%   ORIGINAL: h4/enumeral/bt__Axiom
% 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__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/bool/TRUTH: T
% Assm: h4/enumeral/nt0: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm: h4/enumeral/node0: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% 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/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/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/bt__repfns_c0: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% 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/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/enumeral/datatype__bt: !bt. h4/bool/DATATYPE (bt h4/enumeral/nt h4/enumeral/node)
% 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__nchotomy: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = h4/enumeral/node b a b0)
% Assm: h4/enumeral/bt__distinct0: !a2 a1 a0. ~(h4/enumeral/nt = h4/enumeral/node a0 a1 a2)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% 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/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/enumeral/bt__case__def0_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/enumeral/bt__size__def_c0: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/0
% 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/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/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__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/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/sum/IS__SUM__REP0: !f. h4/sum/IS__SUM__REP f <=> (?v1 v2. f = (\b x y. x = v1 /\ b) \/ f = (\b x y. y = v2 /\ ~b))
% Assm: h4/sum/INR__neq__INL: !v2 v1. ~(h4/sum/INR v2 = h4/sum/INL v1)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/sum/cond__sum__expand_c1: !z y x P. h4/bool/COND P (h4/sum/INR x) (h4/sum/INL y) = h4/sum/INL z <=> ~P /\ z = y
% Assm: h4/bool/EXISTS__SIMP: !t. (?x. t) <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/sum/INL__DEF: !e. h4/sum/INL e = h4/sum/ABS__sum (\b x y. x = e /\ b)
% Assm: h4/sum/INR__DEF: !e. h4/sum/INR e = h4/sum/ABS__sum (\b x y. y = e /\ ~b)
% Assm: h4/sum/sum__ISO__DEF_c1: !r. h4/sum/IS__SUM__REP r <=> h4/sum/REP__sum (h4/sum/ABS__sum r) = r
% Assm: h4/sum/sum__ISO__DEF_c0: !a. h4/sum/ABS__sum (h4/sum/REP__sum a) = a
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/list/list__Axiom__old: !x f. h4/bool/_3F_21 (\fn1. fn1 h4/list/NIL = x /\ (!h t. fn1 (h4/list/CONS h t) = f (fn1 t) h t))
% Assm: h4/bool/EQ__IMP__THM: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/BOOL__CASES__AX: !t. (t <=> T) \/ (t <=> F)
% Assm: h4/sum/sum__distinct: !y x. ~(h4/sum/INL x = h4/sum/INR y)
% Assm: h4/sum/INR__INL__11_c0: !y x. h4/sum/INL x = h4/sum/INL y <=> x = y
% Assm: h4/sum/INR__INL__11_c1: !y x. h4/sum/INR x = h4/sum/INR y <=> x = y
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/sum/cond__sum__expand_c0: !z y x P. h4/bool/COND P (h4/sum/INR x) (h4/sum/INL y) = h4/sum/INR z <=> P /\ z = x
% Assm: h4/list/CONS0: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm: h4/list/NIL0: h4/list/NIL = h4/list/_20_40ind__typelist0
% 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/list__repfns_c0: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm: h4/list/hidden____20__40ind____typelist0____def: h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/bool/EXISTS__UNIQUE__DEF: h4/bool/_3F_21 = (\P. $exists P /\ (!x y. P x /\ P y ==> x = y))
% Assm: h4/rich__list/FOLDL__REVERSE: !l f e. h4/list/FOLDL f e (h4/list/REVERSE l) = h4/list/FOLDR (\x y. f y x) e l
% Assm: h4/list/REVERSE__REVERSE: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm: h4/rich__list/FOLDL__FOLDR__REVERSE: !l f e. h4/list/FOLDL f e l = h4/list/FOLDR (\x y. f y x) e (h4/list/REVERSE l)
% Assm: h4/list/FOLDL__SNOC: !x l f e. h4/list/FOLDL f e (h4/list/SNOC x l) = f (h4/list/FOLDL f e l) x
% 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/LIST__REL__MAP2: !l2 l1 f R. h4/list/LIST__REL (\a b. R a b) l1 (h4/list/MAP f l2) <=> h4/list/LIST__REL (\a b. R a (f b)) l1 l2
% Assm: h4/option/option__case__def_c1: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/list/SNOC0_c1: !x_27 x l. h4/list/SNOC x (h4/list/CONS x_27 l) = h4/list/CONS x_27 (h4/list/SNOC x l)
% Assm: h4/list/SNOC0_c0: !x. h4/list/SNOC x h4/list/NIL = h4/list/CONS x h4/list/NIL
% Assm: h4/list/FOLDL0_c1: !x l f e. h4/list/FOLDL f e (h4/list/CONS x l) = h4/list/FOLDL f (f e x) l
% Assm: h4/list/FOLDL0_c0: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm: h4/list/LIST__REL__def_c3: !bs b as a R. h4/list/LIST__REL R (h4/list/CONS a as) (h4/list/CONS b bs) <=> R a b /\ h4/list/LIST__REL R as bs
% 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/TYPE__DEFINITION0: h4/bool/TYPE__DEFINITION = (\P rep. (!x_27 x_27_27. rep x_27 = rep x_27_27 ==> x_27 = x_27_27) /\ (!x. P x <=> (?x_27. x = rep x_27)))
