h4/enumeral/bl__CASE (happ (happ (happ h4/enumeral/onebl a0) a1) a2) v f f1 = happ (happ (happ f1 a0) a1) a2
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c0]: !v f1 f. h4/enumeral/bl__CASE h4/enumeral/nbl v f f1 = v
% Assm [h4s_enumerals_blu_u_Axiom]: !f2 f1 f0. ?fn. happ fn h4/enumeral/nbl = f0 /\ (!a. happ fn (happ h4/enumeral/zerbl a) = happ (happ f1 a) (happ fn a)) /\ (!a0 a1 a2. happ fn (happ (happ (happ h4/enumeral/onebl a0) a1) a2) = happ (happ (happ (happ f2 a0) a1) a2) (happ fn a2))
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_enumerals_BLu_u_CONS0]: !bl a. h4/enumeral/BL__CONS a bl = h4/enumeral/BL__ACCUM a h4/enumeral/nt bl
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c1]: !v f a2 a1 a0. h4/enumeral/bt__CASE (happ (happ (happ h4/enumeral/node a0) a1) a2) v f = happ (happ (happ f a0) a1) a2
% Assm [h4s_enumerals_btu_u_caseu_u_defu_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_enumerals_btu_u_Axiom]: !f1 f0. ?fn. happ fn h4/enumeral/nt = f0 /\ (!a0 a1 a2. happ fn (happ (happ (happ h4/enumeral/node a0) a1) a2) = happ (happ (happ (happ (happ f1 a1) a0) a2) (happ fn a0)) (happ fn a2))
% Assm [h4s_enumerals_btu_u_sizeu_u_defu_c0]: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/0
% Assm [h4s_enumerals_datatypeu_u_bt]: !bt. h4/bool/DATATYPE (happ (happ bt h4/enumeral/nt) h4/enumeral/node)
% Assm [h4s_enumerals_datatypeu_u_bl]: !bl. h4/bool/DATATYPE (happ (happ (happ bl h4/enumeral/nbl) h4/enumeral/zerbl) h4/enumeral/onebl)
% Assm [h4s_lists_LASTu_u_EL]: !ls. ~(ls = h4/list/NIL) ==> h4/list/LAST ls = happ (h4/list/EL (h4/prim__rec/PRE (h4/list/LENGTH ls))) ls
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_lists_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_listu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27list_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (h4/ind__type/FCONS a1 _0) /\ happ _27list_27 a1) ==> happ _27list_27 a0_270) ==> happ _27list_27 r) <=> h4/list/_20_40ind__typelist3 (h4/list/_20_40ind__typelist2 r) = r)
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% Assm [h4s_lists_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_richu_u_lists_PREFIXu_u_FOLDR]: !_1. (!P x l_27. happ (happ (happ _1 P) x) l_27 = h4/bool/COND (happ P x) (happ (happ h4/list/CONS x) l_27) h4/list/NIL) ==> (!_0. (!P x. happ (happ _0 P) x = happ (happ _1 P) x) ==> (!l P. h4/rich__list/PREFIX P l = h4/list/FOLDR (happ _0 P) h4/list/NIL l))
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (happ (happ h4/list/CONS h) t))) ==> (!l. happ P l)
% Assm [h4s_lists_LENGTH0u_c0]: h4/list/LENGTH h4/list/NIL = h4/num/0
% Assm [h4s_lists_LENGTH0u_c1]: !t h. h4/list/LENGTH (happ (happ h4/list/CONS h) t) = h4/num/SUC (h4/list/LENGTH t)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c2]: !t. F ==> t <=> T
% Assm [h4s_lists_ELu_u_restrictedu_c1]: !n ls l. happ (h4/list/EL (h4/num/SUC n)) (happ (happ h4/list/CONS l) ls) = happ (h4/list/EL n) ls
% Assm [h4s_lists_ELu_u_restrictedu_c0]: h4/list/EL h4/num/0 = h4/list/HD
% Assm [h4s_lists_LASTu_u_CONSu_c0]: !x. h4/list/LAST (happ (happ h4/list/CONS x) h4/list/NIL) = x
% Assm [h4s_lists_LASTu_u_CONSu_c1]: !z y x. h4/list/LAST (happ (happ h4/list/CONS x) (happ (happ h4/list/CONS y) z)) = h4/list/LAST (happ (happ h4/list/CONS y) z)
