%   ORIGINAL: h4/patricia__casts/word__ptree__case__cong
% 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/patricia__casts/word__ptree__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\a0_27. !_27word__ptree_27. (!a0_270. (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 a10) (\n. h4/ind__type/BOTTOM)) a0 a1) ==> _27word__ptree_27 a0_270) ==> _27word__ptree_27 a0_27) rep
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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/patricia__casts/Word__ptree0: h4/patricia__casts/Word__ptree = h4/patricia__casts/_20_40ind__typepatricia__casts0
% Assm: h4/patricia__casts/hidden____20__40ind____typepatricia____casts0____def: h4/patricia__casts/_20_40ind__typepatricia__casts0 = (\a0 a1. h4/patricia__casts/_20_40ind__typepatricia__casts1 ((\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 a10) (\n. h4/ind__type/BOTTOM)) a0 a1))
% Assm: h4/patricia__casts/word__ptree__repfns_c1: !r. (\a0_27. !_27word__ptree_27. (!a0_270. (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a00 a10) (\n. h4/ind__type/BOTTOM)) a0 a1) ==> _27word__ptree_27 a0_270) ==> _27word__ptree_27 a0_27) r <=> h4/patricia__casts/_20_40ind__typepatricia__casts2 (h4/patricia__casts/_20_40ind__typepatricia__casts1 r) = r
% Assm: h4/patricia__casts/word__ptree__case__def: !f a1 a0. h4/patricia__casts/word__ptree__CASE (h4/patricia__casts/Word__ptree a0 a1) f = f a0 a1
% Assm: h4/patricia__casts/word__ptree__size__def: !f1 f a1 a0. h4/patricia__casts/word__ptree__size f f1 (h4/patricia__casts/Word__ptree a0 a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/patricia/ptree__size f1 a1)
% Assm: h4/patricia__casts/word__ptree__11: !a1_27 a1 a0_27 a0. h4/patricia__casts/Word__ptree a0 a1 = h4/patricia__casts/Word__ptree a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/patricia__casts/word__ptree__repfns_c0: !a. h4/patricia__casts/_20_40ind__typepatricia__casts1 (h4/patricia__casts/_20_40ind__typepatricia__casts2 a) = a
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/SND0: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm: h4/ind__type/CONSTR__REC: !Fn. ?f. !c i r. f (h4/ind__type/CONSTR c i r) = Fn c i r (\n. f (r n))
% Assm: h4/ind__type/FCONS0_c0: !f a. h4/ind__type/FCONS a f h4/num/0 = a
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/DATATYPE__TAG__THM: !x. h4/bool/DATATYPE x <=> T
% Assm: h4/patricia__casts/datatype__word__ptree: !word__ptree. h4/bool/DATATYPE (word__ptree h4/patricia__casts/Word__ptree)
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/one/one__axiom: !g f. f = g
% Assm: h4/bool/ETA__AX: !t. (\x. t x) = t
% Assm: h4/one/one__TY__DEF: ?rep. h4/bool/TYPE__DEFINITION (\b. b) rep
% Assm: h4/bool/TYPE__DEFINITION__THM: !rep P. h4/bool/TYPE__DEFINITION P rep <=> (!x_27 x_27_27. rep x_27 = rep x_27_27 ==> x_27 = x_27_27) /\ (!x. P x <=> (?x_27. x = rep x_27))
% Assm: h4/patricia/TRAVERSE__TRANSFORM: !t f. h4/patricia/TRAVERSE (h4/patricia/TRANSFORM f t) = h4/patricia/TRAVERSE t
% Assm: h4/patricia/TRANSFORM__BRANCH: !r p m l f. h4/patricia/TRANSFORM f (h4/patricia/BRANCH (h4/pair/_2C p (h4/pair/_2C m (h4/pair/_2C l r)))) = h4/patricia/BRANCH (h4/pair/_2C p (h4/pair/_2C m (h4/pair/_2C (h4/patricia/TRANSFORM f l) (h4/patricia/TRANSFORM f r))))
% Assm: h4/patricia/PTREE__TRAVERSE__EQ: !t2 t1. h4/patricia/IS__PTREE t1 /\ h4/patricia/IS__PTREE t2 ==> ((!k. h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t1)) <=> h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t2))) <=> h4/patricia/TRAVERSE t1 = h4/patricia/TRAVERSE t2)
% Assm: h4/patricia/PEEK__TRANSFORM: !t k f. h4/patricia/PEEK (h4/patricia/TRANSFORM f t) k = h4/option/option__CASE (h4/patricia/PEEK t k) h4/option/NONE (\x. h4/option/SOME (f x))
% Assm: h4/patricia/TRANSFORM__EMPTY: !t f. h4/patricia/TRANSFORM f t = h4/patricia/Empty <=> t = h4/patricia/Empty
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/patricia/TRANSFORM__def_c1: !j f d. h4/patricia/TRANSFORM f (h4/patricia/Leaf j d) = h4/patricia/Leaf j (f d)
% Assm: h4/patricia/TRANSFORM__def_c0: !f. h4/patricia/TRANSFORM f h4/patricia/Empty = h4/patricia/Empty
% Assm: h4/patricia/Empty0: h4/patricia/Empty = h4/patricia/_20_40ind__typepatricia0
% Assm: h4/patricia/ptree__repfns_c0: !a. h4/patricia/_20_40ind__typepatricia3 (h4/patricia/_20_40ind__typepatricia4 a) = a
% Assm: h4/patricia/hidden____20__40ind____typepatricia2____def: h4/patricia/_20_40ind__typepatricia2 = (\a0 a1 a2 a3. h4/patricia/_20_40ind__typepatricia3 ((\a00 a10 a20 a30. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 (h4/pair/_2C h4/bool/ARB a10)) (h4/ind__type/FCONS a20 (h4/ind__type/FCONS a30 (\n. h4/ind__type/BOTTOM)))) a0 a1 (h4/patricia/_20_40ind__typepatricia4 a2) (h4/patricia/_20_40ind__typepatricia4 a3)))
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/patricia/Leaf0: h4/patricia/Leaf = h4/patricia/_20_40ind__typepatricia1
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/patricia/TRANSFORM__def_c2: !r p m l f. h4/patricia/TRANSFORM f (h4/patricia/Branch p m l r) = h4/patricia/Branch p m (h4/patricia/TRANSFORM f l) (h4/patricia/TRANSFORM f r)
% Assm: h4/patricia/Branch0: h4/patricia/Branch = h4/patricia/_20_40ind__typepatricia2
% Assm: h4/patricia/hidden____20__40ind____typepatricia0____def: h4/patricia/_20_40ind__typepatricia0 = h4/patricia/_20_40ind__typepatricia3 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM))
% Assm: h4/patricia/hidden____20__40ind____typepatricia1____def: h4/patricia/_20_40ind__typepatricia1 = (\a0 a1. h4/patricia/_20_40ind__typepatricia3 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a00 (h4/pair/_2C a10 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a0 a1))
% Assm: h4/patricia/ptree__repfns_c1: !r. (\a0_27. !_27ptree_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) (\n. h4/ind__type/BOTTOM) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a00 (h4/pair/_2C a10 h4/bool/ARB)) (\n. h4/ind__type/BOTTOM)) a0 a1) \/ (?a0 a1 a2 a3. a0_270 = (\a00 a10 a20 a30. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a00 (h4/pair/_2C h4/bool/ARB a10)) (h4/ind__type/FCONS a20 (h4/ind__type/FCONS a30 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 a3 /\ _27ptree_27 a2 /\ _27ptree_27 a3) ==> _27ptree_27 a0_270) ==> _27ptree_27 a0_27) r <=> h4/patricia/_20_40ind__typepatricia4 (h4/patricia/_20_40ind__typepatricia3 r) = r
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/patricia/ptree__case__def_c2: !v f1 f a3 a2 a1 a0. h4/patricia/ptree__CASE (h4/patricia/Branch a0 a1 a2 a3) v f f1 = f1 a0 a1 a2 a3
% Assm: h4/patricia/ptree__case__def_c0: !v f1 f. h4/patricia/ptree__CASE h4/patricia/Empty v f f1 = v
% Assm: h4/relation/WFREC__COROLLARY: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. f x = M (h4/relation/RESTRICT f R x) x)
% Assm: h4/patricia/ptree__case__def_c1: !v f1 f a1 a0. h4/patricia/ptree__CASE (h4/patricia/Leaf a0 a1) v f f1 = f a0 a1
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/option/SOME__11: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm: h4/patricia/TRAVERSE__def_c2: !r p m l. h4/patricia/TRAVERSE (h4/patricia/Branch p m l r) = h4/list/APPEND (h4/patricia/TRAVERSE l) (h4/patricia/TRAVERSE r)
% Assm: h4/patricia/TRAVERSE__def_c1: !j d. h4/patricia/TRAVERSE (h4/patricia/Leaf j d) = h4/list/CONS j h4/list/NIL
% Assm: h4/list/APPEND__11_c0: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm: h4/list/CONS__11: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm: h4/patricia/TRAVERSE__def_c0: h4/patricia/TRAVERSE h4/patricia/Empty = h4/list/NIL