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/LIST__REL__EL__EQN: !l2 l1 R. h4/list/LIST__REL R l1 l2 <=> h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ (!n. h4/prim__rec/_3C n (h4/list/LENGTH l1) ==> R (h4/list/EL n l1) (h4/list/EL n l2))
% Assm: h4/list/EL__MAP: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> (!f. h4/list/EL n (h4/list/MAP f l) = f (h4/list/EL n l))
% Assm: h4/bool/AND__CONG: !Q_27 Q P_27 P. (Q ==> (P <=> P_27)) /\ (P_27 ==> (Q <=> Q_27)) ==> (P /\ Q <=> P_27 /\ Q_27)
% Assm: h4/pair/EXISTS__PROD: !P. (?p. P p) <=> (?p__1 p__2. P (h4/pair/_2C p__1 p__2))
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/list/LIST__REL__def0: h4/list/LIST__REL = (\R a0 a1. !LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = h4/list/CONS h1 t1 /\ a10 = h4/list/CONS h2 t2 /\ R h1 h2 /\ LIST__REL_27 t1 t2) ==> LIST__REL_27 a00 a10) ==> LIST__REL_27 a0 a1)
% Assm: h4/marker/Cong__def: !x. h4/marker/Cong x <=> x
% Assm: h4/bool/BOUNDED__THM: !v. h4/bool/BOUNDED v <=> T
% Assm: h4/bool/UNWIND__THM2: !a P. (?x. x = a /\ P x) <=> P a
% Assm: h4/option/option__CLAUSES_c15: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/bool/SWAP__FORALL__THM: !P. (!x y. P x y) <=> (!y x. P x y)
% Assm: h4/sum/sum__INDUCT: !P. (!x. P (h4/sum/INL x)) /\ (!y. P (h4/sum/INR y)) ==> (!s. P s)
% Assm: h4/sum/sum__CASES: !ss. (?x. ss = h4/sum/INL x) \/ (?y. ss = h4/sum/INR y)
% Assm: h4/relation/nf__def: !x R. h4/relation/nf R x <=> (!y. ~R x y)
% Assm: h4/bool/TYPE__DEFINITION__THM: !rep P. h4/bool/TYPE__DEFINITION P rep <=> (!x_27 x_27_27. rep x_27 = rep x_27_27 ==> x_27 = x_27_27) /\ (!x. P x <=> (?x_27. x = rep x_27))
% Assm: h4/rich__list/LIST__REL__APPEND__SING: !x2 x1 l2 l1 R. h4/list/LIST__REL R (h4/list/APPEND l1 (h4/list/CONS x1 h4/list/NIL)) (h4/list/APPEND l2 (h4/list/CONS x2 h4/list/NIL)) <=> h4/list/LIST__REL R l1 l2 /\ R x1 x2
% Assm: h4/list/MEM__MAP: !x l f. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/MAP f l)) <=> (?y. x = f y /\ h4/bool/IN y (h4/list/LIST__TO__SET l))
% Assm: h4/list/LIST__REL__def_c0: !R. h4/list/LIST__REL R h4/list/NIL h4/list/NIL <=> T
% Assm: h4/list/LENGTH__APPEND: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm: h4/list/APPEND__ASSOC: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm: h4/numeral/numeral__distrib_c13: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm: h4/arithmetic/EQ__MONO__ADD__EQ: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm: h4/rich__list/EVERY2__APPEND__suff: !l4 l3 l2 l1 R. h4/list/LIST__REL R l1 l2 /\ h4/list/LIST__REL R l3 l4 ==> h4/list/LIST__REL R (h4/list/APPEND l1 l3) (h4/list/APPEND l2 l4)
% Assm: h4/rich__list/EVERY2__APPEND: !l4 l3 l2 l1 R. h4/list/LIST__REL R l1 l2 /\ h4/list/LIST__REL R l3 l4 <=> h4/list/LIST__REL R (h4/list/APPEND l1 l3) (h4/list/APPEND l2 l4) /\ h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ h4/list/LENGTH l3 = h4/list/LENGTH l4
% Assm: h4/bool/IMP__CLAUSES_c0: !t. T ==> t <=> t
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/list/LIST__TO__SET0_c1: !t h. h4/list/LIST__TO__SET (h4/list/CONS h t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm: h4/list/LIST__TO__SET0_c0: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm: h4/pred__set/IN__INSERT: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm: h4/bool/NOT__EXISTS__THM: !P. ~(?x. P x) <=> (!x. ~P x)
% Assm: h4/bool/LEFT__AND__FORALL__THM: !Q P. (!x. P x) /\ Q <=> (!x. P x /\ Q)
% Assm: h4/bool/EXISTS__OR__THM: !Q P. (?x. P x \/ Q x) <=> (?x. P x) \/ (?x. Q x)
% Assm: h4/bool/RIGHT__OR__EXISTS__THM: !Q P. P \/ (?x. Q x) <=> (?x. P \/ Q x)
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/bool/LEFT__EXISTS__AND__THM: !Q P. (?x. P x /\ Q) <=> (?x. P x) /\ Q
% Assm: h4/bool/RIGHT__EXISTS__AND__THM: !Q P. (?x. P /\ Q x) <=> P /\ (?x. Q x)
% Goal: !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))
%   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_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_bools_TRUTH]: T
% Assm [h4s_enumerals_nt0]: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm [h4s_enumerals_node0]: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% 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_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_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_btu_u_repfnsu_c0]: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% 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_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_enumerals_datatypeu_u_bt]: !bt. h4/bool/DATATYPE (happ (happ bt h4/enumeral/nt) h4/enumeral/node)
% 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_nchotomy]: !bb. bb = h4/enumeral/nt \/ (?b a b0. bb = happ (happ (happ h4/enumeral/node b) a) b0)
