%   ORIGINAL: h4/enumeral/bt__11
% 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__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/bool/TRUTH: T
% Assm: h4/enumeral/node0: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% 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/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_c0: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% 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/nt0: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% 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/enumeral/bt__size__def_c1: !f a2 a1 a0. h4/enumeral/bt__size f (h4/enumeral/node a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (f a1) (h4/enumeral/bt__size f a2)))
% Assm: h4/enumeral/bt__induction: !P. P h4/enumeral/nt /\ (!b b0. P b /\ P b0 ==> (!a. P (h4/enumeral/node b a b0))) ==> (!b. P b)
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/ind__type/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_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/bool/ABS__REP__THM: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. abs (rep a) = a) /\ (!r. P r <=> rep (abs r) = r))
% Assm: h4/enumeral/bl__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 a2 /\ _27bl_27 a2) ==> _27bl_27 a0_270) ==> _27bl_27 a0_27) rep
% Assm: h4/enumeral/datatype__bt: !bt. h4/bool/DATATYPE (bt h4/enumeral/nt h4/enumeral/node)
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/enumeral/bt__case__def0_c1: !v f a2 a1 a0. h4/enumeral/bt__CASE (h4/enumeral/node a0 a1 a2) v f = f a0 a1 a2
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/enumeral/bl__repfns_c1: !r. (\a0_27. !_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) a /\ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 a2 /\ _27bl_27 a2) ==> _27bl_27 a0_270) ==> _27bl_27 a0_27) r <=> h4/enumeral/_20_40ind__typeenumeral8 (h4/enumeral/_20_40ind__typeenumeral7 r) = r
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral6____def: h4/enumeral/_20_40ind__typeenumeral6 = (\a0 a1 a2. h4/enumeral/_20_40ind__typeenumeral7 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 a10) (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM))) a0 a1 (h4/enumeral/_20_40ind__typeenumeral8 a2)))
% Assm: h4/enumeral/bt__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 /\ _27bt_27 a0 /\ _27bt_27 a2) ==> _27bt_27 a0_270) ==> _27bt_27 a0_27) rep
% Assm: h4/enumeral/bt__Axiom: !f1 f0. ?fn. fn h4/enumeral/nt = f0 /\ (!a0 a1 a2. fn (h4/enumeral/node a0 a1 a2) = f1 a1 a0 a2 (fn a0) (fn a2))
% Assm: h4/enumeral/bl__repfns_c0: !a. h4/enumeral/_20_40ind__typeenumeral7 (h4/enumeral/_20_40ind__typeenumeral8 a) = a
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral4____def: h4/enumeral/_20_40ind__typeenumeral4 = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (\n. h4/ind__type/BOTTOM))
% Assm: h4/enumeral/hidden____20__40ind____typeenumeral5____def: h4/enumeral/_20_40ind__typeenumeral5 = (\a. h4/enumeral/_20_40ind__typeenumeral7 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/enumeral/_20_40ind__typeenumeral8 a)))
% Assm: h4/enumeral/onebl0: h4/enumeral/onebl = h4/enumeral/_20_40ind__typeenumeral6
% Assm: h4/enumeral/bt__case__def0_c0: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm: h4/enumeral/zerbl0: h4/enumeral/zerbl = h4/enumeral/_20_40ind__typeenumeral5
% Assm: h4/enumeral/nbl0: h4/enumeral/nbl = h4/enumeral/_20_40ind__typeenumeral4
% Assm: h4/enumeral/bl__11_c1: !a2_27 a2 a1_27 a1 a0_27 a0. h4/enumeral/onebl a0 a1 a2 = h4/enumeral/onebl a0_27 a1_27 a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm: h4/enumeral/bl__nchotomy: !bb. bb = h4/enumeral/nbl \/ (?b. bb = h4/enumeral/zerbl b) \/ (?a b0 b. bb = h4/enumeral/onebl a b0 b)
% Assm: h4/enumeral/bl__case__cong: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nbl ==> v = v_27) /\ (!a. M_27 = h4/enumeral/zerbl a ==> f a = f_27 a) /\ (!a0 a1 a2. M_27 = h4/enumeral/onebl a0 a1 a2 ==> f1 a0 a1 a2 = f1_27 a0 a1 a2) ==> h4/enumeral/bl__CASE M v f f1 = h4/enumeral/bl__CASE M_27 v_27 f_27 f1_27
% Assm: h4/enumeral/bl__distinct_c2: !a2 a1 a0 a. ~(h4/enumeral/zerbl a = h4/enumeral/onebl a0 a1 a2)
% Assm: h4/enumeral/bl__size__def_c2: !f a2 a1 a0. h4/enumeral/bl__size f (h4/enumeral/onebl a0 a1 a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (f a0) (h4/arithmetic/_2B (h4/enumeral/bt__size f a1) (h4/enumeral/bl__size f a2)))