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% Assm: h4/patricia/BRANCH__primitive__def: h4/patricia/BRANCH = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\BRANCH a. h4/pair/pair__CASE a (\p v1. h4/pair/pair__CASE v1 (\m v3. h4/pair/pair__CASE v3 (\v4 t. h4/patricia/ptree__CASE v4 (h4/combin/I t) (\v18 v19. h4/patricia/ptree__CASE t (h4/combin/I (h4/patricia/Leaf v18 v19)) (\v30 v31. h4/combin/I (h4/patricia/Branch p m (h4/patricia/Leaf v18 v19) (h4/patricia/Leaf v30 v31))) (\v32 v33 v34 v35. h4/combin/I (h4/patricia/Branch p m (h4/patricia/Leaf v18 v19) (h4/patricia/Branch v32 v33 v34 v35)))) (\v20 v21 v22 v23. h4/patricia/ptree__CASE t (h4/combin/I (h4/patricia/Branch v20 v21 v22 v23)) (\v42 v43. h4/combin/I (h4/patricia/Branch p m (h4/patricia/Branch v20 v21 v22 v23) (h4/patricia/Leaf v42 v43))) (\v44 v45 v46 v47. h4/combin/I (h4/patricia/Branch p m (h4/patricia/Branch v20 v21 v22 v23) (h4/patricia/Branch v44 v45 v46 v47))))))))
% Assm: h4/bool/IMP__CLAUSES_c4: !t. t ==> F <=> ~t
% Assm: h4/patricia/MEM__TRAVERSE__PEEK: !t k. h4/patricia/IS__PTREE t ==> (h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t)) <=> h4/option/IS__SOME (h4/patricia/PEEK t k))
% Assm: h4/bool/EQ__REFL: !x. x = x
% Assm: h4/patricia/PTREE__EQ: !t2 t1. h4/patricia/IS__PTREE t1 /\ h4/patricia/IS__PTREE t2 ==> ((!k. h4/patricia/PEEK t1 k = h4/patricia/PEEK t2 k) <=> t1 = t2)
% Assm: h4/patricia/TRANSFORM__IS__PTREE: !t f. h4/patricia/IS__PTREE t ==> h4/patricia/IS__PTREE (h4/patricia/TRANSFORM f t)
% Assm: h4/bool/BOOL__EQ__DISTINCT_c0: ~(T <=> F)
% Assm: h4/sat/AND__INV2: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm: h4/sat/pth__nn: !p. ~ ~p ==> p
% Assm: h4/sat/dc__eq: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm: h4/sat/AND__INV__IMP: !A. A ==> ~A ==> F
% Assm: h4/option/IS__SOME__DEF_c1: h4/option/IS__SOME h4/option/NONE <=> F
% Assm: h4/option/IS__SOME__DEF_c0: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm: h4/option/NOT__NONE__SOME: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm: h4/sat/pth__no2: !q p. ~(p \/ q) ==> ~q
% Assm: h4/option/option__nchotomy: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm: h4/one/one1: !v. v = h4/one/one0
% Assm: h4/sat/pth__no1: !q p. ~(p \/ q) ==> ~p
% Assm: h4/sat/pth__ni2: !q p. ~(p ==> q) ==> ~q
% Assm: h4/sat/pth__ni1: !q p. ~(p ==> q) ==> p
% Assm: h4/sat/OR__DUAL3: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm: h4/sat/dc__imp: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm: h4/sat/OR__DUAL2: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm: h4/sat/NOT__NOT: !t. ~ ~t <=> t
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/patricia/PEEK__tupled__primitive__def: h4/patricia/PEEK__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!p r l k m. R (h4/pair/_2C (h4/bool/COND (h4/bit/BIT m k) l r) k) (h4/pair/_2C (h4/patricia/Branch p m l r) k)))) (\PEEK__tupled a. h4/pair/pair__CASE a (\v k. h4/patricia/ptree__CASE v (h4/combin/I h4/option/NONE) (\j d. h4/combin/I (h4/bool/COND (k = j) (h4/option/SOME d) h4/option/NONE)) (\p m l r. h4/combin/I (PEEK__tupled (h4/pair/_2C (h4/bool/COND (h4/bit/BIT m k) l r) k)))))
% Assm: h4/patricia/PEEK__curried__def: !x1 x. h4/patricia/PEEK x x1 = h4/patricia/PEEK__tupled (h4/pair/_2C x x1)
% Assm: h4/patricia/ptree__size__def_c2: !f a3 a2 a1 a0. h4/patricia/ptree__size f (h4/patricia/Branch a0 a1 a2 a3) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B a0 (h4/arithmetic/_2B a1 (h4/arithmetic/_2B (h4/patricia/ptree__size f a2) (h4/patricia/ptree__size f a3))))
% Assm: h4/bool/COND__CLAUSES_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/COND__CLAUSES_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 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/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/numeral/numeral__distrib_c1: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm: h4/arithmetic/ADD__ASSOC: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/arithmetic/LESS__MONO__ADD__EQ: !p n m. h4/prim__rec/_3C (h4/arithmetic/_2B m p) (h4/arithmetic/_2B n p) <=> h4/prim__rec/_3C m n
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/option/option__case__def_c1: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = f x
% Assm: h4/option/option__case__def_c0: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/bool/bool__case__thm_c1: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm: h4/bool/bool__case__thm_c0: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Goal: !f_27 f M_27 M. M = M_27 /\ (!a0 a1. M_27 = h4/patricia__casts/Word__ptree a0 a1 ==> f a0 a1 = f_27 a0 a1) ==> h4/patricia__casts/word__ptree__CASE M f = h4/patricia__casts/word__ptree__CASE M_27 f_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_patriciau_u_castss_wordu_u_ptreeu_u_TYu_u_DEF]: !_1. (!n. happ _1 n = h4/ind__type/BOTTOM) ==> (!_0. (!a0_27. happ _0 a0_27 <=> (!_27word__ptree_27. (!a0_270. (?a0 a1. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 a1) _1) ==> happ _27word__ptree_27 a0_270) ==> happ _27word__ptree_27 a0_27)) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep))
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% 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_patriciau_u_castss_Wordu_u_ptree0]: h4/patricia__casts/Word__ptree = h4/patricia__casts/_20_40ind__typepatricia__casts0
% Assm [h4s_patriciau_u_castss_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatriciau_u_u_u_casts0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/patricia__casts/_20_40ind__typepatricia__casts0 x) x = h4/patricia__casts/_20_40ind__typepatricia__casts1 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C x x) _0))
% Assm [h4s_patriciau_u_castss_wordu_u_ptreeu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27word__ptree_27. (!a0_270. (?a0 a1. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C a0 a1) _0) ==> happ _27word__ptree_27 a0_270) ==> happ _27word__ptree_27 r) <=> h4/patricia__casts/_20_40ind__typepatricia__casts2 (h4/patricia__casts/_20_40ind__typepatricia__casts1 r) = r)
% Assm [h4s_patriciau_u_castss_wordu_u_ptreeu_u_caseu_u_def]: !f a1 a0. h4/patricia__casts/word__ptree__CASE (happ (happ h4/patricia__casts/Word__ptree a0) a1) f = happ (happ f a0) a1
% Assm [h4s_patriciau_u_castss_wordu_u_ptreeu_u_sizeu_u_def]: !f1 f a1 a0. h4/patricia__casts/word__ptree__size f f1 (happ (happ h4/patricia__casts/Word__ptree a0) a1) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/patricia/ptree__size f1 a1)
% Assm [h4s_patriciau_u_castss_wordu_u_ptreeu_u_11]: !a1_27 a1 a0_27 a0. happ (happ h4/patricia__casts/Word__ptree a0) a1 = happ (happ h4/patricia__casts/Word__ptree a0_27) a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_patriciau_u_castss_wordu_u_ptreeu_u_repfnsu_c0]: !a. h4/patricia__casts/_20_40ind__typepatricia__casts1 (h4/patricia__casts/_20_40ind__typepatricia__casts2 a) = a
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm [h4s_pairs_SND0]: !y x. h4/pair/SND (h4/pair/_2C x y) = y
% Assm [h4s_indu_u_types_CONSTRu_u_REC]: !_0. (!f r n. happ (happ (happ _0 f) r) n = happ f (happ r n)) ==> (!Fn. ?f. !c i r. happ f (h4/ind__type/CONSTR c i r) = happ (happ (happ (happ Fn c) i) r) (happ (happ _0 f) r))
% Assm [h4s_indu_u_types_FCONS0u_c0]: !f a. happ (h4/ind__type/FCONS a f) h4/num/0 = a
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_DATATYPEu_u_TAGu_u_THM]: !x. h4/bool/DATATYPE x <=> T
% Assm [h4s_patriciau_u_castss_datatypeu_u_wordu_u_ptree]: !word__ptree. h4/bool/DATATYPE (happ word__ptree h4/patricia__casts/Word__ptree)
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_ones_oneu_u_axiom]: !g f. f = g