% Assm [h4s_enumerals_btu_u_distinct0]: !a2 a1 a0. ~(h4/enumeral/nt = happ (happ (happ h4/enumeral/node a0) a1) a2)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% 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_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_enumerals_btu_u_caseu_u_def0u_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_enumerals_btu_u_sizeu_u_defu_c0]: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/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_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_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_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_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_sums_ISu_u_SUMu_u_REP0]: !f. h4/sum/IS__SUM__REP f <=> (?v1 v2. (!x x x. happ (happ (happ f x) x) x <=> x = v1 /\ x) \/ (!x x x. happ (happ (happ f x) x) x <=> x = v2 /\ ~x))
% Assm [h4s_sums_INRu_u_nequ_u_INL]: !v2 v1. ~(h4/sum/INR v2 = h4/sum/INL v1)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_sums_condu_u_sumu_u_expandu_c1]: !z y x P. h4/bool/COND P (h4/sum/INR x) (h4/sum/INL y) = h4/sum/INL z <=> ~P /\ z = y
% Assm [h4s_bools_EXISTSu_u_SIMP]: !t. (?x. t) <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_sums_INLu_u_DEF]: !_2. (!x e b y. happ (happ (happ (happ _2 x) e) b) y <=> x = e /\ b) ==> (!_1. (!e b x. happ (happ (happ _1 e) b) x = happ (happ (happ _2 x) e) b) ==> (!_0. (!e b. happ (happ _0 e) b = happ (happ _1 e) b) ==> (!e. h4/sum/INL e = h4/sum/ABS__sum (happ _0 e))))
% Assm [h4s_sums_INRu_u_DEF]: !_2. (!e b y. happ (happ (happ _2 e) b) y <=> y = e /\ ~b) ==> (!_1. (!e b x. happ (happ (happ _1 e) b) x = happ (happ _2 e) b) ==> (!_0. (!e b. happ (happ _0 e) b = happ (happ _1 e) b) ==> (!e. h4/sum/INR e = h4/sum/ABS__sum (happ _0 e))))
% Assm [h4s_sums_sumu_u_ISOu_u_DEFu_c1]: !r. h4/sum/IS__SUM__REP r <=> h4/sum/REP__sum (h4/sum/ABS__sum r) = r
% Assm [h4s_sums_sumu_u_ISOu_u_DEFu_c0]: !a. h4/sum/ABS__sum (h4/sum/REP__sum a) = a
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_lists_listu_u_Axiomu_u_old]: !_0. (!x f fn1. happ (happ (happ _0 x) f) fn1 <=> happ fn1 h4/list/NIL = x /\ (!h t. happ fn1 (happ (happ h4/list/CONS h) t) = happ (happ (happ f (happ fn1 t)) h) t)) ==> (!x f. h4/bool/_3F_21 (happ (happ _0 x) f))
% Assm [h4s_bools_EQu_u_IMPu_u_THM]: !t2 t1. (t1 <=> t2) <=> (t1 ==> t2) /\ (t2 ==> t1)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_BOOLu_u_CASESu_u_AX]: !t. (t <=> T) \/ (t <=> F)
% Assm [h4s_sums_sumu_u_distinct]: !y x. ~(h4/sum/INL x = h4/sum/INR y)
% Assm [h4s_sums_INRu_u_INLu_u_11u_c0]: !y x. h4/sum/INL x = h4/sum/INL y <=> x = y
% Assm [h4s_sums_INRu_u_INLu_u_11u_c1]: !y x. h4/sum/INR x = h4/sum/INR y <=> x = y
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_sums_condu_u_sumu_u_expandu_c0]: !z y x P. h4/bool/COND P (h4/sum/INR x) (h4/sum/INL y) = h4/sum/INR z <=> P /\ z = x
% Assm [h4s_lists_CONS0]: h4/list/CONS = h4/list/_20_40ind__typelist1
% Assm [h4s_lists_NIL0]: h4/list/NIL = h4/list/_20_40ind__typelist0
% 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_listu_u_repfnsu_c0]: !a. h4/list/_20_40ind__typelist2 (h4/list/_20_40ind__typelist3 a) = a
% Assm [h4s_lists_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/list/_20_40ind__typelist0 = h4/list/_20_40ind__typelist2 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_bools_EXISTSu_u_UNIQUEu_u_DEF]: !x. h4/bool/_3F_21 x <=> $exists x /\ (!x y. happ x x /\ happ x y ==> x = y)
% Assm [h4s_richu_u_lists_FOLDLu_u_REVERSE]: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f y) x) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!l f e. h4/list/FOLDL f e (h4/list/REVERSE l) = h4/list/FOLDR (happ _0 f) e l))
% Assm [h4s_lists_REVERSEu_u_REVERSE]: !l. h4/list/REVERSE (h4/list/REVERSE l) = l
% Assm [h4s_richu_u_lists_FOLDLu_u_FOLDRu_u_REVERSE]: !_1. (!f x y. happ (happ (happ _1 f) x) y = happ (happ f y) x) ==> (!_0. (!f x. happ (happ _0 f) x = happ (happ _1 f) x) ==> (!l f e. h4/list/FOLDL f e l = h4/list/FOLDR (happ _0 f) e (h4/list/REVERSE l)))
% Assm [h4s_lists_FOLDLu_u_SNOC]: !x l f e. h4/list/FOLDL f e (h4/list/SNOC x l) = happ (happ f (h4/list/FOLDL f e l)) x
% 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_LISTu_u_RELu_u_MAP2]: !_3. (!R a f b. happ (happ (happ (happ _3 R) a) f) b <=> happ (happ R a) (happ f b)) ==> (!_2. (!R f a. happ (happ (happ _2 R) f) a = happ (happ (happ _3 R) a) f) ==> (!_1. (!R a b. happ (happ (happ _1 R) a) b <=> happ (happ R a) b) ==> (!_0. (!R a. happ (happ _0 R) a = happ (happ _1 R) a) ==> (!l2 l1 f R. h4/list/LIST__REL (happ _0 R) l1 (h4/list/MAP f l2) <=> h4/list/LIST__REL (happ (happ _2 R) f) l1 l2))))
% Assm [h4s_options_optionu_u_caseu_u_defu_c1]: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = happ f x
% Assm [h4s_lists_SNOC0u_c1]: !x_27 x l. h4/list/SNOC x (happ (happ h4/list/CONS x_27) l) = happ (happ h4/list/CONS x_27) (h4/list/SNOC x l)