% Assm: h4/enumeral/bl__distinct_c1: !a2 a1 a0. ~(h4/enumeral/nbl = h4/enumeral/onebl a0 a1 a2)
% Assm: h4/enumeral/bl__induction: !P. P h4/enumeral/nbl /\ (!b. P b ==> P (h4/enumeral/zerbl b)) /\ (!b. P b ==> (!b0 a. P (h4/enumeral/onebl a b0 b))) ==> (!b. P b)
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/enumeral/bl__case__def_c2: !v f1 f a2 a1 a0. h4/enumeral/bl__CASE (h4/enumeral/onebl a0 a1 a2) v f f1 = f1 a0 a1 a2
% Assm: h4/enumeral/bl__case__def_c1: !v f1 f a. h4/enumeral/bl__CASE (h4/enumeral/zerbl a) v f f1 = f a
% Assm: h4/enumeral/bl__case__def_c0: !v f1 f. h4/enumeral/bl__CASE h4/enumeral/nbl v f f1 = v
% Assm: h4/enumeral/bl__Axiom: !f2 f1 f0. ?fn. fn h4/enumeral/nbl = f0 /\ (!a. fn (h4/enumeral/zerbl a) = f1 a (fn a)) /\ (!a0 a1 a2. fn (h4/enumeral/onebl a0 a1 a2) = f2 a0 a1 a2 (fn a2))
% Assm: h4/enumeral/bt__size__def_c0: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/0
% Assm: h4/enumeral/datatype__bl: !bl. h4/bool/DATATYPE (bl h4/enumeral/nbl h4/enumeral/zerbl h4/enumeral/onebl)
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/combin/UPDATE__def: !b a. h4/combin/UPDATE a b = (\f c. h4/bool/COND (a = c) b (f c))
% Assm: h4/bool/EXISTS__UNIQUE__DEF: h4/bool/_3F_21 = (\P. $exists P /\ (!x y. P x /\ P y ==> x = y))
% Assm: h4/bool/EXISTS__UNIQUE__THM: !P. h4/bool/_3F_21 (\x. P x) <=> (?x. P x) /\ (!x y. P x /\ P y ==> x = y)
% Assm: h4/pred__set/COMMUTING__ITSET__INSERT: !s f. (!x y z. f x (f y z) = f y (f x z)) /\ h4/pred__set/FINITE s ==> (!x b. h4/pred__set/ITSET f (h4/pred__set/INSERT x s) b = h4/pred__set/ITSET f (h4/pred__set/DELETE s x) (f x b))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/pred__set/CARD__INSERT: !s. h4/pred__set/FINITE s ==> (!x. h4/pred__set/CARD (h4/pred__set/INSERT x s) = h4/bool/COND (h4/bool/IN x s) (h4/pred__set/CARD s) (h4/num/SUC (h4/pred__set/CARD s)))
% Assm: h4/pred__set/CHOICE__INSERT__REST: !s. ~(s = h4/pred__set/EMPTY) ==> h4/pred__set/INSERT (h4/pred__set/CHOICE s) (h4/pred__set/REST s) = s
% Assm: h4/pred__set/FINITE__INSERT: !x s. h4/pred__set/FINITE (h4/pred__set/INSERT x s) <=> h4/pred__set/FINITE s
% Assm: h4/pred__set/CHOICE__NOT__IN__REST: !s. ~h4/bool/IN (h4/pred__set/CHOICE s) (h4/pred__set/REST s)
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/pred__set/ITSET__INSERT: !s. h4/pred__set/FINITE s ==> (!f x b. h4/pred__set/ITSET f (h4/pred__set/INSERT x s) b = h4/pred__set/ITSET f (h4/pred__set/REST (h4/pred__set/INSERT x s)) (f (h4/pred__set/CHOICE (h4/pred__set/INSERT x s)) b))
% Assm: h4/bool/CONJ__ASSOC: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm: h4/pred__set/IN__DELETE: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm: h4/pred__set/DELETE__NON__ELEMENT: !x s. ~h4/bool/IN x s <=> h4/pred__set/DELETE s x = s
% Assm: h4/pred__set/DELETE__INSERT: !y x s. h4/pred__set/DELETE (h4/pred__set/INSERT x s) y = h4/bool/COND (x = y) (h4/pred__set/DELETE s y) (h4/pred__set/INSERT x (h4/pred__set/DELETE s y))
% Assm: h4/pred__set/INSERT__COMM: !y x s. h4/pred__set/INSERT x (h4/pred__set/INSERT y s) = h4/pred__set/INSERT y (h4/pred__set/INSERT x s)
% Assm: h4/pred__set/NOT__EMPTY__INSERT: !x s. ~(h4/pred__set/EMPTY = h4/pred__set/INSERT x s)
% Assm: h4/bool/NOT__FORALL__THM: !P. ~(!x. P x) <=> (?x. ~P x)
% Assm: h4/pred__set/NOT__IN__EMPTY: !x. ~h4/bool/IN x 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/EXTENSION: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/pred__set/INSERT__DELETE: !x s. h4/bool/IN x s ==> h4/pred__set/INSERT x (h4/pred__set/DELETE s x) = s
% Assm: h4/pred__set/ABSORPTION: !x s. h4/bool/IN x s <=> h4/pred__set/INSERT x s = s
% Assm: h4/numeral/numeral__lte_c2: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm: h4/numeral/numeral__distrib_c27: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__CLAUSES_c2: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm: h4/arithmetic/COMPLETE__INDUCTION: !P. (!n. (!m. h4/prim__rec/_3C m n ==> P m) ==> P n) ==> (!n. P n)
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/bool/F__IMP: !t. ~t ==> t ==> F
% Assm: h4/arithmetic/TWO: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm: h4/arithmetic/EQ__LESS__EQ: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/marker/Abbrev__def: !x. h4/marker/Abbrev x <=> x
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/bool/RIGHT__FORALL__IMP__THM: !Q P. (!x. P ==> Q x) <=> P ==> (!x. Q x)