% Assm [h4s_bools_ETAu_u_AX]: !t x. happ t x = happ t x
% Assm [h4s_ones_oneu_u_TYu_u_DEF]: !_0. (!b. happ _0 b <=> b) ==> (?rep. h4/bool/TYPE__DEFINITION _0 rep)
% Assm [h4s_bools_TYPEu_u_DEFINITIONu_u_THM]: !rep P. h4/bool/TYPE__DEFINITION P rep <=> (!x_27 x_27_27. happ rep x_27 = happ rep x_27_27 ==> x_27 = x_27_27) /\ (!x. happ P x <=> (?x_27. x = happ rep x_27))
% Assm [h4s_patricias_TRAVERSEu_u_TRANSFORM]: !t f. h4/patricia/TRAVERSE (h4/patricia/TRANSFORM f t) = h4/patricia/TRAVERSE t
% Assm [h4s_patricias_TRANSFORMu_u_BRANCH]: !r p m l f. h4/patricia/TRANSFORM f (happ h4/patricia/BRANCH (h4/pair/_2C p (h4/pair/_2C m (h4/pair/_2C l r)))) = happ h4/patricia/BRANCH (h4/pair/_2C p (h4/pair/_2C m (h4/pair/_2C (h4/patricia/TRANSFORM f l) (h4/patricia/TRANSFORM f r))))
% Assm [h4s_patricias_PTREEu_u_TRAVERSEu_u_EQ]: !t2 t1. h4/patricia/IS__PTREE t1 /\ h4/patricia/IS__PTREE t2 ==> ((!k. h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t1)) <=> h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t2))) <=> h4/patricia/TRAVERSE t1 = h4/patricia/TRAVERSE t2)
% Assm [h4s_patricias_PEEKu_u_TRANSFORM]: !_0. (!f x. happ (happ _0 f) x = h4/option/SOME (happ f x)) ==> (!t k f. h4/patricia/PEEK (h4/patricia/TRANSFORM f t) k = h4/option/option__CASE (h4/patricia/PEEK t k) h4/option/NONE (happ _0 f))
% Assm [h4s_patricias_TRANSFORMu_u_EMPTY]: !t f. h4/patricia/TRANSFORM f t = h4/patricia/Empty <=> t = h4/patricia/Empty
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_patricias_TRANSFORMu_u_defu_c1]: !j f d. h4/patricia/TRANSFORM f (happ (happ h4/patricia/Leaf j) d) = happ (happ h4/patricia/Leaf j) (happ f d)
% Assm [h4s_patricias_TRANSFORMu_u_defu_c0]: !f. h4/patricia/TRANSFORM f h4/patricia/Empty = h4/patricia/Empty
% Assm [h4s_patricias_Empty0]: h4/patricia/Empty = h4/patricia/_20_40ind__typepatricia0
% Assm [h4s_patricias_ptreeu_u_repfnsu_c0]: !a. h4/patricia/_20_40ind__typepatricia3 (h4/patricia/_20_40ind__typepatricia4 a) = a
% Assm [h4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x' x x'. happ (happ (happ (happ h4/patricia/_20_40ind__typepatricia2 x) x') x) x' = h4/patricia/_20_40ind__typepatricia3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C x (h4/pair/_2C h4/bool/ARB x')) (h4/ind__type/FCONS (h4/patricia/_20_40ind__typepatricia4 x) (h4/ind__type/FCONS (h4/patricia/_20_40ind__typepatricia4 x') _0))))
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_patricias_Leaf0]: h4/patricia/Leaf = h4/patricia/_20_40ind__typepatricia1
% 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_patricias_TRANSFORMu_u_defu_c2]: !r p m l f. h4/patricia/TRANSFORM f (happ (happ (happ (happ h4/patricia/Branch p) m) l) r) = happ (happ (happ (happ h4/patricia/Branch p) m) (h4/patricia/TRANSFORM f l)) (h4/patricia/TRANSFORM f r)
% Assm [h4s_patricias_Branch0]: h4/patricia/Branch = h4/patricia/_20_40ind__typepatricia2
% Assm [h4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/patricia/_20_40ind__typepatricia0 = h4/patricia/_20_40ind__typepatricia3 (h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0)
% Assm [h4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x. happ (happ h4/patricia/_20_40ind__typepatricia1 x) x = h4/patricia/_20_40ind__typepatricia3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C x (h4/pair/_2C x h4/bool/ARB)) _0))
% Assm [h4s_patricias_ptreeu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27ptree_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 (h4/pair/_2C h4/bool/ARB (h4/pair/_2C h4/bool/ARB h4/bool/ARB)) _0 \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) (h4/pair/_2C a0 (h4/pair/_2C a1 h4/bool/ARB)) _0) \/ (?a0 a1 a2 a3. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) (h4/pair/_2C a0 (h4/pair/_2C h4/bool/ARB a1)) (h4/ind__type/FCONS a2 (h4/ind__type/FCONS a3 _0)) /\ happ _27ptree_27 a2 /\ happ _27ptree_27 a3) ==> happ _27ptree_27 a0_270) ==> happ _27ptree_27 r) <=> h4/patricia/_20_40ind__typepatricia4 (h4/patricia/_20_40ind__typepatricia3 r) = r)
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% 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_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_patricias_ptreeu_u_caseu_u_defu_c2]: !v f1 f a3 a2 a1 a0. h4/patricia/ptree__CASE (happ (happ (happ (happ h4/patricia/Branch a0) a1) a2) a3) v f f1 = happ (happ (happ (happ f1 a0) a1) a2) a3
% Assm [h4s_patricias_ptreeu_u_caseu_u_defu_c0]: !v f1 f. h4/patricia/ptree__CASE h4/patricia/Empty v f f1 = v
% Assm [h4s_relations_WFRECu_u_COROLLARY]: !f R M. f = h4/relation/WFREC R M ==> h4/relation/WF R ==> (!x. happ f x = happ (happ M (h4/relation/RESTRICT f R x)) x)
% Assm [h4s_patricias_ptreeu_u_caseu_u_defu_c1]: !v f1 f a1 a0. h4/patricia/ptree__CASE (happ (happ h4/patricia/Leaf a0) a1) v f f1 = happ (happ f a0) a1
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_pairs_pairu_u_caseu_u_thm]: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = happ (happ f x) y
% Assm [h4s_options_SOMEu_u_11]: !y x. h4/option/SOME x = h4/option/SOME y <=> x = y
% Assm [h4s_patricias_TRAVERSEu_u_defu_c2]: !r p m l. h4/patricia/TRAVERSE (happ (happ (happ (happ h4/patricia/Branch p) m) l) r) = h4/list/APPEND (h4/patricia/TRAVERSE l) (h4/patricia/TRAVERSE r)
% Assm [h4s_patricias_TRAVERSEu_u_defu_c1]: !j d. h4/patricia/TRAVERSE (happ (happ h4/patricia/Leaf j) d) = h4/list/CONS j h4/list/NIL
% Assm [h4s_lists_APPENDu_u_11u_c0]: !l3 l2 l1. h4/list/APPEND l1 l2 = h4/list/APPEND l1 l3 <=> l2 = l3
% Assm [h4s_lists_CONSu_u_11]: !a1_27 a1 a0_27 a0. h4/list/CONS a0 a1 = h4/list/CONS a0_27 a1_27 <=> a0 = a0_27 /\ a1 = a1_27
% Assm [h4s_patricias_TRAVERSEu_u_defu_c0]: h4/patricia/TRAVERSE h4/patricia/Empty = h4/list/NIL
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% Assm [h4s_patricias_BRANCHu_u_primitiveu_u_def]: !_26. (!p m v20 v21 v22 v23 v44 v45 v46 v47. happ (happ (happ (happ (happ (happ (happ (happ (happ (happ _26 p) m) v20) v21) v22) v23) v44) v45) v46) v47 = h4/combin/I (happ (happ (happ (happ h4/patricia/Branch p) m) (happ (happ (happ (happ h4/patricia/Branch v20) v21) v22) v23)) (happ (happ (happ (happ h4/patricia/Branch v44) v45) v46) v47))) ==> (!_25. (!p m v20 v21 v22 v23 v44 v45 v46. happ (happ (happ (happ (happ (happ (happ (happ (happ _25 p) m) v20) v21) v22) v23) v44) v45) v46 = happ (happ (happ (happ (happ (happ (happ (happ (happ _26 p) m) v20) v21) v22) v23) v44) v45) v46) ==> (!_24. (!p m v20 v21 v22 v23 v44 v45. happ (happ (happ (happ (happ (happ (happ (happ _24 p) m) v20) v21) v22) v23) v44) v45 = happ (happ (happ (happ (happ (happ (happ (happ _25 p) m) v20) v21) v22) v23) v44) v45) ==> (!_23. (!p m v20 v21 v22 v23 v44. happ (happ (happ (happ (happ (happ (happ _23 p) m) v20) v21) v22) v23) v44 = happ (happ (happ (happ (happ (happ (happ _24 p) m) v20) v21) v22) v23) v44) ==> (!_22. (!p m v20 v21 v22 v23 v42 v43. happ (happ (happ (happ (happ (happ (happ (happ _22 p) m) v20) v21) v22) v23) v42) v43 = h4/combin/I (happ (happ (happ (happ h4/patricia/Branch p) m) (happ (happ (happ (happ h4/patricia/Branch v20) v21) v22) v23)) (happ (happ h4/patricia/Leaf v42) v43))) ==> (!_21. (!p m v20 v21 v22 v23 v42. happ (happ (happ (happ (happ (happ (happ _21 p) m) v20) v21) v22) v23) v42 = happ (happ (happ (happ (happ (happ (happ _22 p) m) v20) v21) v22) v23) v42) ==> (!_20. (!t p m v20 v21 v22 v23. happ (happ (happ (happ (happ (happ (happ _20 t) p) m) v20) v21) v22) v23 = h4/patricia/ptree__CASE t (h4/combin/I (happ (happ (happ (happ h4/patricia/Branch v20) v21) v22) v23)) (happ (happ (happ (happ (happ (happ _21 p) m) v20) v21) v22) v23) (happ (happ (happ (happ (happ (happ _23 p) m) v20) v21) v22) v23)) ==> (!