% Assm [h4s_lists_SNOC0u_c0]: !x. h4/list/SNOC x h4/list/NIL = happ (happ h4/list/CONS x) h4/list/NIL
% Assm [h4s_lists_FOLDL0u_c1]: !x l f e. h4/list/FOLDL f e (happ (happ h4/list/CONS x) l) = h4/list/FOLDL f (happ (happ f e) x) l
% Assm [h4s_lists_FOLDL0u_c0]: !f e. h4/list/FOLDL f e h4/list/NIL = e
% Assm [h4s_lists_LISTu_u_RELu_u_defu_c3]: !bs b as a R. h4/list/LIST__REL R (happ (happ h4/list/CONS a) as) (happ (happ h4/list/CONS b) bs) <=> happ (happ R a) b /\ h4/list/LIST__REL R as bs
% 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_TYPEu_u_DEFINITION0]: !x x. h4/bool/TYPE__DEFINITION x x <=> (!x_27 x_27_27. happ x x_27 = happ x x_27_27 ==> x_27 = x_27_27) /\ (!x. happ x x <=> (?x_27. x = happ x x_27))
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (happ (happ h4/list/CONS h) t) = happ (happ h4/list/CONS (happ f h)) (h4/list/MAP f t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_LISTu_u_RELu_u_ELu_u_EQN]: !l2 l1 R. h4/list/LIST__REL R l1 l2 <=> h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ (!n. h4/prim__rec/_3C n (h4/list/LENGTH l1) ==> happ (happ R (h4/list/EL n l1)) (h4/list/EL n l2))
% Assm [h4s_lists_ELu_u_MAP]: !n l. h4/prim__rec/_3C n (h4/list/LENGTH l) ==> (!f. h4/list/EL n (h4/list/MAP f l) = happ f (h4/list/EL n l))
% Assm [h4s_bools_ANDu_u_CONG]: !Q_27 Q P_27 P. (Q ==> (P <=> P_27)) /\ (P_27 ==> (Q <=> Q_27)) ==> (P /\ Q <=> P_27 /\ Q_27)
% Assm [h4s_pairs_EXISTSu_u_PROD]: !P. (?p. happ P p) <=> (?p__1 p__2. happ P (h4/pair/_2C p__1 p__2))
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_lists_LISTu_u_RELu_u_def0]: !x x x. h4/list/LIST__REL x x x <=> (!LIST__REL_27. (!a00 a10. a00 = h4/list/NIL /\ a10 = h4/list/NIL \/ (?h1 h2 t1 t2. a00 = happ (happ h4/list/CONS h1) t1 /\ a10 = happ (happ h4/list/CONS h2) t2 /\ happ (happ x h1) h2 /\ happ (happ LIST__REL_27 t1) t2) ==> happ (happ LIST__REL_27 a00) a10) ==> happ (happ LIST__REL_27 x) x)
% Assm [h4s_markers_Congu_u_def]: !x. h4/marker/Cong x <=> x
% Assm [h4s_bools_BOUNDEDu_u_THM]: !v. h4/bool/BOUNDED v <=> T
% Assm [h4s_bools_UNWINDu_u_THM2]: !a P. (?x. x = a /\ happ P x) <=> happ P a
% Assm [h4s_options_optionu_u_CLAUSESu_c15]: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = happ f x
% Assm [h4s_bools_SWAPu_u_FORALLu_u_THM]: !P. (!x y. happ (happ P x) y) <=> (!y x. happ (happ P x) y)
% Assm [h4s_sums_sumu_u_INDUCT]: !P. (!x. happ P (h4/sum/INL x)) /\ (!y. happ P (h4/sum/INR y)) ==> (!s. happ P s)
% Assm [h4s_sums_sumu_u_CASES]: !ss. (?x. ss = h4/sum/INL x) \/ (?y. ss = h4/sum/INR y)
% Assm [h4s_relations_nfu_u_def]: !x R. h4/relation/nf R x <=> (!y. ~happ (happ R x) y)
% Assm [h4s_bools_TYPEu_u_DEFINITIONu_u_THM]: !rep P. h4/bool/TYPE__DEFINITION P rep <=> (!x_27 x_27_27. happ rep x_27 = happ rep x_27_27 ==> x_27 = x_27_27) /\ (!x. happ P x <=> (?x_27. x = happ rep x_27))
% Assm [h4s_richu_u_lists_LISTu_u_RELu_u_APPENDu_u_SING]: !x2 x1 l2 l1 R. h4/list/LIST__REL R (h4/list/APPEND l1 (happ (happ h4/list/CONS x1) h4/list/NIL)) (h4/list/APPEND l2 (happ (happ h4/list/CONS x2) h4/list/NIL)) <=> h4/list/LIST__REL R l1 l2 /\ happ (happ R x1) x2
% Assm [h4s_lists_MEMu_u_MAP]: !x l f. h4/bool/IN x (h4/list/LIST__TO__SET (h4/list/MAP f l)) <=> (?y. x = happ f y /\ h4/bool/IN y (h4/list/LIST__TO__SET l))
% Assm [h4s_lists_LISTu_u_RELu_u_defu_c0]: !R. h4/list/LIST__REL R h4/list/NIL h4/list/NIL <=> T
% Assm [h4s_lists_LENGTHu_u_APPEND]: !l2 l1. h4/list/LENGTH (h4/list/APPEND l1 l2) = h4/arithmetic/_2B (h4/list/LENGTH l1) (h4/list/LENGTH l2)
% Assm [h4s_lists_APPENDu_u_ASSOC]: !l3 l2 l1. h4/list/APPEND l1 (h4/list/APPEND l2 l3) = h4/list/APPEND (h4/list/APPEND l1 l2) l3
% Assm [h4s_numerals_numeralu_u_distribu_c13]: h4/num/SUC h4/num/0 = h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)
% Assm [h4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ]: !p n m. h4/arithmetic/_2B m p = h4/arithmetic/_2B n p <=> m = n
% Assm [h4s_richu_u_lists_EVERY2u_u_APPENDu_u_suff]: !l4 l3 l2 l1 R. h4/list/LIST__REL R l1 l2 /\ h4/list/LIST__REL R l3 l4 ==> h4/list/LIST__REL R (h4/list/APPEND l1 l3) (h4/list/APPEND l2 l4)
% Assm [h4s_richu_u_lists_EVERY2u_u_APPEND]: !l4 l3 l2 l1 R. h4/list/LIST__REL R l1 l2 /\ h4/list/LIST__REL R l3 l4 <=> h4/list/LIST__REL R (h4/list/APPEND l1 l3) (h4/list/APPEND l2 l4) /\ h4/list/LENGTH l1 = h4/list/LENGTH l2 /\ h4/list/LENGTH l3 = h4/list/LENGTH l4
% Assm [h4s_bools_IMPu_u_CLAUSESu_c0]: !t. T ==> t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c1]: !t h. h4/list/LIST__TO__SET (happ (happ h4/list/CONS h) t) = h4/pred__set/INSERT h (h4/list/LIST__TO__SET t)
% Assm [h4s_lists_LISTu_u_TOu_u_SET0u_c0]: h4/list/LIST__TO__SET h4/list/NIL = h4/pred__set/EMPTY
% Assm [h4s_predu_u_sets_INu_u_INSERT]: !y x s. h4/bool/IN x (h4/pred__set/INSERT y s) <=> x = y \/ h4/bool/IN x s
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x h4/pred__set/EMPTY