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/dc__disj: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm: h4/arithmetic/ADD__MONO__LESS__EQ: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/dc__neg: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm: h4/sat/dc__conj: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/bool/DISJ__ASSOC: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm: h4/bool/DISJ__SYM: !B A. A \/ B <=> B \/ A
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/DISJ__COMM: !B A. A \/ B <=> B \/ A
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/DE__MORGAN__THM_c1: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Goal: !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
%   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_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_bools_TRUTH]: T
% Assm [h4s_enumerals_node0]: h4/enumeral/node = h4/enumeral/_20_40ind__typeenumeral1
% 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_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_c0]: !a. h4/enumeral/_20_40ind__typeenumeral2 (h4/enumeral/_20_40ind__typeenumeral3 a) = a
% 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_nt0]: h4/enumeral/nt = h4/enumeral/_20_40ind__typeenumeral0
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% 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_enumerals_btu_u_sizeu_u_defu_c1]: !f a2 a1 a0. h4/enumeral/bt__size f (happ (happ (happ h4/enumeral/node a0) a1) a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (h4/enumeral/bt__size f a0) (h4/arithmetic/_2B (happ f a1) (h4/enumeral/bt__size f a2)))
% Assm [h4s_enumerals_btu_u_induction]: !P. happ P h4/enumeral/nt /\ (!b b0. happ P b /\ happ P b0 ==> (!a. happ P (happ (happ (happ h4/enumeral/node b) a) b0))) ==> (!b. happ P b)
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_indu_u_types_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_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_bools_ABSu_u_REPu_u_THM]: !P. (?rep. h4/bool/TYPE__DEFINITION P rep) ==> (?rep abs. (!a. happ abs (happ rep a) = a) /\ (!r. happ P r <=> happ rep (happ abs r) = r))
% Assm [h4s_enumerals_blu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _1 \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _1) /\ happ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a0 a1) (h4/ind__type/FCONS a2 _1) /\ happ _27bl_27 a2) ==> happ _27bl_27 a0_270) ==> happ _27bl_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_enumerals_datatypeu_u_bt]: !bt. h4/bool/DATATYPE (happ (happ bt h4/enumeral/nt) h4/enumeral/node)
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_enumerals_btu_u_caseu_u_def0u_c1]: !v f a2 a1 a0. h4/enumeral/bt__CASE (happ (happ (happ h4/enumeral/node a0) a1) a2) v f = happ (happ (happ f a0) a1) a2
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_enumerals_blu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27bl_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0 \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS a _0) /\ happ _27bl_27 a) \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a0 a1) (h4/ind__type/FCONS a2 _0) /\ happ _27bl_27 a2) ==> happ _27bl_27 a0_270) ==> happ _27bl_27 r) <=> h4/enumeral/_20_40ind__typeenumeral8 (h4/enumeral/_20_40ind__typeenumeral7 r) = r)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral6u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x. happ (happ (happ h4/enumeral/_20_40ind__typeenumeral6 x) x) x = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C x x) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral8 x) _0)))
% Assm [h4s_enumerals_btu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27bt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _1 \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a1 (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a2 _1)) /\ happ _27bt_27 a0 /\ happ _27bt_27 a2) ==> happ _27bt_27 a0_270) ==> happ _27bt_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_enumerals_btu_u_Axiom]: !f1 f0. ?fn. happ fn h4/enumeral/nt = f0 /\ (!a0 a1 a2. happ fn (happ (happ (happ h4/enumeral/node a0) a1) a2) = happ (happ (happ (happ (happ f1 a1) a0) a2) (happ fn a0)) (happ fn a2))
% Assm [h4s_enumerals_blu_u_repfnsu_c0]: !a. h4/enumeral/_20_40ind__typeenumeral7 (h4/enumeral/_20_40ind__typeenumeral8 a) = a
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral4u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/enumeral/_20_40ind__typeenumeral4 = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB h4/bool/ARB) _0)