% Assm [h4s_lists_HD0]: !t h. happ h4/list/HD (happ (happ h4/list/CONS h) t) = h
% Assm [h4s_primu_u_recs_PRE0u_c1]: !m. h4/prim__rec/PRE (h4/num/SUC m) = m
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_lists_NULLu_u_EQ]: !l. h4/list/NULL l <=> l = h4/list/NIL
% Assm [h4s_richu_u_lists_SPLITP0u_c0]: !P. h4/rich__list/SPLITP P h4/list/NIL = h4/pair/_2C h4/list/NIL h4/list/NIL
% 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_FOLDR0u_c0]: !f e. h4/list/FOLDR f e h4/list/NIL = e
% Assm [h4s_richu_u_lists_SPLITP0u_c1]: !x l P. h4/rich__list/SPLITP P (happ (happ h4/list/CONS x) l) = h4/bool/COND (happ P x) (h4/pair/_2C h4/list/NIL (happ (happ h4/list/CONS x) l)) (h4/pair/_2C (happ (happ h4/list/CONS x) (h4/pair/FST (h4/rich__list/SPLITP P l))) (h4/pair/SND (h4/rich__list/SPLITP P l)))
% 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_combins_ou_u_THM]: !x g f. happ (h4/combin/o f g) x = happ f (happ g x)
% Assm [h4s_richu_u_lists_PREFIXu_u_DEF]: !l P. h4/rich__list/PREFIX P l = h4/pair/FST (h4/rich__list/SPLITP (h4/combin/o $not P) l)
% Assm [h4s_bools_EXCLUDEDu_u_MIDDLE]: !t. t \/ ~t
% Assm [h4s_lists_SNOC0u_c0]: !x. h4/list/SNOC x h4/list/NIL = happ (happ h4/list/CONS x) h4/list/NIL
% Assm [h4s_lists_NOTu_u_CONSu_u_NIL]: !a1 a0. ~(happ (happ h4/list/CONS a0) a1 = h4/list/NIL)
% Assm [h4s_lists_NULL0u_c0]: h4/list/NULL h4/list/NIL
% Assm [h4s_lists_NULL0u_c1]: !t h. ~h4/list/NULL (happ (happ h4/list/CONS h) t)
% Assm [h4s_lists_listu_u_Axiom]: !f1 f0. ?fn. happ fn h4/list/NIL = f0 /\ (!a0 a1. happ fn (happ (happ h4/list/CONS a0) a1) = happ (happ (happ f1 a0) a1) (happ fn a1))
% Assm [h4s_richu_u_lists_DROPu_u_LENGTHu_u_NILu_u_rwt]: !m l. m = h4/list/LENGTH l ==> h4/list/DROP m l = h4/list/NIL
% Assm [h4s_richu_u_lists_DROPu_u_LENGTHu_u_NIL]: !l. h4/list/DROP (h4/list/LENGTH l) l = h4/list/NIL
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_lists_lupdateu_u_append2]: !x v l2 l1. h4/list/LUPDATE v (h4/list/LENGTH l1) (h4/list/APPEND (h4/list/APPEND l1 (happ (happ h4/list/CONS x) h4/list/NIL)) l2) = h4/list/APPEND (h4/list/APPEND l1 (happ (happ h4/list/CONS v) h4/list/NIL)) l2
% Assm [h4s_strings_IMPLODEu_u_defu_c0]: h4/string/IMPLODE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_LUPDATEu_u_defu_c2]: !x n l e. h4/list/LUPDATE e (h4/num/SUC n) (happ (happ h4/list/CONS x) l) = happ (happ h4/list/CONS x) (h4/list/LUPDATE e n l)
% 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_lists_APPEND0u_c1]: !l2 l1 h. h4/list/APPEND (happ (happ h4/list/CONS h) l1) l2 = happ (happ h4/list/CONS h) (h4/list/APPEND l1 l2)
% Assm [h4s_lists_APPEND0u_c0]: !l. h4/list/APPEND h4/list/NIL l = l
% Assm [h4s_lists_MAP20u_c0]: !f. h4/list/MAP2 f h4/list/NIL h4/list/NIL = h4/list/NIL
% Assm [h4s_bools_EQu_u_EXPAND]: !t2 t1. (t1 <=> t2) <=> t1 /\ t2 \/ ~t1 /\ ~t2
% Goal: !t. h4/enumeral/bt__to__list t = h4/enumeral/bt__to__list__ac t h4/list/NIL
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1427985,TV_Q1427981]: ![V_f, V_g]: (![V_x]: s(TV_Q1427981,happ(s(t_fun(TV_Q1427985,TV_Q1427981),V_f),s(TV_Q1427985,V_x))) = s(TV_Q1427981,happ(s(t_fun(TV_Q1427985,TV_Q1427981),V_g),s(TV_Q1427985,V_x))) => s(t_fun(TV_Q1427985,TV_Q1427981),V_f) = s(t_fun(TV_Q1427985,TV_Q1427981),V_g))).