% Assm [h4s_bools_NOTu_u_EXISTSu_u_THM]: !P. ~(?x. happ P x) <=> (!x. ~happ P x)
% Assm [h4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM]: !Q P. (!x. happ P x) /\ Q <=> (!x. happ P x /\ Q)
% Assm [h4s_bools_EXISTSu_u_ORu_u_THM]: !Q P. (?x. happ P x \/ happ Q x) <=> (?x. happ P x) \/ (?x. happ Q x)
% Assm [h4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM]: !Q P. P \/ (?x. happ Q x) <=> (?x. P \/ happ Q x)
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. happ P x /\ Q) <=> (?x. happ P x) /\ Q
% Assm [h4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM]: !Q P. (?x. P /\ happ Q x) <=> P /\ (?x. happ Q x)
% Goal: !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))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q1427565,TV_Q1427561]: ![V_f, V_g]: (![V_x]: s(TV_Q1427561,happ(s(t_fun(TV_Q1427565,TV_Q1427561),V_f),s(TV_Q1427565,V_x))) = s(TV_Q1427561,happ(s(t_fun(TV_Q1427565,TV_Q1427561),V_g),s(TV_Q1427565,V_x))) => s(t_fun(TV_Q1427565,TV_Q1427561),V_f) = s(t_fun(TV_Q1427565,TV_Q1427561),V_g))).
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_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_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_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_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_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_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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_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_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_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_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_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_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_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_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_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_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_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_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_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_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_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_bools_EQu_u_CLAUSESu_c0, axiom, ![V_t]: (s(t_bool,t) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_sums_ISu_u_SUMu_u_REP0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: (p(s(t_bool,h4s_sums_isu_u_sumu_u_rep(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f)))) <=> ?[V_v1, V_v2]: (![V_x, V_x0, V_x1]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f),s(t_bool,V_x))),s(TV_u_27a,V_x0))),s(TV_u_27b,V_x1)))) <=> (s(TV_u_27a,V_x0) = s(TV_u_27a,V_v1) & p(s(t_bool,V_x)))) | ![V_x, V_x0, V_x1]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_f),s(t_bool,V_x))),s(TV_u_27a,V_x0))),s(TV_u_27b,V_x1)))) <=> (s(TV_u_27b,V_x1) = s(TV_u_27b,V_v2) & ~ (p(s(t_bool,V_x)))))))).
fof(ah4s_sums_INRu_u_nequ_u_INL, axiom, ![TV_u_27b,TV_u_27a]: ![V_v2, V_v1]: ~ (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_v2))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_v1))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_sums_condu_u_sumu_u_expandu_c1, axiom, ![TV_u_27c,TV_u_27d]: ![V_z, V_y, V_x, V_P]: (s(t_h4s_sums_sum(TV_u_27d,TV_u_27c),h4s_bools_cond(s(t_bool,V_P),s(t_h4s_sums_sum(TV_u_27d,TV_u_27c),h4s_sums_inr(s(TV_u_27c,V_x))),s(t_h4s_sums_sum(TV_u_27d,TV_u_27c),h4s_sums_inl(s(TV_u_27d,V_y))))) = s(t_h4s_sums_sum(TV_u_27d,TV_u_27c),h4s_sums_inl(s(TV_u_27d,V_z))) <=> (~ (p(s(t_bool,V_P))) & s(TV_u_27d,V_z) = s(TV_u_27d,V_y)))).
fof(ah4s_bools_EXISTSu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (?[V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_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_sums_INLu_u_DEF, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_2]: (![V_x, V_e, V_b, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27b,t_bool)))),V_uu_2),s(TV_u_27a,V_x))),s(TV_u_27a,V_e))),s(t_bool,V_b))),s(TV_u_27b,V_y)))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_e) & p(s(t_bool,V_b)))) => ![V_uu_1]: (![V_e, V_b, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_1),s(TV_u_27a,V_e))),s(t_bool,V_b))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27b,t_bool)))),V_uu_2),s(TV_u_27a,V_x))),s(TV_u_27a,V_e))),s(t_bool,V_b))) => ![V_uu_0]: (![V_e, V_b]: s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_0),s(TV_u_27a,V_e))),s(t_bool,V_b))) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_1),s(TV_u_27a,V_e))),s(t_bool,V_b))) => ![V_e]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_e))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_absu_u_sum(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27a,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_0),s(TV_u_27a,V_e))))))))).