% Assm [h4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral5u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/enumeral/_20_40ind__typeenumeral5 x = h4/enumeral/_20_40ind__typeenumeral7 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C h4/bool/ARB h4/bool/ARB) (h4/ind__type/FCONS (h4/enumeral/_20_40ind__typeenumeral8 x) _0)))
% Assm [h4s_enumerals_onebl0]: h4/enumeral/onebl = h4/enumeral/_20_40ind__typeenumeral6
% Assm [h4s_enumerals_btu_u_caseu_u_def0u_c0]: !v f. h4/enumeral/bt__CASE h4/enumeral/nt v f = v
% Assm [h4s_enumerals_zerbl0]: h4/enumeral/zerbl = h4/enumeral/_20_40ind__typeenumeral5
% Assm [h4s_enumerals_nbl0]: h4/enumeral/nbl = h4/enumeral/_20_40ind__typeenumeral4
% Assm [h4s_enumerals_blu_u_11u_c1]: !a2_27 a2 a1_27 a1 a0_27 a0. happ (happ (happ h4/enumeral/onebl a0) a1) a2 = happ (happ (happ h4/enumeral/onebl a0_27) a1_27) a2_27 <=> a0 = a0_27 /\ a1 = a1_27 /\ a2 = a2_27
% Assm [h4s_enumerals_blu_u_nchotomy]: !bb. bb = h4/enumeral/nbl \/ (?b. bb = happ h4/enumeral/zerbl b) \/ (?a b0 b. bb = happ (happ (happ h4/enumeral/onebl a) b0) b)
% Assm [h4s_enumerals_blu_u_caseu_u_cong]: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/enumeral/nbl ==> v = v_27) /\ (!a. M_27 = happ h4/enumeral/zerbl a ==> happ f a = happ f_27 a) /\ (!a0 a1 a2. M_27 = happ (happ (happ h4/enumeral/onebl a0) a1) a2 ==> happ (happ (happ f1 a0) a1) a2 = happ (happ (happ f1_27 a0) a1) a2) ==> h4/enumeral/bl__CASE M v f f1 = h4/enumeral/bl__CASE M_27 v_27 f_27 f1_27
% Assm [h4s_enumerals_blu_u_distinctu_c2]: !a2 a1 a0 a. ~(happ h4/enumeral/zerbl a = happ (happ (happ h4/enumeral/onebl a0) a1) a2)
% Assm [h4s_enumerals_blu_u_sizeu_u_defu_c2]: !f a2 a1 a0. h4/enumeral/bl__size f (happ (happ (happ h4/enumeral/onebl a0) a1) a2) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B (happ f a0) (h4/arithmetic/_2B (h4/enumeral/bt__size f a1) (h4/enumeral/bl__size f a2)))
% Assm [h4s_enumerals_blu_u_distinctu_c1]: !a2 a1 a0. ~(h4/enumeral/nbl = happ (happ (happ h4/enumeral/onebl a0) a1) a2)
% Assm [h4s_enumerals_blu_u_induction]: !P. happ P h4/enumeral/nbl /\ (!b. happ P b ==> happ P (happ h4/enumeral/zerbl b)) /\ (!b. happ P b ==> (!b0 a. happ P (happ (happ (happ h4/enumeral/onebl a) b0) b))) ==> (!b. happ P b)
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c2]: !v f1 f a2 a1 a0. h4/enumeral/bl__CASE (happ (happ (happ h4/enumeral/onebl a0) a1) a2) v f f1 = happ (happ (happ f1 a0) a1) a2
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c1]: !v f1 f a. h4/enumeral/bl__CASE (happ h4/enumeral/zerbl a) v f f1 = happ f a
% Assm [h4s_enumerals_blu_u_caseu_u_defu_c0]: !v f1 f. h4/enumeral/bl__CASE h4/enumeral/nbl v f f1 = v
% Assm [h4s_enumerals_blu_u_Axiom]: !f2 f1 f0. ?fn. happ fn h4/enumeral/nbl = f0 /\ (!a. happ fn (happ h4/enumeral/zerbl a) = happ (happ f1 a) (happ fn a)) /\ (!a0 a1 a2. happ fn (happ (happ (happ h4/enumeral/onebl a0) a1) a2) = happ (happ (happ (happ f2 a0) a1) a2) (happ fn a2))
% Assm [h4s_enumerals_btu_u_sizeu_u_defu_c0]: !f. h4/enumeral/bt__size f h4/enumeral/nt = h4/num/0
% Assm [h4s_enumerals_datatypeu_u_bl]: !bl. h4/bool/DATATYPE (happ (happ (happ bl h4/enumeral/nbl) h4/enumeral/zerbl) h4/enumeral/onebl)
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_combins_UPDATEu_u_def]: !b a x x. ?v. (v <=> a = x) /\ h4/combin/UPDATE a b x x = h4/bool/COND v b (happ x x)
% 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_bools_EXISTSu_u_UNIQUEu_u_THM]: !_0. (!P x. happ (happ _0 P) x <=> happ P x) ==> (!P. h4/bool/_3F_21 (happ _0 P) <=> (?x. happ P x) /\ (!x y. happ P x /\ happ P y ==> x = y))
% Assm [h4s_predu_u_sets_COMMUTINGu_u_ITSETu_u_INSERT]: !s f. (!x y z. happ (happ f x) (happ (happ f y) z) = happ (happ f y) (happ (happ f x) z)) /\ h4/pred__set/FINITE s ==> (!x b. h4/pred__set/ITSET f (h4/pred__set/INSERT x s) b = h4/pred__set/ITSET f (h4/pred__set/DELETE s x) (happ (happ f x) b))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_predu_u_sets_CARDu_u_INSERT]: !s. h4/pred__set/FINITE s ==> (!x. h4/pred__set/CARD (h4/pred__set/INSERT x s) = h4/bool/COND (h4/bool/IN x s) (h4/pred__set/CARD s) (h4/num/SUC (h4/pred__set/CARD s)))
% Assm [h4s_predu_u_sets_CHOICEu_u_INSERTu_u_REST]: !s. ~(s = h4/pred__set/EMPTY) ==> h4/pred__set/INSERT (h4/pred__set/CHOICE s) (h4/pred__set/REST s) = s
% Assm [h4s_predu_u_sets_FINITEu_u_INSERT]: !x s. h4/pred__set/FINITE (h4/pred__set/INSERT x s) <=> h4/pred__set/FINITE s