_19. (!t p m v20 v21 v22. happ (happ (happ (happ (happ (happ _19 t) p) m) v20) v21) v22 = happ (happ (happ (happ (happ (happ _20 t) p) m) v20) v21) v22) ==> (!_18. (!t p m v20 v21. happ (happ (happ (happ (happ _18 t) p) m) v20) v21 = happ (happ (happ (happ (happ _19 t) p) m) v20) v21) ==> (!_17. (!t p m v20. happ (happ (happ (happ _17 t) p) m) v20 = happ (happ (happ (happ _18 t) p) m) v20) ==> (!_16. (!p m v18 v19 v32 v33 v34 v35. happ (happ (happ (happ (happ (happ (happ (happ _16 p) m) v18) v19) v32) v33) v34) v35 = h4/combin/I (happ (happ (happ (happ h4/patricia/Branch p) m) (happ (happ h4/patricia/Leaf v18) v19)) (happ (happ (happ (happ h4/patricia/Branch v32) v33) v34) v35))) ==> (!_15. (!p m v18 v19 v32 v33 v34. happ (happ (happ (happ (happ (happ (happ _15 p) m) v18) v19) v32) v33) v34 = happ (happ (happ (happ (happ (happ (happ _16 p) m) v18) v19) v32) v33) v34) ==> (!_14. (!p m v18 v19 v32 v33. happ (happ (happ (happ (happ (happ _14 p) m) v18) v19) v32) v33 = happ (happ (happ (happ (happ (happ _15 p) m) v18) v19) v32) v33) ==> (!_13. (!p m v18 v19 v32. happ (happ (happ (happ (happ _13 p) m) v18) v19) v32 = happ (happ (happ (happ (happ _14 p) m) v18) v19) v32) ==> (!_12. (!p m v18 v19 v30 v31. happ (happ (happ (happ (happ (happ _12 p) m) v18) v19) v30) v31 = h4/combin/I (happ (happ (happ (happ h4/patricia/Branch p) m) (happ (happ h4/patricia/Leaf v18) v19)) (happ (happ h4/patricia/Leaf v30) v31))) ==> (!_11. (!p m v18 v19 v30. happ (happ (happ (happ (happ _11 p) m) v18) v19) v30 = happ (happ (happ (happ (happ _12 p) m) v18) v19) v30) ==> (!_10. (!t p m v18 v19. happ (happ (happ (happ (happ _10 t) p) m) v18) v19 = h4/patricia/ptree__CASE t (h4/combin/I (happ (happ h4/patricia/Leaf v18) v19)) (happ (happ (happ (happ _11 p) m) v18) v19) (happ (happ (happ (happ _13 p) m) v18) v19)) ==> (!_9. (!t p m v18. happ (happ (happ (happ _9 t) p) m) v18 = happ (happ (happ (happ _10 t) p) m) v18) ==> (!_8. (!v4 p m t. happ (happ (happ (happ _8 v4) p) m) t = h4/patricia/ptree__CASE v4 (h4/combin/I t) (happ (happ (happ _9 t) p) m) (happ (happ (happ _17 t) p) m)) ==> (!_7. (!p m v4. happ (happ (happ _7 p) m) v4 = happ (happ (happ _8 v4) p) m) ==> (!_6. (!p m v3. happ (happ (happ _6 p) m) v3 = h4/pair/pair__CASE v3 (happ (happ _7 p) m)) ==> (!_5. (!p m. happ (happ _5 p) m = happ (happ _6 p) m) ==> (!_4. (!p v1. happ (happ _4 p) v1 = h4/pair/pair__CASE v1 (happ _5 p)) ==> (!_3. (!p. happ _3 p = happ _4 p) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!BRANCH. happ _1 BRANCH = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/patricia/BRANCH = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))))))))))))))
% Assm [h4s_bools_IMPu_u_CLAUSESu_c4]: !t. t ==> F <=> ~t
% Assm [h4s_patricias_MEMu_u_TRAVERSEu_u_PEEK]: !t k. h4/patricia/IS__PTREE t ==> (h4/bool/IN k (h4/list/LIST__TO__SET (h4/patricia/TRAVERSE t)) <=> h4/option/IS__SOME (h4/patricia/PEEK t k))
% Assm [h4s_bools_EQu_u_REFL]: !x. x = x
% Assm [h4s_patricias_PTREEu_u_EQ]: !t2 t1. h4/patricia/IS__PTREE t1 /\ h4/patricia/IS__PTREE t2 ==> ((!k. h4/patricia/PEEK t1 k = h4/patricia/PEEK t2 k) <=> t1 = t2)
% Assm [h4s_patricias_TRANSFORMu_u_ISu_u_PTREE]: !t f. h4/patricia/IS__PTREE t ==> h4/patricia/IS__PTREE (h4/patricia/TRANSFORM f t)
% Assm [h4s_bools_BOOLu_u_EQu_u_DISTINCTu_c0]: ~(T <=> F)
% Assm [h4s_sats_ANDu_u_INV2]: !A. (~A ==> F) ==> (A ==> F) ==> F
% Assm [h4s_sats_pthu_u_nn]: !p. ~ ~p ==> p
% Assm [h4s_sats_dcu_u_eq]: !r q p. (p <=> q <=> r) <=> (p \/ q \/ r) /\ (p \/ ~r \/ ~q) /\ (q \/ ~r \/ ~p) /\ (r \/ ~q \/ ~p)
% Assm [h4s_sats_ANDu_u_INVu_u_IMP]: !A. A ==> ~A ==> F
% Assm [h4s_options_ISu_u_SOMEu_u_DEFu_c1]: h4/option/IS__SOME h4/option/NONE <=> F
% Assm [h4s_options_ISu_u_SOMEu_u_DEFu_c0]: !x. h4/option/IS__SOME (h4/option/SOME x) <=> T
% Assm [h4s_options_NOTu_u_NONEu_u_SOME]: !x. ~(h4/option/NONE = h4/option/SOME x)
% Assm [h4s_sats_pthu_u_no2]: !q p. ~(p \/ q) ==> ~q
% Assm [h4s_options_optionu_u_nchotomy]: !opt. opt = h4/option/NONE \/ (?x. opt = h4/option/SOME x)
% Assm [h4s_ones_one1]: !v. v = h4/one/one0
% 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_ni1]: !q p. ~(p ==> q) ==> p
% Assm [h4s_sats_ORu_u_DUAL3]: !B A. ~(~A \/ B) ==> F <=> A ==> ~B ==> F
% Assm [h4s_sats_dcu_u_imp]: !r q p. (p <=> q ==> r) <=> (p \/ q) /\ (p \/ ~r) /\ (~q \/ r \/ ~p)
% Assm [h4s_sats_ORu_u_DUAL2]: !B A. ~(A \/ B) ==> F <=> (A ==> F) ==> ~B ==> F
% Assm [h4s_sats_NOTu_u_NOT]: !t. ~ ~t <=> t
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_patricias_PEEKu_u_tupledu_u_primitiveu_u_def]: !_10. (!PEEK__tupled m l k r. happ (happ (happ (happ (happ _10 PEEK__tupled) m) l) k) r = h4/combin/I (happ PEEK__tupled (h4/pair/_2C (h4/bool/COND (h4/bit/BIT m k) l r) k))) ==> (!_9. (!PEEK__tupled m k l. happ (happ (happ (happ _9 PEEK__tupled) m) k) l = happ (happ (happ (happ _10 PEEK__tupled) m) l) k) ==> (!_8. (!PEEK__tupled k m. happ (happ (happ _8 PEEK__tupled) k) m = happ (happ (happ _9 PEEK__tupled) m) k) ==> (!_7. (!PEEK__tupled k p. happ (happ (happ _7 PEEK__tupled) k) p = happ (happ _8 PEEK__tupled) k) ==> (!_6. (!k j d. ?v. (v <=> k = j) /\ happ (happ (happ _6 k) j) d = h4/combin/I (h4/bool/COND v (h4/option/SOME d) h4/option/NONE)) ==> (!_5. (!k j. happ (happ _5 k) j = happ (happ _6 k) j) ==> (!_4. (!v PEEK__tupled k. happ (happ (happ _4 v) PEEK__tupled) k = h4/patricia/ptree__CASE v (h4/combin/I h4/option/NONE) (happ _5 k) (happ (happ _7 PEEK__tupled) k)) ==> (!_3. (!PEEK__tupled v. happ (happ _3 PEEK__tupled) v = happ (happ _4 v) PEEK__tupled) ==> (!_2. (!PEEK__tupled a. happ (happ _2 PEEK__tupled) a = h4/pair/pair__CASE a (happ _3 PEEK__tupled)) ==> (!_1. (!PEEK__tupled. happ _1 PEEK__tupled = happ _2 PEEK__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!p r l k m. happ (happ R (h4/pair/_2C (h4/bool/COND (h4/bit/BIT m k) l r) k)) (h4/pair/_2C (happ (happ (happ (happ h4/patricia/Branch p) m) l) r) k))) ==> h4/patricia/PEEK__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))
% Assm [h4s_patricias_PEEKu_u_curriedu_u_def]: !x1 x. h4/patricia/PEEK x x1 = happ h4/patricia/PEEK__tupled (h4/pair/_2C x x1)
% Assm [h4s_patricias_ptreeu_u_sizeu_u_defu_c2]: !f a3 a2 a1 a0. h4/patricia/ptree__size f (happ (happ (happ (happ h4/patricia/Branch a0) a1) a2) a3) = h4/arithmetic/_2B (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) (h4/arithmetic/_2B a0 (h4/arithmetic/_2B a1 (h4/arithmetic/_2B (h4/patricia/ptree__size f a2) (h4/patricia/ptree__size f a3))))
% Assm [h4s_bools_CONDu_u_CLAUSESu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_CONDu_u_CLAUSESu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 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_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_numerals_numeralu_u_distribu_c1]: !n. h4/arithmetic/_2B n h4/num/0 = n
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% Assm [h4s_arithmetics_ADDu_u_ASSOC]: !p n m. h4/arithmetic/_2B m (h4/arithmetic/_2B n p) = h4/arithmetic/_2B (h4/arithmetic/_2B m n) p
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_pairs_UNCURRYu_u_DEF]: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = happ (happ f x) y
% Assm [h4s_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_relations_RESTRICTu_u_LEMMA]: !z y f R. happ (happ R y) z ==> happ (h4/relation/RESTRICT f R z) y = happ f y
% Assm [h4s_relations_invu_u_imageu_u_def]: !f R x x'. happ (happ (h4/relation/inv__image R f) x) x' <=> happ (happ R (happ f x)) (happ f x')
% Assm [h4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ]: !p n m. happ (happ h4/prim__rec/_3C (h4/arithmetic/_2B m p)) (h4/arithmetic/_2B n p) <=> happ (happ h4/prim__rec/_3C m) n