fof(ah4s_sums_INRu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_2]: (![V_e, V_b, V_y]: (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_2),s(TV_u_27b,V_e))),s(t_bool,V_b))),s(TV_u_27b,V_y)))) <=> (s(TV_u_27b,V_y) = s(TV_u_27b,V_e) & ~ (p(s(t_bool,V_b))))) => ![V_uu_1]: (![V_e, V_b, V_x]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_1),s(TV_u_27b,V_e))),s(t_bool,V_b))),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(t_bool,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27b,t_bool))),V_uu_2),s(TV_u_27b,V_e))),s(t_bool,V_b))) => ![V_uu_0]: (![V_e, V_b]: s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_0),s(TV_u_27b,V_e))),s(t_bool,V_b))) = s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_1),s(TV_u_27b,V_e))),s(t_bool,V_b))) => ![V_e]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_e))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_absu_u_sum(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),happ(s(t_fun(TV_u_27b,t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)))),V_uu_0),s(TV_u_27b,V_e))))))))).
fof(ah4s_sums_sumu_u_ISOu_u_DEFu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_r]: (p(s(t_bool,h4s_sums_isu_u_sumu_u_rep(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_r)))) <=> s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),h4s_sums_repu_u_sum(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_absu_u_sum(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_r))))) = s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_r))).
fof(ah4s_sums_sumu_u_ISOu_u_DEFu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_a]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_absu_u_sum(s(t_fun(t_bool,t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),h4s_sums_repu_u_sum(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_a))))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_a)).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_lists_listu_u_Axiomu_u_old, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_x, V_f, V_fn1]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool)),happ(s(t_fun(TV_u_27b,t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool))),V_uu_0),s(TV_u_27b,V_x))),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),V_f))),s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn1)))) <=> (s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_x) & ![V_h, V_t]: s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn1),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_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),V_f),s(TV_u_27b,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),V_fn1),s(t_h4s_lists_list(TV_u_27a),V_t))))),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) => ![V_x, V_f]: p(s(t_bool,h4s_bools_u_3fu_21(s(t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool),happ(s(t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool)),happ(s(t_fun(TV_u_27b,t_fun(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),t_fun(t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b),t_bool))),V_uu_0),s(TV_u_27b,V_x))),s(t_fun(TV_u_27b,t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),TV_u_27b))),V_f)))))))).
fof(ah4s_bools_EQu_u_IMPu_u_THM, axiom, ![V_t2, V_t1]: (s(t_bool,V_t1) = s(t_bool,V_t2) <=> ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) & (p(s(t_bool,V_t2)) => p(s(t_bool,V_t1)))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_BOOLu_u_CASESu_u_AX, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_sums_sumu_u_distinct, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: ~ (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))))).
fof(ah4s_sums_INRu_u_INLu_u_11u_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_sums_INRu_u_INLu_u_11u_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: (s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_x))) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))) <=> s(TV_u_27b,V_x) = s(TV_u_27b,V_y))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_sums_condu_u_sumu_u_expandu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_x, V_P]: (s(t_h4s_sums_sum(TV_u_27b,TV_u_27a),h4s_bools_cond(s(t_bool,V_P),s(t_h4s_sums_sum(TV_u_27b,TV_u_27a),h4s_sums_inr(s(TV_u_27a,V_x))),s(t_h4s_sums_sum(TV_u_27b,TV_u_27a),h4s_sums_inl(s(TV_u_27b,V_y))))) = s(t_h4s_sums_sum(TV_u_27b,TV_u_27a),h4s_sums_inr(s(TV_u_27a,V_z))) <=> (p(s(t_bool,V_P)) & s(TV_u_27a,V_z) = s(TV_u_27a,V_x)))).
fof(ah4s_lists_CONS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons) = s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_u_20u_40indu_u_typelist1)).
fof(ah4s_lists_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_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_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_hiddenu_u_u_u_20u_u_40indu_u_u_u_typelist0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist0) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_u_20u_40indu_u_typelist2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_bools_EXISTSu_u_UNIQUEu_u_DEF, axiom, ![TV_u_27a]: ![V_x]: (p(s(t_bool,h4s_bools_u_3fu_21(s(t_fun(TV_u_27a,t_bool),V_x)))) <=> (p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_x)))) & ![V_x0, V_y]: ((p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x0)))) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_y))))) => s(TV_u_27a,V_x0) = s(TV_u_27a,V_y))))).
fof(ah4s_richu_u_lists_FOLDLu_u_REVERSE, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f, V_x, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) => ![V_l, V_f, V_e]: s(TV_u_27a,h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27b),V_l))))) = s(TV_u_27a,h4s_lists_foldr(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),V_l)))))).
fof(ah4s_lists_REVERSEu_u_REVERSE, axiom, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),V_l)).
fof(ah4s_richu_u_lists_FOLDLu_u_FOLDRu_u_REVERSE, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_f, V_x, V_y]: s(TV_u_27a,happ(s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))),s(TV_u_27a,V_y))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_x))) => ![V_uu_0]: (![V_f, V_x]: s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) = s(t_fun(TV_u_27a,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27b,V_x))) => ![V_l, V_f, V_e]: s(TV_u_27a,h4s_lists_foldl(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),V_l))) = s(TV_u_27a,h4s_lists_foldr(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27a))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27a)),V_f))),s(TV_u_27a,V_e),s(t_h4s_lists_list(TV_u_27b),h4s_lists_reverse(s(t_h4s_lists_list(TV_u_27b),V_l)))))))).
fof(ah4s_lists_FOLDLu_u_SNOC, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(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_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),V_l))))),s(TV_u_27a,V_x)))).