% Assm [h4s_predu_u_sets_CHOICEu_u_NOTu_u_INu_u_REST]: !s. ~h4/bool/IN (h4/pred__set/CHOICE s) (h4/pred__set/REST s)
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_predu_u_sets_ITSETu_u_INSERT]: !s. h4/pred__set/FINITE s ==> (!f x b. h4/pred__set/ITSET f (h4/pred__set/INSERT x s) b = h4/pred__set/ITSET f (h4/pred__set/REST (h4/pred__set/INSERT x s)) (happ (happ f (h4/pred__set/CHOICE (h4/pred__set/INSERT x s))) b))
% Assm [h4s_bools_CONJu_u_ASSOC]: !t3 t2 t1. t1 /\ t2 /\ t3 <=> (t1 /\ t2) /\ t3
% Assm [h4s_predu_u_sets_INu_u_DELETE]: !y x s. h4/bool/IN x (h4/pred__set/DELETE s y) <=> h4/bool/IN x s /\ ~(x = y)
% Assm [h4s_predu_u_sets_DELETEu_u_NONu_u_ELEMENT]: !x s. ~h4/bool/IN x s <=> h4/pred__set/DELETE s x = s
% Assm [h4s_predu_u_sets_DELETEu_u_INSERT]: !y x s. ?v. (v <=> x = y) /\ h4/pred__set/DELETE (h4/pred__set/INSERT x s) y = h4/bool/COND v (h4/pred__set/DELETE s y) (h4/pred__set/INSERT x (h4/pred__set/DELETE s y))
% Assm [h4s_predu_u_sets_INSERTu_u_COMM]: !y x s. h4/pred__set/INSERT x (h4/pred__set/INSERT y s) = h4/pred__set/INSERT y (h4/pred__set/INSERT x s)
% Assm [h4s_predu_u_sets_NOTu_u_EMPTYu_u_INSERT]: !x s. ~(h4/pred__set/EMPTY = h4/pred__set/INSERT x s)
% Assm [h4s_bools_NOTu_u_FORALLu_u_THM]: !P. ~(!x. happ P x) <=> (?x. ~happ P x)
% Assm [h4s_predu_u_sets_NOTu_u_INu_u_EMPTY]: !x. ~h4/bool/IN x 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_EXTENSION]: !t s. s = t <=> (!x. h4/bool/IN x s <=> h4/bool/IN x t)
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_predu_u_sets_INSERTu_u_DELETE]: !x s. h4/bool/IN x s ==> h4/pred__set/INSERT x (h4/pred__set/DELETE s x) = s
% Assm [h4s_predu_u_sets_ABSORPTION]: !x s. h4/bool/IN x s <=> h4/pred__set/INSERT x s = s
% Assm [h4s_numerals_numeralu_u_lteu_c2]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT2 n) h4/arithmetic/ZERO <=> F
% Assm [h4s_numerals_numeralu_u_distribu_c27]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/NUMERAL n) h4/num/0 <=> h4/arithmetic/_3C_3D n h4/arithmetic/ZERO
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c2]: !n m. h4/arithmetic/_2B (h4/num/SUC m) n = h4/num/SUC (h4/arithmetic/_2B m n)
% Assm [h4s_arithmetics_COMPLETEu_u_INDUCTION]: !P. (!n. (!m. h4/prim__rec/_3C m n ==> happ P m) ==> happ P n) ==> (!n. happ P n)
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_bools_Fu_u_IMP]: !t. ~t ==> t ==> F
% Assm [h4s_arithmetics_TWO]: h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO) = h4/num/SUC (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO))
% Assm [h4s_arithmetics_EQu_u_LESSu_u_EQ]: !n m. m = n <=> h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_markers_Abbrevu_u_def]: !x. h4/marker/Abbrev x <=> x
% Assm [h4s_sats_pthu_u_no1]: !q p. ~(p \/ q) ==> ~p
% Assm [h4s_sats_pthu_u_ni2]: !q p. ~(p ==> q) ==> ~q
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_sats_pthu_u_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_bools_RIGHTu_u_FORALLu_u_IMPu_u_THM]: !Q P. (!x. P ==> happ Q x) <=> P ==> (!x. happ Q x)
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_dcu_u_disj]: !r q p. (p <=> q \/ r) <=> (p \/ ~q) /\ (p \/ ~r) /\ (q \/ r \/ ~p)
% Assm [h4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ]: !p n m. h4/arithmetic/_3C_3D (h4/arithmetic/_2B m n) (h4/arithmetic/_2B m p) <=> h4/arithmetic/_3C_3D n p
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_dcu_u_neg]: !q p. (p <=> ~q) <=> (p \/ q) /\ (~q \/ ~p)
% Assm [h4s_sats_dcu_u_conj]: !r q p. (p <=> q /\ r) <=> (p \/ ~q \/ ~r) /\ (q \/ ~p) /\ (r \/ ~p)
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_bools_DISJu_u_ASSOC]: !C B A. A \/ B \/ C <=> (A \/ B) \/ C
% Assm [h4s_bools_DISJu_u_SYM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_DISJu_u_COMM]: !B A. A \/ B <=> B \/ A
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c1]: !B A. ~(A \/ B) <=> ~A /\ ~B
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Goal: !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
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_Q1427882,TV_Q1427878]: ![V_f, V_g]: (![V_x]: s(TV_Q1427878,happ(s(t_fun(TV_Q1427882,TV_Q1427878),V_f),s(TV_Q1427882,V_x))) = s(TV_Q1427878,happ(s(t_fun(TV_Q1427882,TV_Q1427878),V_g),s(TV_Q1427882,V_x))) => s(t_fun(TV_Q1427882,TV_Q1427878),V_f) = s(t_fun(TV_Q1427882,TV_Q1427878),V_g))).
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_bools_TRUTH, axiom, p(s(t_bool,t))).