fof(ah4s_enumerals_btu_u_tou_u_list0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(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_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),V_r)))))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_ETAu_u_AX, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_t),s(TV_u_27a,V_x)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_enumerals_btu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_a))))) = s(t_h4s_enumerals_bt(TV_u_27a),V_a)).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral1u_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, V_xi_]: s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral1),s(t_h4s_enumerals_bt(TV_u_27a),V_x))),s(TV_u_27a,V_x0))),s(t_h4s_enumerals_bt(TV_u_27a),V_xi_))) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(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_x0),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_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(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_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_xi_))),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_enumerals_btu_u_tou_u_listu_u_ac0u_c1, axiom, ![TV_u_27a]: ![V_x, V_r, V_m, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_l))),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_r))),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(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_x))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),V_r),s(t_h4s_lists_list(TV_u_27a),V_m)))))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_FCONS0u_c1, axiom, ![TV_u_27a]: ![V_n, V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))) = s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),V_f),s(t_h4s_nums_num,V_n)))).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral0u_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_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral0) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(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_enumerals_node0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node) = s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral1)).
fof(ah4s_enumerals_nt0, axiom, ![TV_u_27a]: s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral0)).
fof(ah4s_enumerals_btu_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_27btu_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, V_a2]: (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_a1),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_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_a2),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_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_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_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(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_enumerals_btu_u_tou_u_list0u_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_enumerals_btu_u_tou_u_listu_u_ac0u_c0, axiom, ![TV_u_27a]: ![V_m]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(t_h4s_lists_list(TV_u_27a),V_m))) = s(t_h4s_lists_list(TV_u_27a),V_m)).
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_enumerals_blu_u_TYu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0u_27]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_27)))) <=> ![V_uu_27blu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a))))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_a0),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_27)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_0),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_rep))))))).
fof(ah4s_enumerals_blu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27blu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a))))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_a0),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r)))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral6u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_x1]: s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral6),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_x0))),s(t_h4s_enumerals_bl(TV_u_27a),V_x1))) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_x1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))))).
fof(ah4s_enumerals_btu_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_a0u_27]: (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_a0u_27)))) <=> ![V_uu_27btu_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_1))) | ?[V_a0, V_a1, V_a2]: (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_a1),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_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_a2),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_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_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_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_27)))))) => ?[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_enumerals_bt(TV_u_27a),t_h4s_indu_u_types_recspace(TV_u_27a)),V_rep))))))).
fof(ah4s_enumerals_blu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) = s(t_h4s_enumerals_bl(TV_u_27a),V_a)).
fof(ah4s_enumerals_onebl0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl) = s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral6)).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral4u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral4) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral5u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_u_20u_40indu_u_typeenumeral5),s(t_h4s_enumerals_bl(TV_u_27a),V_x))) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(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(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))))).
fof(ah4s_enumerals_zerbl0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl) = s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_u_20u_40indu_u_typeenumeral5)).
fof(ah4s_enumerals_nbl0, axiom, ![TV_u_27a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral4)).
fof(ah4s_enumerals_btu_u_distinct0, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0]: ~ (s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_BLu_u_ACCUM0u_c1, axiom, ![TV_u_27a]: ![V_bl, V_ac, V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_accum(s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),V_ac),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_bl))))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_ac))),s(t_h4s_enumerals_bl(TV_u_27a),V_bl)))).
fof(ah4s_enumerals_btu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a1))),s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))))))))).