% Assm [h4s_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm [h4s_options_optionu_u_caseu_u_defu_c1]: !x v f. h4/option/option__CASE (h4/option/SOME x) v f = happ f x
% Assm [h4s_options_optionu_u_caseu_u_defu_c0]: !v f. h4/option/option__CASE h4/option/NONE v f = v
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c1]: !t2 t1. h4/bool/COND F t1 t2 = t2
% Assm [h4s_bools_boolu_u_caseu_u_thmu_c0]: !t2 t1. h4/bool/COND T t1 t2 = t1
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Goal: !f_27 f M_27 M. M = M_27 /\ (!a0 a1. M_27 = happ (happ h4/patricia__casts/Word__ptree a0) a1 ==> happ (happ f a0) a1 = happ (happ f_27 a0) a1) ==> h4/patricia__casts/word__ptree__CASE M f = h4/patricia__casts/word__ptree__CASE M_27 f_27
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q1295107,TV_Q1295103]: ![V_f, V_g]: (![V_x]: s(TV_Q1295103,happ(s(t_fun(TV_Q1295107,TV_Q1295103),V_f),s(TV_Q1295107,V_x))) = s(TV_Q1295103,happ(s(t_fun(TV_Q1295107,TV_Q1295103),V_g),s(TV_Q1295107,V_x))) => s(t_fun(TV_Q1295107,TV_Q1295103),V_f) = s(t_fun(TV_Q1295107,TV_Q1295103),V_g))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_TYu_u_DEF, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_1]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_1),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),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(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_0),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_a0u_27)))) <=> ![V_uu_27wordu_u_ptreeu_27]: (![V_a0u_270]: (?[V_a0, V_a1]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_1))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_27wordu_u_ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_27wordu_u_ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),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(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_0),s(t_fun(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_rep))))))).
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_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_patriciau_u_castss_Wordu_u_ptree0, axiom, ![TV_u_27a,TV_u_27b]: s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree) = s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts0)).
fof(ah4s_patriciau_u_castss_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatriciau_u_u_u_casts0u_u_u_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts0),s(t_fun(TV_u_27a,t_h4s_ones_one),V_x))),s(t_h4s_patricias_ptree(TV_u_27b),V_x0))) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_h4s_ones_one),V_x),s(t_h4s_patricias_ptree(TV_u_27b),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_0))))))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_repfnsu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27wordu_u_ptreeu_27]: (![V_a0u_270]: (?[V_a0, V_a1]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)),h4s_pairs_u_2c(s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b)))),V_uu_0))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_27wordu_u_ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),t_bool),V_uu_27wordu_u_ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts2(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),V_r)))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_caseu_u_def, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_f, V_a1, V_a0]: s(TV_u_27c,h4s_patriciau_u_castss_wordu_u_ptreeu_u_case(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))),s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_f))) = s(TV_u_27c,happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_f),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1)))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_sizeu_u_def, axiom, ![TV_u_27a,TV_u_27b]: ![V_f1, V_f, V_a1, V_a0]: s(t_h4s_nums_num,h4s_patriciau_u_castss_wordu_u_ptreeu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_fun(TV_u_27b,t_h4s_nums_num),V_f1),s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))))) = 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_patricias_ptreeu_u_size(s(t_fun(TV_u_27b,t_h4s_nums_num),V_f1),s(t_h4s_patricias_ptree(TV_u_27b),V_a1)))))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_11, axiom, ![TV_u_27a,TV_u_27b]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0u_27))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1u_27))) <=> (s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0) = s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0u_27) & s(t_h4s_patricias_ptree(TV_u_27b),V_a1) = s(t_h4s_patricias_ptree(TV_u_27b),V_a1u_27)))).
fof(ah4s_patriciau_u_castss_wordu_u_ptreeu_u_repfnsu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_a]: s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts1(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_fun(TV_u_27a,t_h4s_ones_one),t_h4s_patricias_ptree(TV_u_27b))),h4s_patriciau_u_castss_u_20u_40indu_u_typepatriciau_u_casts2(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_a))))) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_a)).
fof(ah4s_pairs_FST0, axiom, ![TV_u_27b,TV_u_27a]: ![V_y, V_x]: s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27a,V_x)).
fof(ah4s_pairs_SND0, axiom, ![TV_u_27a,TV_u_27b]: ![V_y, V_x]: s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,V_x),s(TV_u_27b,V_y))))) = s(TV_u_27b,V_y)).
fof(ah4s_indu_u_types_CONSTRu_u_REC, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_0]: (![V_f, V_r, V_n]: s(TV_u_27b,happ(s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_h4s_nums_num,V_n))) = s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r),s(t_h4s_nums_num,V_n))))) => ![V_Fn]: ?[V_f]: ![V_c, V_i, V_r]: s(TV_u_27b,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f),s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,V_c),s(TV_u_27a,V_i),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))) = s(TV_u_27b,happ(s(t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)),happ(s(t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_fun(t_h4s_nums_num,TV_u_27b),TV_u_27b)))),V_Fn),s(t_h4s_nums_num,V_c))),s(TV_u_27a,V_i))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))),s(t_fun(t_h4s_nums_num,TV_u_27b),happ(s(t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b)),happ(s(t_fun(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),t_fun(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),t_fun(t_h4s_nums_num,TV_u_27b))),V_uu_0),s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),TV_u_27b),V_f))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_r))))))).
fof(ah4s_indu_u_types_FCONS0u_c0, axiom, ![TV_u_27a]: ![V_f, V_a]: s(TV_u_27a,happ(s(t_fun(t_h4s_nums_num,TV_u_27a),h4s_indu_u_types_fcons(s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,TV_u_27a),V_f))),s(t_h4s_nums_num,h4s_nums_0))) = s(TV_u_27a,V_a)).
fof(ah4s_bools_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_bools_TRUTH, axiom, p(s(t_bool,t))).
fof(ah4s_bools_DATATYPEu_u_TAGu_u_THM, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_bools_datatype(s(TV_u_27a,V_x))) = s(t_bool,t)).
fof(ah4s_patriciau_u_castss_datatypeu_u_wordu_u_ptree, axiom, ![TV_u_27a,TV_u_27b]: ![V_wordu_u_ptree]: p(s(t_bool,h4s_bools_datatype(s(t_bool,happ(s(t_fun(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),t_bool),V_wordu_u_ptree),s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree))))))).
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_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_ones_oneu_u_axiom, axiom, ![TV_u_27a]: ![V_g, V_f]: s(t_fun(TV_u_27a,t_h4s_ones_one),V_f) = s(t_fun(TV_u_27a,t_h4s_ones_one),V_g)).