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_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_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_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral2(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral3(s(t_h4s_enumerals_bt(TV_u_27a),V_a))))) = s(t_h4s_enumerals_bt(TV_u_27a),V_a)).
fof(ah4s_enumerals_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_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_bools_JRHu_u_INDUCTu_u_UTIL, axiom, ![TV_u_27a]: ![V_t, V_P]: (![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_t) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) => p(s(t_bool,d_exists(s(t_fun(TV_u_27a,t_bool),V_P)))))).
fof(ah4s_enumerals_btu_u_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_enumerals_btu_u_sizeu_u_defu_c1, axiom, ![TV_u_27a]: ![V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a1))),s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a2)))))))))).
fof(ah4s_enumerals_btu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt)))) & ![V_b, V_b0]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b)))) & p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))))) => ![V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_b))),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0)))))))) => ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bt(TV_u_27a),V_b)))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_BETAu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_f]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_y)))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_indu_u_types_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_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_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_bools_ABSu_u_REPu_u_THM, axiom, ![TV_u_27b,TV_u_27a]: ![V_P]: (?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) => ?[V_rep, V_abs]: (![V_a]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_a))))) = s(TV_u_27b,V_a) & ![V_r]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_r)))) <=> s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_abs),s(TV_u_27a,V_r))))) = s(TV_u_27a,V_r))))).
fof(ah4s_enumerals_blu_u_TYu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0u_27]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_27)))) <=> ![V_uu_27blu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a))))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_a0),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_1))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_27)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_0),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_rep))))))).
fof(ah4s_enumerals_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_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_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_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_enumerals_blu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27blu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a))))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_a0),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),t_bool),V_uu_27blu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),V_r)))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral6u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_x1]: s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral6),s(TV_u_27a,V_x))),s(t_h4s_enumerals_bt(TV_u_27a),V_x0))),s(t_h4s_enumerals_bl(TV_u_27a),V_x1))) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(t_h4s_enumerals_bt(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_x1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))))).
fof(ah4s_enumerals_btu_u_TYu_u_DEF, axiom, ![TV_u_27a]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_uu_0]: (![V_a0u_27]: (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_27)))) <=> ![V_uu_27btu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_1))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27btu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_27)))))) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_0),s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_indu_u_types_recspace(TV_u_27a)),V_rep))))))).
fof(ah4s_enumerals_btu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(TV_u_27b,V_f0) & ![V_a0, V_a1, V_a2]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_h4s_enumerals_bt(TV_u_27a)))),h4s_enumerals_node),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(TV_u_27b,t_fun(TV_u_27b,TV_u_27b))))),V_f1),s(TV_u_27a,V_a1))),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),V_a0))))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bt(TV_u_27a),V_a2))))))).
fof(ah4s_enumerals_blu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) = s(t_h4s_enumerals_bl(TV_u_27a),V_a)).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral4u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral4) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))).
fof(ah4s_enumerals_hiddenu_u_u_u_20u_u_40indu_u_u_u_typeenumeral5u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_u_20u_40indu_u_typeenumeral5),s(t_h4s_enumerals_bl(TV_u_27a),V_x))) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral7(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_enumerals_bt(TV_u_27a),h4s_bools_arb))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a))),h4s_enumerals_u_20u_40indu_u_typeenumeral8(s(t_h4s_enumerals_bl(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(TV_u_27a,t_h4s_enumerals_bt(TV_u_27a)))),V_uu_0))))))))).
fof(ah4s_enumerals_onebl0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl) = s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_u_20u_40indu_u_typeenumeral6)).
fof(ah4s_enumerals_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_zerbl0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl) = s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_u_20u_40indu_u_typeenumeral5)).
fof(ah4s_enumerals_nbl0, axiom, ![TV_u_27a]: s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_u_20u_40indu_u_typeenumeral4)).
fof(ah4s_enumerals_blu_u_11u_c1, axiom, ![TV_u_27a]: ![V_a2u_27, V_a2, V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0u_27))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1u_27))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & (s(t_h4s_enumerals_bt(TV_u_27a),V_a1) = s(t_h4s_enumerals_bt(TV_u_27a),V_a1u_27) & s(t_h4s_enumerals_bl(TV_u_27a),V_a2) = s(t_h4s_enumerals_bl(TV_u_27a),V_a2u_27))))).
fof(ah4s_enumerals_blu_u_nchotomy, axiom, ![TV_u_27a]: ![V_bb]: (s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) | (?[V_b]: s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_b))) | ?[V_a, V_b0, V_b]: s(t_h4s_enumerals_bl(TV_u_27a),V_bb) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))))).
fof(ah4s_enumerals_blu_u_caseu_u_cong, axiom, ![TV_u_27a,TV_u_27b]: ![V_vu_27, V_v, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_enumerals_bl(TV_u_27a),V_M) = s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) & ((s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) => s(TV_u_27b,V_v) = s(TV_u_27b,V_vu_27)) & (![V_a]: (s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) => s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fu_27),s(t_h4s_enumerals_bl(TV_u_27a),V_a)))) & ![V_a0, V_a1, V_a2]: (s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) => s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1u_27),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))))) => s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),V_M),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),V_Mu_27),s(TV_u_27b,V_vu_27),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fu_27),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1u_27))))).
fof(ah4s_enumerals_blu_u_distinctu_c2, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0, V_a]: ~ (s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_blu_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_enumerals_blu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,happ(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(TV_u_27a,V_a0))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_nums_num,h4s_enumerals_blu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))))))))).
fof(ah4s_enumerals_blu_u_distinctu_c1, axiom, ![TV_u_27a]: ![V_a2, V_a1, V_a0]: ~ (s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl) = s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))).
fof(ah4s_enumerals_blu_u_induction, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl)))) & (![V_b]: (p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))) => p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_b))))))) & ![V_b]: (p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))) => ![V_b0, V_a]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a))),s(t_h4s_enumerals_bt(TV_u_27a),V_b0))),s(t_h4s_enumerals_bl(TV_u_27a),V_b))))))))) => ![V_b]: p(s(t_bool,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_bool),V_P),s(t_h4s_enumerals_bl(TV_u_27a),V_b)))))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_IMPu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_enumerals_blu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))).
fof(ah4s_enumerals_blu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_h4s_enumerals_bl(TV_u_27a),V_a)))).