fof(ah4s_enumerals_blu_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0]: ~ (s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_blu_u_distinctu_c2, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0, V_a]: ~ (s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_btu_u_distinct, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0]: ~ (s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_BLu_u_ACCUM0u_c0, axiom, ![TV_u_27a]: ![V_ac, V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_accum(s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),V_ac),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_ac))),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl)))).
fof(ah4s_enumerals_blu_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_enumerals_blu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_nums_num,h4s_enumerals_blu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))))))))).
fof(ah4s_enumerals_btu_u_nchotomy, axiom, ![TV_u_27a]: ![V_bb]: (s(t_h4s_enumerals_bt(TV_u_27a),V_bb) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) | ?[V_b, V_a, V_b0]: s(t_h4s_enumerals_bt(TV_u_27a),V_bb) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_b))),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))))).
fof(ah4s_enumerals_blu_u_nchotomy, axiom, ![TV_u_27a]: ![V_bb]: (s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) | (?[V_b]: s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_b))) | ?[V_a, V_b0, V_b]: s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))))).
fof(ah4s_enumerals_blu_u_11u_c1, axiom, ![TV_u_27a]: ![V_a2u_27, V_a2, V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0u_27))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1u_27))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & (s(t_h4s_enumerals_bt(TV_u_27a),V_a1) = s(t_h4s_enumerals_bt(TV_u_27a),V_a1u_27) & s(t_h4s_enumerals_bl(TV_u_27a),V_a2) = s(t_h4s_enumerals_bl(TV_u_27a),V_a2u_27))))).
fof(ah4s_enumerals_BLu_u_ACCUM0u_c2, axiom, ![TV_u_27a]: ![V_rft, V_r, V_bl, V_ac, V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_accum(s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),V_ac),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_r))),s(t_h4s_enumerals_bt(TV_u_27a),V_rft))),s(t_h4s_enumerals_bl(TV_u_27a),V_bl))))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_accum(s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_ac))),s(TV_u_27a,V_r))),s(t_h4s_enumerals_bt(TV_u_27a),V_rft))),s(t_h4s_enumerals_bl(TV_u_27a),V_bl)))))).
fof(ah4s_enumerals_btu_u_caseu_u_cong, axiom, ![TV_u_27a,TV_u_27b]: ![V_vu_27, V_v, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_enumerals_bt(TV_u_27a),V_M) = s(t_h4s_enumerals_bt(TV_u_27a),V_Mu_27) & ((s(t_h4s_enumerals_bt(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt) => s(TV_u_27b,V_v) = s(TV_u_27b,V_vu_27)) & ![V_a0, V_a1, V_a2]: (s(t_h4s_enumerals_bt(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))) => s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_fu_27),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))))) => s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),V_M),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),V_Mu_27),s(TV_u_27b,V_vu_27),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_fu_27))))).
fof(ah4s_enumerals_btu_u_110, axiom, ![TV_u_27a]: ![V_a2u_27, V_a2, V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0u_27))),s(TV_u_27a,V_a1u_27))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2u_27))) <=> (s(t_h4s_enumerals_bt(TV_u_27a),V_a0) = s(t_h4s_enumerals_bt(TV_u_27a),V_a0u_27) & (s(TV_u_27a,V_a1) = s(TV_u_27a,V_a1u_27) & s(t_h4s_enumerals_bt(TV_u_27a),V_a2) = s(t_h4s_enumerals_bt(TV_u_27a),V_a2u_27))))).
fof(ah4s_enumerals_btu_u_11, axiom, ![TV_u_27a]: ![V_a2u_27, V_a2, V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))) = s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0u_27))),s(TV_u_27a,V_a1u_27))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2u_27))) <=> (s(t_h4s_enumerals_bt(TV_u_27a),V_a0) = s(t_h4s_enumerals_bt(TV_u_27a),V_a0u_27) & (s(TV_u_27a,V_a1) = s(TV_u_27a,V_a1u_27) & s(t_h4s_enumerals_bt(TV_u_27a),V_a2) = s(t_h4s_enumerals_bt(TV_u_27a),V_a2u_27))))).
fof(ah4s_enumerals_blu_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_enumerals_bl(TV_u_27a),V_M) = s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) & ((s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) => s(TV_u_27b,V_v) = s(TV_u_27b,V_vu_27)) & (![V_a]: (s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) => s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fu_27),s(t_h4s_enumerals_bl(TV_u_27a),V_a)))) & ![V_a0, V_a1, V_a2]: (s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) => s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1u_27),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))))) => s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),V_M),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27),s(TV_u_27b,V_vu_27),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fu_27),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1u_27))))).