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_ones_oneu_u_TYu_u_DEF, axiom, ![V_uu_0]: (![V_b]: s(t_bool,happ(s(t_fun(t_bool,t_bool),V_uu_0),s(t_bool,V_b))) = s(t_bool,V_b) => ?[V_rep]: p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(t_bool,t_bool),V_uu_0),s(t_fun(t_h4s_ones_one,t_bool),V_rep)))))).
fof(ah4s_bools_TYPEu_u_DEFINITIONu_u_THM, axiom, ![TV_u_27a,TV_u_27b]: ![V_rep, V_P]: (p(s(t_bool,h4s_bools_typeu_u_definition(s(t_fun(TV_u_27a,t_bool),V_P),s(t_fun(TV_u_27b,TV_u_27a),V_rep)))) <=> (![V_xu_27, V_xu_27u_27]: (s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27))) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27u_27))) => s(TV_u_27b,V_xu_27) = s(TV_u_27b,V_xu_27u_27)) & ![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) <=> ?[V_xu_27]: s(TV_u_27a,V_x) = s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_rep),s(TV_u_27b,V_xu_27))))))).
fof(ah4s_patricias_TRAVERSEu_u_TRANSFORM, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_f]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_t))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_t)))).
fof(ah4s_patricias_TRANSFORMu_u_BRANCH, axiom, ![TV_u_27b,TV_u_27a]: ![V_r, V_p, V_m, V_l, V_f]: s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),h4s_patricias_branch),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_p),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_patricias_ptree(TV_u_27a),V_r))))))))))) = s(t_h4s_patricias_ptree(TV_u_27b),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b)))),t_h4s_patricias_ptree(TV_u_27b)),h4s_patricias_branch),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_p),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_m),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_r)))))))))))).
fof(ah4s_patricias_PTREEu_u_TRAVERSEu_u_EQ, axiom, ![TV_u_27a,TV_u_27b]: ![V_t2, V_t1]: ((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t1)))) & p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27b),V_t2))))) => (![V_k]: s(t_bool,h4s_bools_in(s(t_h4s_nums_num,V_k),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_t1))))))) = s(t_bool,h4s_bools_in(s(t_h4s_nums_num,V_k),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27b),V_t2))))))) <=> s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_t1))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27b),V_t2)))))).
fof(ah4s_patricias_PEEKu_u_TRANSFORM, axiom, ![TV_u_27a,TV_u_27b]: ![V_uu_0]: (![V_f, V_x]: s(t_h4s_options_option(TV_u_27b),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27b),h4s_options_some(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))) => ![V_t, V_k, V_f]: s(t_h4s_options_option(TV_u_27b),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_k))) = s(t_h4s_options_option(TV_u_27b),h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27a),V_t),s(t_h4s_nums_num,V_k))),s(t_h4s_options_option(TV_u_27b),h4s_options_none),s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,t_h4s_options_option(TV_u_27b))),V_uu_0),s(t_fun(TV_u_27a,TV_u_27b),V_f))))))).
fof(ah4s_patricias_TRANSFORMu_u_EMPTY, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_f]: (s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_t))) = s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_empty) <=> s(t_h4s_patricias_ptree(TV_u_27a),V_t) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty))).
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_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_patricias_TRANSFORMu_u_defu_c1, axiom, ![TV_u_27a,TV_u_27b]: ![V_j, V_f, V_d]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_transform(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_patricias_ptree(TV_u_27b),happ(s(t_fun(TV_u_27b,t_h4s_patricias_ptree(TV_u_27b)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27b,t_h4s_patricias_ptree(TV_u_27b))),h4s_patricias_leaf),s(t_h4s_nums_num,V_j))),s(TV_u_27b,V_d))))) = s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_j))),s(TV_u_27a,happ(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(TV_u_27b,V_d)))))).
fof(ah4s_patricias_TRANSFORMu_u_defu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_f]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_transform(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_empty))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty)).
fof(ah4s_patricias_Empty0, axiom, ![TV_u_27a]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia0)).
fof(ah4s_patricias_ptreeu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_patricias_u_20u_40indu_u_typepatricia4(s(t_h4s_patricias_ptree(TV_u_27a),V_a))))) = s(t_h4s_patricias_ptree(TV_u_27a),V_a)).
fof(ah4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia2u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_bottom) => ![V_x, V_xi_, V_x0, V_xi_0]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_u_20u_40indu_u_typepatricia2),s(t_h4s_nums_num,V_x))),s(t_h4s_nums_num,V_xi_))),s(t_h4s_patricias_ptree(TV_u_27a),V_x0))),s(t_h4s_patricias_ptree(TV_u_27a),V_xi_0))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),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(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_nums_num,V_xi_))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_patricias_u_20u_40indu_u_typepatricia4(s(t_h4s_patricias_ptree(TV_u_27a),V_x0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_patricias_u_20u_40indu_u_typepatricia4(s(t_h4s_patricias_ptree(TV_u_27a),V_xi_0))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))))))))))).
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_patricias_Leaf0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf) = s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_u_20u_40indu_u_typepatricia1)).
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_patricias_TRANSFORMu_u_defu_c2, axiom, ![TV_u_27a,TV_u_27b]: ![V_r, V_p, V_m, V_l, V_f]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_transform(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_patricias_ptree(TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27b),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27b),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patricias_ptree(TV_u_27b))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27b),V_l))),s(t_h4s_patricias_ptree(TV_u_27b),V_r))))) = s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_transform(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_patricias_ptree(TV_u_27b),V_l))))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_transform(s(t_fun(TV_u_27b,TV_u_27a),V_f),s(t_h4s_patricias_ptree(TV_u_27b),V_r)))))).
fof(ah4s_patricias_Branch0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_u_20u_40indu_u_typepatricia2)).
fof(ah4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_bottom) => s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia0) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bools_arb),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_nums_num,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))))))).
fof(ah4s_patricias_hiddenu_u_u_u_20u_u_40indu_u_u_u_typepatricia1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_bottom) => ![V_x, V_x0]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_u_20u_40indu_u_typepatricia1),s(t_h4s_nums_num,V_x))),s(TV_u_27a,V_x0))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),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(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,V_x0),s(t_h4s_nums_num,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))))))).
fof(ah4s_patricias_ptreeu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27ptreeu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,h4s_bools_arb),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_nums_num,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))) | (?[V_a0, V_a1]: s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),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(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_a0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,V_a1),s(t_h4s_nums_num,h4s_bools_arb))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))) | ?[V_a0, V_a1, V_a2, V_a3]: (s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a0u_270) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),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(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_a0),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num),h4s_pairs_u_2c(s(TV_u_27a,h4s_bools_arb),s(t_h4s_nums_num,V_a1))))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a3),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num)))),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),t_bool),V_uu_27ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a2)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),t_bool),V_uu_27ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a3)))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),t_bool),V_uu_27ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),t_bool),V_uu_27ptreeu_27),s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),h4s_patricias_u_20u_40indu_u_typepatricia4(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_u_20u_40indu_u_typepatricia3(s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_r))))) = s(t_h4s_indu_u_types_recspace(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(TV_u_27a,t_h4s_nums_num))),V_r)))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_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_c2, axiom, (~ (p(s(t_bool,f0))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_EQu_u_SYMu_u_EQ, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_y) <=> s(TV_u_27a,V_y) = s(TV_u_27a,V_x))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f0)) => p(s(t_bool,V_t)))).
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_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_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_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f0) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_patricias_ptreeu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a3, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_a0))),s(t_h4s_nums_num,V_a1))),s(t_h4s_patricias_ptree(TV_u_27a),V_a2))),s(t_h4s_patricias_ptree(TV_u_27a),V_a3))),s(TV_u_27b,V_v),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27b)),V_f),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b)))),V_f1))) = s(TV_u_27b,happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b)))),V_f1),s(t_h4s_nums_num,V_a0))),s(t_h4s_nums_num,V_a1))),s(t_h4s_patricias_ptree(TV_u_27a),V_a2))),s(t_h4s_patricias_ptree(TV_u_27a),V_a3)))).
fof(ah4s_patricias_ptreeu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f1, V_f]: s(TV_u_27b,h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty),s(TV_u_27b,V_v),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27b)),V_f),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b)))),V_f1))) = s(TV_u_27b,V_v)).
fof(ah4s_relations_WFRECu_u_COROLLARY, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_M]: (s(t_fun(TV_u_27a,TV_u_27b),V_f) = s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_wfrec(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M))) => (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R)))) => ![V_x]: s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_fun(TV_u_27a,TV_u_27b),t_fun(TV_u_27a,TV_u_27b)),V_M),s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_x))))),s(TV_u_27a,V_x)))))).
fof(ah4s_patricias_ptreeu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_a0))),s(TV_u_27a,V_a1))),s(TV_u_27b,V_v),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27b)),V_f),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),TV_u_27b)))),V_f1))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,TV_u_27b)),V_f),s(t_h4s_nums_num,V_a0))),s(TV_u_27a,V_a1)))).