fof(ah4s_enumerals_blu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f1, V_f]: s(TV_u_27b,h4s_enumerals_blu_u_case(s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl),s(TV_u_27b,V_v),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b))),V_f1))) = s(TV_u_27b,V_v)).
fof(ah4s_enumerals_blu_u_Axiom, axiom, ![TV_u_27b,TV_u_27a]: ![V_f2, V_f1, V_f0]: ?[V_fn]: (s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl))) = s(TV_u_27b,V_f0) & (![V_a]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl),s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),V_f1),s(t_h4s_enumerals_bl(TV_u_27a),V_a))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),V_a))))) & ![V_a0, V_a1, V_a2]: s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)),happ(s(t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(TV_u_27b,TV_u_27b)))),V_f2),s(TV_u_27a,V_a0))),s(t_h4s_enumerals_bt(TV_u_27a),V_a1))),s(t_h4s_enumerals_bl(TV_u_27a),V_a2))),s(TV_u_27b,happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),TV_u_27b),V_fn),s(t_h4s_enumerals_bl(TV_u_27a),V_a2)))))))).
fof(ah4s_enumerals_btu_u_sizeu_u_defu_c0, axiom, ![TV_u_27a]: ![V_f]: s(t_h4s_nums_num,h4s_enumerals_btu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_enumerals_bt(TV_u_27a),h4s_enumerals_nt))) = s(t_h4s_nums_num,h4s_nums_0)).
fof(ah4s_enumerals_datatypeu_u_bl, axiom, ![TV_u_27a]: ![V_bl]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool),happ(s(t_fun(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool)),happ(s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_fun(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),t_fun(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),t_bool))),V_bl),s(t_h4s_enumerals_bl(TV_u_27a),h4s_enumerals_nbl))),s(t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)),h4s_enumerals_zerbl))),s(t_fun(TV_u_27a,t_fun(t_h4s_enumerals_bt(TV_u_27a),t_fun(t_h4s_enumerals_bl(TV_u_27a),t_h4s_enumerals_bl(TV_u_27a)))),h4s_enumerals_onebl))))))).
fof(ah4s_bools_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_combins_UPDATEu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_b, V_a, V_x, V_x0]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_a) = s(TV_u_27a,V_x0)) & s(TV_u_27b,h4s_combins_update(s(TV_u_27a,V_a),s(TV_u_27b,V_b),s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))) = s(TV_u_27b,h4s_bools_cond(s(t_bool,V_v),s(TV_u_27b,V_b),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_x),s(TV_u_27a,V_x0))))))).
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_bools_EXISTSu_u_UNIQUEu_u_THM, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_P, V_x]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P))),s(TV_u_27a,V_x))) = s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))) => ![V_P]: (p(s(t_bool,h4s_bools_u_3fu_21(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(t_fun(TV_u_27a,t_bool),t_fun(TV_u_27a,t_bool)),V_uu_0),s(t_fun(TV_u_27a,t_bool),V_P)))))) <=> (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) & ![V_x, V_y]: ((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_y))))) => s(TV_u_27a,V_x) = s(TV_u_27a,V_y)))))).
fof(ah4s_predu_u_sets_COMMUTINGu_u_ITSETu_u_INSERT, axiom, ![TV_u_27a,TV_u_27b]: ![V_s, V_f]: ((![V_x, V_y, V_z]: s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,V_z))))) = s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_y))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_z))))) & p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s))))) => ![V_x, V_b]: s(TV_u_27b,h4s_predu_u_sets_itset(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_b))) = s(TV_u_27b,h4s_predu_u_sets_itset(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_x))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_b))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_predu_u_sets_CARDu_u_INSERT, axiom, ![TV_u_27a]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ![V_x]: s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_h4s_nums_num,h4s_bools_cond(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_predu_u_sets_card(s(t_fun(TV_u_27a,t_bool),V_s))))))))).
fof(ah4s_predu_u_sets_CHOICEu_u_INSERTu_u_REST, axiom, ![TV_u_27a]: ![V_s]: (~ (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty)) => s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_fun(TV_u_27a,t_bool),V_s))).
fof(ah4s_predu_u_sets_FINITEu_u_INSERT, axiom, ![TV_u_27a]: ![V_x, V_s]: s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))) = s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))).
fof(ah4s_predu_u_sets_CHOICEu_u_NOTu_u_INu_u_REST, axiom, ![TV_u_27a]: ![V_s]: ~ (p(s(t_bool,h4s_bools_in(s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),V_s))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),V_s)))))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_predu_u_sets_ITSETu_u_INSERT, axiom, ![TV_u_27a,TV_u_27b]: ![V_s]: (p(s(t_bool,h4s_predu_u_sets_finite(s(t_fun(TV_u_27a,t_bool),V_s)))) => ![V_f, V_x, V_b]: s(TV_u_27b,h4s_predu_u_sets_itset(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27b,V_b))) = s(TV_u_27b,h4s_predu_u_sets_itset(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_rest(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))),s(TV_u_27b,happ(s(t_fun(TV_u_27b,TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27b)),V_f),s(TV_u_27a,h4s_predu_u_sets_choice(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))))),s(TV_u_27b,V_b))))))).
fof(ah4s_bools_CONJu_u_ASSOC, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) & (p(s(t_bool,V_t2)) & p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) & p(s(t_bool,V_t3))))).
fof(ah4s_predu_u_sets_INu_u_DELETE, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_y)))))) <=> (p(s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))) & ~ (s(TV_u_27a,V_x) = s(TV_u_27a,V_y))))).