fof(ah4s_enumerals_blu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl)))) & (![V_b]: (p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))) => p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_b))))))) & ![V_b]: (p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))) => ![V_b0, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))),s(t_h4s_enumerals_bl(TV_u_27a),V_b))))))))) => ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))))).
fof(ah4s_enumerals_btu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt)))) & ![V_b, V_b0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b)))) & p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))))) => ![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_b))),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0)))))))) => ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b)))))).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t0) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
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,t0)).
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,t0)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_enumerals_btu_u_caseu_u_def0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))).
fof(ah4s_enumerals_btu_u_caseu_u_def0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t0))) <=> 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_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_enumerals_blu_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_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a)))).
fof(ah4s_enumerals_blu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))).
fof(ah4s_enumerals_blu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f1, V_f]: s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,V_v)).
fof(ah4s_enumerals_blu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f2, V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl))) = s(TV_u_27b,V_f0) & (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),V_f1),s(t_h4s_enumerals_bl(TV_u_27a),V_a))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) & ![V_a0, V_a1, V_a2]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)))),V_f2),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))))))).
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_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_enumerals_BLu_u_CONS0, axiom, ![TV_u_27a]: ![V_bl, V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_cons(s(TV_u_27a,V_a),s(t_h4s_enumerals_bl(TV_u_27a),V_bl))) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_blu_u_accum(s(TV_u_27a,V_a),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(t_h4s_enumerals_bl(TV_u_27a),V_bl)))).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))).
fof(ah4s_enumerals_btu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_enumerals_btu_u_case(s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b))),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_enumerals_btu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1, V_a2]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))))),V_f1),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))))).
fof(ah4s_enumerals_btu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_enumerals_datatypeu_u_bt, axiom, ![TV_u_27a]: ![V_bt]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),t_bool),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),t_bool)),V_bt),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node))))))).
fof(ah4s_enumerals_datatypeu_u_bl, axiom, ![TV_u_27a]: ![V_bl]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool),happ(s(t_fun(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool)),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool))),V_bl),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl))),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl))),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl))))))).
fof(ah4s_lists_LASTu_u_EL, axiom, ![TV_u_27a]: ![V_ls]: (~ (s(t_h4s_lists_list(TV_u_27a),V_ls) = 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),V_ls))) = s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_ls))))))),s(t_h4s_lists_list(TV_u_27a),V_ls))))).
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_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_lists_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_listu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27listu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | ?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27listu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist3(s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_lists_NIL0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0)).
fof(ah4s_lists_listu_u_repfnsu_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_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_richu_u_lists_PREFIXu_u_FOLDR, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_P, V_x, V_lu_27]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_lu_27))) = s(t_h4s_lists_list(TV_u_27a),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_lu_27))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) => ![V_uu_0]: (![V_P, V_x]: s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_1),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) => ![V_l, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_prefix(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_foldr(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)))),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_LENGTH0u_c0, axiom, ![TV_u_27a]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_lists_LENGTH0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_lists_ELu_u_restrictedu_c1, axiom, ![TV_u_27b]: ![V_n, V_ls, V_l]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_n))))),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_l))),s(t_h4s_lists_list(TV_u_27b),V_ls))))) = s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),TV_u_27b),h4s_lists_el(s(t_h4s_nums_num,V_n))),s(t_h4s_lists_list(TV_u_27b),V_ls)))).
fof(ah4s_lists_ELu_u_restrictedu_c0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_el(s(t_h4s_nums_num,h4s_nums_0))) = s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_hd)).
fof(ah4s_lists_LASTu_u_CONSu_c0, axiom, ![TV_u_27a]: ![V_x]: 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_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))) = s(TV_u_27a,V_x)).
fof(ah4s_lists_LASTu_u_CONSu_c1, axiom, ![TV_u_27a]: ![V_z, V_y, V_x]: 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_x))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_y))),s(t_h4s_lists_list(TV_u_27a),V_z))))))) = s(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_y))),s(t_h4s_lists_list(TV_u_27a),V_z)))))).