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_pairs_pairu_u_caseu_u_thm, axiom, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_y, V_x, V_f]: s(TV_u_27a,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27b,TV_u_27c),h4s_pairs_u_2c(s(TV_u_27b,V_x),s(TV_u_27c,V_y))),s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f))) = s(TV_u_27a,happ(s(t_fun(TV_u_27c,TV_u_27a),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27c,TV_u_27a)),V_f),s(TV_u_27b,V_x))),s(TV_u_27c,V_y)))).
fof(ah4s_options_SOMEu_u_11, axiom, ![TV_u_27a]: ![V_y, V_x]: (s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_y))) <=> s(TV_u_27a,V_x) = s(TV_u_27a,V_y))).
fof(ah4s_patricias_TRAVERSEu_u_defu_c2, axiom, ![TV_u_27a]: ![V_r, V_p, V_m, V_l]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_patricias_ptree(TV_u_27a),V_r))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_append(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_r)))))).
fof(ah4s_patricias_TRAVERSEu_u_defu_c1, axiom, ![TV_u_27a]: ![V_j, V_d]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_j))),s(TV_u_27a,V_d))))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_cons(s(t_h4s_nums_num,V_j),s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)))).
fof(ah4s_lists_APPENDu_u_11u_c0, axiom, ![TV_u_27a]: ![V_l3, V_l2, V_l1]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l3))) <=> s(t_h4s_lists_list(TV_u_27a),V_l2) = s(t_h4s_lists_list(TV_u_27a),V_l3))).
fof(ah4s_lists_CONSu_u_11, axiom, ![TV_u_27a]: ![V_a1u_27, V_a1, V_a0u_27, V_a0]: (s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0),s(t_h4s_lists_list(TV_u_27a),V_a1))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_a0u_27),s(t_h4s_lists_list(TV_u_27a),V_a1u_27))) <=> (s(TV_u_27a,V_a0) = s(TV_u_27a,V_a0u_27) & s(t_h4s_lists_list(TV_u_27a),V_a1) = s(t_h4s_lists_list(TV_u_27a),V_a1u_27)))).
fof(ah4s_patricias_TRAVERSEu_u_defu_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_empty))) = s(t_h4s_lists_list(t_h4s_nums_num),h4s_lists_nil)).
fof(ah4s_relations_WFu_u_EMPTYu_u_REL, axiom, ![TV_u_27a]: p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_emptyu_u_rel))))).
fof(ah4s_patricias_BRANCHu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_26]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v44, V_v45, V_v46, V_v47]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_26),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))),s(t_h4s_patricias_ptree(TV_u_27a),V_v46))),s(t_h4s_patricias_ptree(TV_u_27a),V_v47))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))),s(t_h4s_patricias_ptree(TV_u_27a),V_v46))),s(t_h4s_patricias_ptree(TV_u_27a),V_v47))))))) => ![V_uu_25]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v44, V_v45, V_v46]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_25),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))),s(t_h4s_patricias_ptree(TV_u_27a),V_v46))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_26),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))),s(t_h4s_patricias_ptree(TV_u_27a),V_v46))) => ![V_uu_24]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v44, V_v45]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_24),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_25),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))),s(t_h4s_nums_num,V_v45))) => ![V_uu_23]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v44]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_23),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_24),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v44))) => ![V_uu_22]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v42, V_v43]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_22),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v42))),s(TV_u_27a,V_v43))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_v42))),s(TV_u_27a,V_v43))))))) => ![V_uu_21]: (![V_p, V_m, V_v20, V_v21, V_v22, V_v23, V_v42]: s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_21),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v42))) = s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_22),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_h4s_nums_num,V_v42))) => ![V_uu_20]: (![V_t, V_p, V_m, V_v20, V_v21, V_v22, V_v23]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_20),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),V_t),s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_21),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))))),V_uu_23),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))),s(t_h4s_patricias_ptree(TV_u_27a),V_v23))))) => ![V_uu_19]: (![V_t, V_p, V_m, V_v20, V_v21, V_v22]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_19),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_20),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))),s(t_h4s_patricias_ptree(TV_u_27a),V_v22))) => ![V_uu_18]: (![V_t, V_p, V_m, V_v20, V_v21]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_18),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_19),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))),s(t_h4s_nums_num,V_v21))) => ![V_uu_17]: (![V_t, V_p, V_m, V_v20]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_17),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_18),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v20))) => ![V_uu_16]: (![V_p, V_m, V_v18, V_v19, V_v32, V_v33, V_v34, V_v35]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_16),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))),s(t_h4s_patricias_ptree(TV_u_27a),V_v34))),s(t_h4s_patricias_ptree(TV_u_27a),V_v35))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))),s(t_h4s_patricias_ptree(TV_u_27a),V_v34))),s(t_h4s_patricias_ptree(TV_u_27a),V_v35))))))) => ![V_uu_15]: (![V_p, V_m, V_v18, V_v19, V_v32, V_v33, V_v34]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_15),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))),s(t_h4s_patricias_ptree(TV_u_27a),V_v34))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_16),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))),s(t_h4s_patricias_ptree(TV_u_27a),V_v34))) => ![V_uu_14]: (![V_p, V_m, V_v18, V_v19, V_v32, V_v33]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_14),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_15),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))),s(t_h4s_nums_num,V_v33))) => ![V_uu_13]: (![V_p, V_m, V_v18, V_v19, V_v32]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_13),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_14),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v32))) => ![V_uu_12]: (![V_p, V_m, V_v18, V_v19, V_v30, V_v31]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),V_uu_12),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v30))),s(TV_u_27a,V_v31))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))))),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_v30))),s(TV_u_27a,V_v31))))))) => ![V_uu_11]: (![V_p, V_m, V_v18, V_v19, V_v30]: s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),V_uu_11),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v30))) = s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),V_uu_12),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_h4s_nums_num,V_v30))) => ![V_uu_10]: (![V_t, V_p, V_m, V_v18, V_v19]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),V_uu_10),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),V_t),s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),h4s_patricias_leaf),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))))),V_uu_11),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))))),V_uu_13),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))),s(TV_u_27a,V_v19))))) => ![V_uu_9]: (![V_t, V_p, V_m, V_v18]: s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),V_uu_9),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))) = s(t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),V_uu_10),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_v18))) => ![V_uu_8]: (![V_v4, V_p, V_m, V_t]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),V_uu_8),s(t_h4s_patricias_ptree(TV_u_27a),V_v4))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_t))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),V_v4),s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a)))))),V_uu_9),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))))))),V_uu_17),s(t_h4s_patricias_ptree(TV_u_27a),V_t))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))))) => ![V_uu_7]: (![V_p, V_m, V_v4]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),V_uu_7),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_v4))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),V_uu_8),s(t_h4s_patricias_ptree(TV_u_27a),V_v4))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))) => ![V_uu_6]: (![V_p, V_m, V_v3]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_6),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),V_v3))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),V_v3),s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),V_uu_7),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))))) => ![V_uu_5]: (![V_p, V_m]: s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_5),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))) = s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_6),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))) => ![V_uu_4]: (![V_p, V_v1]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_p))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),V_v1))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),V_v1),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_5),s(t_h4s_nums_num,V_p))))) => ![V_uu_3]: (![V_p]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_3),s(t_h4s_nums_num,V_p))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_4),s(t_h4s_nums_num,V_p))) => ![V_uu_2]: (![V_a]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),V_a))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),V_a),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_3))) => ![V_uu_1]: (![V_BRANCH]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),V_BRANCH))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),h4s_patricias_branch) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),t_h4s_patricias_ptree(TV_u_27a))),V_uu_1))))))))))))))))))))))))))))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_patricias_MEMu_u_TRAVERSEu_u_PEEK, axiom, ![TV_u_27a]: ![V_t, V_k]: (p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t)))) => s(t_bool,h4s_bools_in(s(t_h4s_nums_num,V_k),s(t_fun(t_h4s_nums_num,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(t_h4s_nums_num),h4s_patricias_traverse(s(t_h4s_patricias_ptree(TV_u_27a),V_t))))))) = s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27a),V_t),s(t_h4s_nums_num,V_k))))))).
fof(ah4s_bools_EQu_u_REFL, axiom, ![TV_u_27a]: ![V_x]: s(TV_u_27a,V_x) = s(TV_u_27a,V_x)).
fof(ah4s_patricias_PTREEu_u_EQ, axiom, ![TV_u_27a]: ![V_t2, V_t1]: ((p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t1)))) & p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t2))))) => (![V_k]: s(t_h4s_options_option(TV_u_27a),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27a),V_t1),s(t_h4s_nums_num,V_k))) = s(t_h4s_options_option(TV_u_27a),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27a),V_t2),s(t_h4s_nums_num,V_k))) <=> s(t_h4s_patricias_ptree(TV_u_27a),V_t1) = s(t_h4s_patricias_ptree(TV_u_27a),V_t2)))).
fof(ah4s_patricias_TRANSFORMu_u_ISu_u_PTREE, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_f]: (p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27a),V_t)))) => p(s(t_bool,h4s_patricias_isu_u_ptree(s(t_h4s_patricias_ptree(TV_u_27b),h4s_patricias_transform(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_t)))))))).
fof(ah4s_bools_BOOLu_u_EQu_u_DISTINCTu_c0, axiom, ~ (s(t_bool,t) = s(t_bool,f0))).
fof(ah4s_sats_ANDu_u_INV2, axiom, ![V_A]: ((~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))) => ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => p(s(t_bool,f0))))).