fof(ah4s_predu_u_sets_DELETEu_u_NONu_u_ELEMENT, axiom, ![TV_u_27a]: ![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),V_s))))) <=> s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_x))) = s(t_fun(TV_u_27a,t_bool),V_s))).
fof(ah4s_predu_u_sets_DELETEu_u_INSERT, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y)) & s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))),s(TV_u_27a,V_y))) = s(t_fun(TV_u_27a,t_bool),h4s_bools_cond(s(t_bool,V_v),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_y))),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_y))))))))).
fof(ah4s_predu_u_sets_INSERTu_u_COMM, axiom, ![TV_u_27a]: ![V_y, V_x, V_s]: s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_y),s(t_fun(TV_u_27a,t_bool),V_s))))) = 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),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s)))))).
fof(ah4s_predu_u_sets_NOTu_u_EMPTYu_u_INSERT, axiom, ![TV_u_27a]: ![V_x, V_s]: ~ (s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_empty) = s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))))).
fof(ah4s_bools_NOTu_u_FORALLu_u_THM, axiom, ![TV_u_27a]: ![V_P]: (~ (![V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))) <=> ?[V_x]: ~ (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x))))))).
fof(ah4s_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_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_EXTENSION, axiom, ![TV_u_27a]: ![V_t, V_s]: (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),V_t) <=> ![V_x]: s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_bool,h4s_bools_in(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_t))))).
fof(ah4s_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_predu_u_sets_INSERTu_u_DELETE, axiom, ![TV_u_27a]: ![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),V_s)))) => s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_delete(s(t_fun(TV_u_27a,t_bool),V_s),s(TV_u_27a,V_x))))) = s(t_fun(TV_u_27a,t_bool),V_s))).
fof(ah4s_predu_u_sets_ABSORPTION, axiom, ![TV_u_27a]: ![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),V_s)))) <=> s(t_fun(TV_u_27a,t_bool),h4s_predu_u_sets_insert(s(TV_u_27a,V_x),s(t_fun(TV_u_27a,t_bool),V_s))) = s(t_fun(TV_u_27a,t_bool),V_s))).
fof(ah4s_numerals_numeralu_u_lteu_c2, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_arithmetics_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c2, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_COMPLETEu_u_INDUCTION, axiom, ![V_P]: (![V_n]: (![V_m]: (p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_m))))) => p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n))))) => ![V_n]: p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_P),s(t_h4s_nums_num,V_n)))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_bools_Fu_u_IMP, axiom, ![V_t]: (~ (p(s(t_bool,V_t))) => (p(s(t_bool,V_t)) => p(s(t_bool,f))))).
fof(ah4s_arithmetics_TWO, axiom, s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))) = s(t_h4s_nums_num,h4s_nums_suc(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_LESSu_u_EQ, axiom, ![V_n, V_m]: (s(t_h4s_nums_num,V_m) = s(t_h4s_nums_num,V_n) <=> (p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m))))))).
fof(ah4s_arithmetics_ADDu_u_CLAUSESu_c0, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_combins_Iu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,h4s_combins_i(s(TV_u_27a,V_x))) = s(TV_u_27a,V_x)).
fof(ah4s_markers_Abbrevu_u_def, axiom, ![V_x]: s(t_bool,h4s_markers_abbrev(s(t_bool,V_x))) = s(t_bool,V_x)).
fof(ah4s_sats_pthu_u_no1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_p))))).
fof(ah4s_sats_pthu_u_ni2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_no2, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) | p(s(t_bool,V_q)))) => ~ (p(s(t_bool,V_q))))).
fof(ah4s_sats_pthu_u_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_bools_RIGHTu_u_FORALLu_u_IMPu_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(ah4s_sats_dcu_u_imp, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) => p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (~ (p(s(t_bool,V_q))) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_sats_dcu_u_disj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_q)))) & ((p(s(t_bool,V_p)) | ~ (p(s(t_bool,V_r)))) & (p(s(t_bool,V_q)) | (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p))))))))).
fof(ah4s_arithmetics_ADDu_u_MONOu_u_LESSu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p)))).
fof(ah4s_sats_pthu_u_nn, axiom, ![V_p]: (~ (~ (p(s(t_bool,V_p)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_dcu_u_neg, axiom, ![V_q, V_p]: ((p(s(t_bool,V_p)) <=> ~ (p(s(t_bool,V_q)))) <=> ((p(s(t_bool,V_p)) | p(s(t_bool,V_q))) & (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p))))))).
fof(ah4s_sats_dcu_u_conj, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> (p(s(t_bool,V_q)) & p(s(t_bool,V_r)))) <=> ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_r))))) & ((p(s(t_bool,V_q)) | ~ (p(s(t_bool,V_p)))) & (p(s(t_bool,V_r)) | ~ (p(s(t_bool,V_p)))))))).
fof(ah4s_sats_dcu_u_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => p(s(t_bool,V_t)))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f))))).
fof(ah4s_bools_DISJu_u_ASSOC, axiom, ![V_C, V_B, V_A]: ((p(s(t_bool,V_A)) | (p(s(t_bool,V_B)) | p(s(t_bool,V_C)))) <=> ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) | p(s(t_bool,V_C))))).
fof(ah4s_bools_DISJu_u_SYM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_sats_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ah4s_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_DISJu_u_COMM, axiom, ![V_B, V_A]: ((p(s(t_bool,V_A)) | p(s(t_bool,V_B))) <=> (p(s(t_bool,V_B)) | p(s(t_bool,V_A))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c1, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) & ~ (p(s(t_bool,V_B)))))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f)))))).
fof(ch4s_enumerals_btu_u_11, conjecture, ![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))))).