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_LISTu_u_RELu_u_MAP2, axiom, ![TV_u_27b,TV_u_27a,TV_u_27c]: ![V_uu_3]: (![V_R, V_a, V_f, V_b]: s(t_bool,happ(s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool)))),V_uu_3),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_a))),s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(TV_u_27c,V_b))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_a))),s(TV_u_27b,happ(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(TV_u_27c,V_b))))) => ![V_uu_2]: (![V_R, V_f, V_a]: s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)))),V_uu_2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27c,t_bool),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27c,t_bool)))),V_uu_3),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_a))),s(t_fun(TV_u_27c,TV_u_27b),V_f))) => ![V_uu_1]: (![V_R, V_a, V_b]: s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) => ![V_uu_0]: (![V_R, V_a]: s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_a))) = s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_1),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(TV_u_27a,V_a))) => ![V_l2, V_l1, V_f, V_R]: s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool))),V_uu_0),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27c,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27c),V_l2))))) = s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)),happ(s(t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool))),happ(s(t_fun(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),t_fun(t_fun(TV_u_27c,TV_u_27b),t_fun(TV_u_27a,t_fun(TV_u_27c,t_bool)))),V_uu_2),s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R))),s(t_fun(TV_u_27c,TV_u_27b),V_f))),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27c),V_l2)))))))).
fof(ah4s_options_optionu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_lists_SNOC0u_c1, axiom, ![TV_u_27a]: ![V_xu_27, V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_xu_27))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_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_FOLDL0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e))),s(TV_u_27a,V_x))),s(t_h4s_lists_list(TV_u_27a),V_l)))).
fof(ah4s_lists_FOLDL0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_e]: s(TV_u_27b,h4s_lists_foldl(s(t_fun(TV_u_27b,t_fun(TV_u_27a,TV_u_27b)),V_f),s(TV_u_27b,V_e),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(TV_u_27b,V_e)).
fof(ah4s_lists_LISTu_u_RELu_u_defu_c3, axiom, ![TV_u_27a,TV_u_27b]: ![V_bs, V_b, V_as, V_a, V_R]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_a))),s(t_h4s_lists_list(TV_u_27a),V_as))),s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_b))),s(t_h4s_lists_list(TV_u_27b),V_bs)))))) <=> (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_a))),s(TV_u_27b,V_b)))) & p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_as),s(t_h4s_lists_list(TV_u_27b),V_bs))))))).
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_TYPEu_u_DEFINITION0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0]: (p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_x),s(t_fun(TV_u_27b,TV_u_27a),V_x0)))) <=> (![V_xu_27, V_xu_27u_27]: (s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27u_27))) => s(TV_u_27b,V_xu_27) = s(TV_u_27b,V_xu_27u_27)) & ![V_x1]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_x),s(TV_u_27a,V_x1)))) <=> ?[V_xu_27]: s(TV_u_27a,V_x1) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_x0),s(TV_u_27b,V_xu_27))))))).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_LISTu_u_RELu_u_ELu_u_EQN, axiom, ![TV_u_27a,TV_u_27b]: ![V_l2, V_l1, V_R]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))) <=> (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) & ![V_n]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1)))))) => p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l1))))),s(TV_u_27b,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27b),V_l2)))))))))).
fof(ah4s_lists_ELu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_n, V_l]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l)))))) => ![V_f]: s(TV_u_27b,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,h4s_lists_el(s(t_h4s_nums_num,V_n),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ah4s_bools_ANDu_u_CONG, axiom, ![V_Qu_27, V_Q, V_Pu_27, V_P]: (((p(s(t_bool,V_Q)) => s(t_bool,V_P) = s(t_bool,V_Pu_27)) & (p(s(t_bool,V_Pu_27)) => s(t_bool,V_Q) = s(t_bool,V_Qu_27))) => ((p(s(t_bool,V_P)) & p(s(t_bool,V_Q))) <=> (p(s(t_bool,V_Pu_27)) & p(s(t_bool,V_Qu_27)))))).
fof(ah4s_pairs_EXISTSu_u_PROD, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: (?[V_p]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_p)))) <=> ?[V_pu_u_1, V_pu_u_2]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_pu_u_1),s(TV_u_27b,V_pu_u_2)))))))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_lists_LISTu_u_RELu_u_def0, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_x0, V_x1]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(t_h4s_lists_list(TV_u_27a),V_x0),s(t_h4s_lists_list(TV_u_27b),V_x1)))) <=> ![V_LISTu_u_RELu_27]: (![V_a00, V_a10]: (((s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil) & s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)) | ?[V_h1, V_h2, V_t1, V_t2]: (s(t_h4s_lists_list(TV_u_27a),V_a00) = s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a))),h4s_lists_cons),s(TV_u_27a,V_h1))),s(t_h4s_lists_list(TV_u_27a),V_t1))) & (s(t_h4s_lists_list(TV_u_27b),V_a10) = s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h2))),s(t_h4s_lists_list(TV_u_27b),V_t2))) & (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_x),s(TV_u_27a,V_h1))),s(TV_u_27b,V_h2)))) & p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_t1))),s(t_h4s_lists_list(TV_u_27b),V_t2)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_a00))),s(t_h4s_lists_list(TV_u_27b),V_a10))))) => p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_bool),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_fun(t_h4s_lists_list(TV_u_27b),t_bool)),V_LISTu_u_RELu_27),s(t_h4s_lists_list(TV_u_27a),V_x0))),s(t_h4s_lists_list(TV_u_27b),V_x1))))))).