fof(ah4s_lists_HD0, axiom, ![TV_u_27a]: ![V_t, V_h]: s(TV_u_27a,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27a),h4s_lists_hd),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(TV_u_27a,V_h)).
fof(ah4s_primu_u_recs_PRE0u_c1, axiom, ![V_m]: s(t_h4s_nums_num,h4s_primu_u_recs_pre(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_NULLu_u_EQ, axiom, ![TV_u_27a]: ![V_l]: (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> s(t_h4s_lists_list(TV_u_27a),V_l) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_richu_u_lists_SPLITP0u_c0, axiom, ![TV_u_27a]: ![V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t0),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_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_richu_u_lists_SPLITP0u_c1, axiom, ![TV_u_27a]: ![V_x, V_l, V_P]: s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_bools_cond(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))))))),s(t_h4s_lists_list(TV_u_27a),h4s_pairs_snd(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))))))).
fof(ah4s_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_combins_ou_u_THM, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_x, V_g, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),h4s_combins_o(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27c,TV_u_27a),V_g))),s(TV_u_27c,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),V_g),s(TV_u_27c,V_x)))))).
fof(ah4s_richu_u_lists_PREFIXu_u_DEF, axiom, ![TV_u_27a]: ![V_l, V_P]: s(t_h4s_lists_list(TV_u_27a),h4s_richu_u_lists_prefix(s(t_fun(TV_u_27a,t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_pairs_fst(s(t_h4s_pairs_prod(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_richu_u_lists_splitp(s(t_fun(TV_u_27a,t_bool),h4s_combins_o(s(t_fun(t_bool,t_bool),d_not),s(t_fun(TV_u_27a,t_bool),V_P))),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_bools_EXCLUDEDu_u_MIDDLE, axiom, ![V_t]: (p(s(t_bool,V_t)) | ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_SNOC0u_c0, axiom, ![TV_u_27a]: ![V_x]: 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_nil))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
fof(ah4s_lists_NOTu_u_CONSu_u_NIL, axiom, ![TV_u_27a]: ![V_a1, V_a0]: ~ (s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_lists_NULL0u_c0, axiom, ![TV_u_27a]: p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))).
fof(ah4s_lists_NULL0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: ~ (p(s(t_bool,h4s_lists_null(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t)))))))).
fof(ah4s_lists_listu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_lists_list(TV_u_27a),V_a1))),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_lists_list(TV_u_27a),V_a1))))))).
fof(ah4s_richu_u_lists_DROPu_u_LENGTHu_u_NILu_u_rwt, axiom, ![TV_u_27a]: ![V_m, V_l]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,V_m),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))).
fof(ah4s_richu_u_lists_DROPu_u_LENGTHu_u_NIL, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_drop(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l))),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t0))) <=> p(s(t_bool,t0)))).
fof(ah4s_lists_lupdateu_u_append2, axiom, ![TV_u_27a]: ![V_x, V_v, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_lupdate(s(TV_u_27a,V_v),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),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_x))),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_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),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_v))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27a),V_l2)))).
fof(ah4s_strings_IMPLODEu_u_defu_c0, axiom, s(t_h4s_lists_list(t_h4s_strings_char),h4s_strings_implode(s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil))) = s(t_h4s_lists_list(t_h4s_strings_char),h4s_lists_nil)).
fof(ah4s_lists_LUPDATEu_u_defu_c2, axiom, ![TV_u_27a]: ![V_x, V_n, 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_suc(s(t_h4s_nums_num,V_n))),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_x))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_lupdate(s(TV_u_27a,V_e),s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
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_lists_APPEND0u_c1, axiom, ![TV_u_27a]: ![V_l2, V_l1, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPEND0u_c0, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27a),V_l))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_lists_MAP20u_c0, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_f]: s(t_h4s_lists_list(TV_u_27c),h4s_lists_map2(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27c),h4s_lists_nil)).
fof(ah4s_bools_EQu_u_EXPAND, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) | (~ (p(s(t_bool,V_t1))) & ~ (p(s(t_bool,V_t2))))))).
fof(ch4s_enumerals_btu_u_tou_u_listu_u_thm, conjecture, ![TV_u_27a]: ![V_t]: s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_list(s(t_h4s_enumerals_bt(TV_u_27a),V_t))) = s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_listu_u_ac(s(t_h4s_enumerals_bt(TV_u_27a),V_t),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))).