fof(ah4s_markers_Congu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_cong(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_bools_BOUNDEDu_u_THM, axiom, ![V_v]: s(t_bool,h4s_bools_bounded(s(t_bool,V_v))) = s(t_bool,t)).
fof(ah4s_bools_UNWINDu_u_THM2, axiom, ![TV_u_27a]: ![V_a, V_P]: (?[V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_a) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_a)))))).
fof(ah4s_options_optionu_u_CLAUSESu_c15, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_bools_SWAPu_u_FORALLu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: (![V_x, V_y]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))) <=> ![V_y, V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_P),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))))).
fof(ah4s_sums_sumu_u_INDUCT, axiom, ![TV_u_27a,TV_u_27b]: ![V_P]: ((![V_x]: p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x)))))) & ![V_y]: p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))))))) => ![V_s]: p(s(t_bool,happ(s(t_fun(t_h4s_sums_sum(TV_u_27a,TV_u_27b),t_bool),V_P),s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_s)))))).
fof(ah4s_sums_sumu_u_CASES, axiom, ![TV_u_27a,TV_u_27b]: ![V_ss]: (?[V_x]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_ss) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))) | ?[V_y]: s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),V_ss) = s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))))).
fof(ah4s_relations_nfu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_x, V_R]: (p(s(t_bool,h4s_relations_nf(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_x)))) <=> ![V_y]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_x))),s(TV_u_27b,V_y))))))).
fof(ah4s_bools_TYPEu_u_DEFINITIONu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_P]: (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_xu_27, V_xu_27u_27]: (s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27u_27))) => s(TV_u_27b,V_xu_27) = s(TV_u_27b,V_xu_27u_27)) & ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) <=> ?[V_xu_27]: s(TV_u_27a,V_x) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27))))))).
fof(ah4s_richu_u_lists_LISTu_u_RELu_u_APPENDu_u_SING, axiom, ![TV_u_27a,TV_u_27b]: ![V_x2, V_x1, V_l2, V_l1, V_R]: (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),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_x1))),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_append(s(t_h4s_lists_list(TV_u_27b),V_l2),s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_x2))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)))))))) <=> (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))) & p(s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27a,V_x1))),s(TV_u_27b,V_x2))))))).
fof(ah4s_lists_MEMu_u_MAP, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_l, V_f]: (p(s(t_bool,h4s_bools_in(s(TV_u_27b,V_x),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_l)))))))) <=> ?[V_y]: (s(TV_u_27b,V_x) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) & p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))))))))).
fof(ah4s_lists_LISTu_u_RELu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_R]: s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))) = s(t_bool,t)).
fof(ah4s_lists_LENGTHu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1]: s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))),s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l2)))))).
fof(ah4s_lists_APPENDu_u_ASSOC, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l2),s(t_h4s_lists_list(TV_u_27a),V_l3))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),V_l3)))).
fof(ah4s_numerals_numeralu_u_distribu_c13, axiom, s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero)))))).
fof(ah4s_arithmetics_EQu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: (s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))) <=> s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n))).
fof(ah4s_richu_u_lists_EVERY2u_u_APPENDu_u_suff, axiom, ![TV_u_27a,TV_u_27b]: ![V_l4, V_l3, V_l2, V_l1, V_R]: ((p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))) & p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l3),s(t_h4s_lists_list(TV_u_27b),V_l4))))) => p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l3))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_append(s(t_h4s_lists_list(TV_u_27b),V_l2),s(t_h4s_lists_list(TV_u_27b),V_l4)))))))).
fof(ah4s_richu_u_lists_EVERY2u_u_APPEND, axiom, ![TV_u_27a,TV_u_27b]: ![V_l4, V_l3, V_l2, V_l1, V_R]: ((p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27b),V_l2)))) & p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),V_l3),s(t_h4s_lists_list(TV_u_27b),V_l4))))) <=> (p(s(t_bool,h4s_lists_listu_u_rel(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_bool)),V_R),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l3))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_append(s(t_h4s_lists_list(TV_u_27b),V_l2),s(t_h4s_lists_list(TV_u_27b),V_l4)))))) & (s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l1))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l2))) & s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27a),V_l3))) = s(t_h4s_nums_num,h4s_lists_length(s(t_h4s_lists_list(TV_u_27b),V_l4))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c1, axiom, ![TV_u_27b]: ![V_t, V_h]: s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b))),h4s_lists_cons),s(TV_u_27b,V_h))),s(t_h4s_lists_list(TV_u_27b),V_t))))) = s(t_fun(TV_u_27b,t_bool),h4s_predu_u_sets_insert(s(TV_u_27b,V_h),s(t_fun(TV_u_27b,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27b),V_t)))))).
fof(ah4s_lists_LISTu_u_TOu_u_SET0u_c0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)).
fof(ah4s_predu_u_sets_INu_u_INSERT, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s)))))) <=> (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) | p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))).
fof(ah4s_predu_u_sets_NOTu_u_INu_u_EMPTY, axiom, ![TV_u_27a]: ![V_x]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)))))).
fof(ah4s_bools_NOTu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ![V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_LEFTu_u_ANDu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_bools_EXISTSu_u_ORu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_RIGHTu_u_ORu_u_EXISTSu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: ((p(s(t_bool,V_P)) | ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> ?[V_x]: (p(s(t_bool,V_P)) | p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_bools_LEFTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & p(s(t_bool,V_Q))))).
fof(ah4s_bools_RIGHTu_u_EXISTSu_u_ANDu_u_THM, axiom, ![TV_u_27a]: ![V_Q, V_P]: (?[V_x]: (p(s(t_bool,V_P)) & p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) <=> (p(s(t_bool,V_P)) & ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ch4s_enumerals_btu_u_Axiom, conjecture, ![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))))))).