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_eq, axiom, ![V_r, V_q, V_p]: ((p(s(t_bool,V_p)) <=> s(t_bool,V_q) = s(t_bool,V_r)) <=> ((p(s(t_bool,V_p)) | (p(s(t_bool,V_q)) | p(s(t_bool,V_r)))) & ((p(s(t_bool,V_p)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_q))))) & ((p(s(t_bool,V_q)) | (~ (p(s(t_bool,V_r))) | ~ (p(s(t_bool,V_p))))) & (p(s(t_bool,V_r)) | (~ (p(s(t_bool,V_q))) | ~ (p(s(t_bool,V_p)))))))))).
fof(ah4s_sats_ANDu_u_INVu_u_IMP, axiom, ![V_A]: (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_A))) => p(s(t_bool,f0))))).
fof(ah4s_options_ISu_u_SOMEu_u_DEFu_c1, axiom, ![TV_u_27a]: s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),h4s_options_none))) = s(t_bool,f0)).
fof(ah4s_options_ISu_u_SOMEu_u_DEFu_c0, axiom, ![TV_u_27a]: ![V_x]: s(t_bool,h4s_options_isu_u_some(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))) = s(t_bool,t)).
fof(ah4s_options_NOTu_u_NONEu_u_SOME, axiom, ![TV_u_27a]: ![V_x]: ~ (s(t_h4s_options_option(TV_u_27a),h4s_options_none) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
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_options_optionu_u_nchotomy, axiom, ![TV_u_27a]: ![V_opt]: (s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_none) | ?[V_x]: s(t_h4s_options_option(TV_u_27a),V_opt) = s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))))).
fof(ah4s_ones_one1, axiom, ![V_v]: s(t_h4s_ones_one,V_v) = s(t_h4s_ones_one,h4s_ones_one0)).
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_ni1, axiom, ![V_q, V_p]: (~ ((p(s(t_bool,V_p)) => p(s(t_bool,V_q)))) => p(s(t_bool,V_p)))).
fof(ah4s_sats_ORu_u_DUAL3, axiom, ![V_B, V_A]: ((~ ((~ (p(s(t_bool,V_A))) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> (p(s(t_bool,V_A)) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
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_ORu_u_DUAL2, axiom, ![V_B, V_A]: ((~ ((p(s(t_bool,V_A)) | p(s(t_bool,V_B)))) => p(s(t_bool,f0))) <=> ((p(s(t_bool,V_A)) => p(s(t_bool,f0))) => (~ (p(s(t_bool,V_B))) => p(s(t_bool,f0)))))).
fof(ah4s_sats_NOTu_u_NOT, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,t))) <=> p(s(t_bool,t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t))) <=> p(s(t_bool,f0)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f0) <=> ~ (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,f0))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f0)))).
fof(ah4s_patricias_PEEKu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_10]: (![V_PEEKu_u_tupled, V_m, V_l, V_k, V_r]: s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_10),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_nums_num,V_k))),s(t_h4s_patricias_ptree(TV_u_27a),V_r))) = s(t_h4s_options_option(TV_u_27a),h4s_combins_i(s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k))),s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_patricias_ptree(TV_u_27a),V_r))),s(t_h4s_nums_num,V_k))))))) => ![V_uu_9]: (![V_PEEKu_u_tupled, V_m, V_k, V_l]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_k))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_10),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_nums_num,V_k))) => ![V_uu_8]: (![V_PEEKu_u_tupled, V_k, V_m]: s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_m))) = s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_9),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_k))) => ![V_uu_7]: (![V_PEEKu_u_tupled, V_k, V_p]: s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_p))) = s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),V_uu_8),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_k))) => ![V_uu_6]: (![V_k, V_j, V_d]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_k) = s(t_h4s_nums_num,V_j)) & s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)))),V_uu_6),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_j))),s(TV_u_27a,V_d))) = s(t_h4s_options_option(TV_u_27a),h4s_combins_i(s(t_h4s_options_option(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_d))),s(t_h4s_options_option(TV_u_27a),h4s_options_none)))))) => ![V_uu_5]: (![V_k, V_j]: s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)))),V_uu_5),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_j))) = s(t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)))),V_uu_6),s(t_h4s_nums_num,V_k))),s(t_h4s_nums_num,V_j))) => ![V_uu_4]: (![V_v, V_PEEKu_u_tupled, V_k]: s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)))),V_uu_4),s(t_h4s_patricias_ptree(TV_u_27a),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_k))) = s(t_h4s_options_option(TV_u_27a),h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),V_v),s(t_h4s_options_option(TV_u_27a),h4s_combins_i(s(t_h4s_options_option(TV_u_27a),h4s_options_none))),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_options_option(TV_u_27a)))),V_uu_5),s(t_h4s_nums_num,V_k))),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_options_option(TV_u_27a))))))),V_uu_7),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_nums_num,V_k))))) => ![V_uu_3]: (![V_PEEKu_u_tupled, V_v]: s(t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_patricias_ptree(TV_u_27a),V_v))) = s(t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)))),V_uu_4),s(t_h4s_patricias_ptree(TV_u_27a),V_v))),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))) => ![V_uu_2]: (![V_PEEKu_u_tupled, V_a]: s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),V_a))) = s(t_h4s_options_option(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),V_a),s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_nums_num,t_h4s_options_option(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))))) => ![V_uu_1]: (![V_PEEKu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),V_PEEKu_u_tupled))) => ![V_uu_0]: (![V_R]: (p(s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),V_R)))) <=> (p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),V_R)))) & ![V_p, V_r, V_l, V_k, V_m]: p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k))),s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_patricias_ptree(TV_u_27a),V_r))),s(t_h4s_nums_num,V_k))))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))),s(t_h4s_patricias_ptree(TV_u_27a),V_r))),s(t_h4s_nums_num,V_k)))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),h4s_patricias_peeku_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a))),V_uu_1))))))))))))))).
fof(ah4s_patricias_PEEKu_u_curriedu_u_def, axiom, ![TV_u_27a]: ![V_x1, V_x]: s(t_h4s_options_option(TV_u_27a),h4s_patricias_peek(s(t_h4s_patricias_ptree(TV_u_27a),V_x),s(t_h4s_nums_num,V_x1))) = s(t_h4s_options_option(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),t_h4s_options_option(TV_u_27a)),h4s_patricias_peeku_u_tupled),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_nums_num),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_x),s(t_h4s_nums_num,V_x1)))))).
fof(ah4s_patricias_ptreeu_u_sizeu_u_defu_c2, axiom, ![TV_u_27a]: ![V_f, V_a3, V_a2, V_a1, V_a0]: s(t_h4s_nums_num,h4s_patricias_ptreeu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))))),h4s_patricias_branch0),s(t_h4s_nums_num,V_a0))),s(t_h4s_nums_num,V_a1))),s(t_h4s_patricias_ptree(TV_u_27a),V_a2))),s(t_h4s_patricias_ptree(TV_u_27a),V_a3))))) = 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,V_a0),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_a1),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_patricias_ptreeu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_a2))),s(t_h4s_nums_num,h4s_patricias_ptreeu_u_size(s(t_fun(TV_u_27a,t_h4s_nums_num),V_f),s(t_h4s_patricias_ptree(TV_u_27a),V_a3)))))))))))).
fof(ah4s_bools_CONDu_u_CLAUSESu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_CONDu_u_CLAUSESu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
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,f0)).
fof(ah4s_numerals_numeralu_u_distribu_c27, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_arithmetics_zero)))).
fof(ah4s_arithmetics_ADDu_u_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_numerals_numeralu_u_distribu_c1, axiom, ![V_n]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,V_n)).
fof(ah4s_arithmetics_ZEROu_u_LESSu_u_EQ, axiom, ![V_n]: p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_nums_0),s(t_h4s_nums_num,V_n))))).
fof(ah4s_arithmetics_ADDu_u_ASSOC, axiom, ![V_p, V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,V_p)))).
fof(ah4s_arithmetics_ADDu_u_COMM, 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_arithmetics_NOTu_u_LESS, axiom, ![V_n, V_m]: (~ (p(s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n))))) <=> p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))))).
fof(ah4s_arithmetics_ADDu_u_SYM, axiom, ![V_n, V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n))) = s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_m)))).
fof(ah4s_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_pairs_PAIR, axiom, ![TV_u_27a,TV_u_27b]: ![V_x]: s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),h4s_pairs_u_2c(s(TV_u_27a,h4s_pairs_fst(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))),s(TV_u_27b,h4s_pairs_snd(s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x))))) = s(t_h4s_pairs_prod(TV_u_27a,TV_u_27b),V_x)).
fof(ah4s_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_pairs_UNCURRYu_u_DEF, axiom, ![TV_u_27c,TV_u_27a,TV_u_27b]: ![V_y, V_x, V_f]: s(TV_u_27c,h4s_pairs_uncurry(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),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_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,TV_u_27c)),V_f),s(TV_u_27a,V_x))),s(TV_u_27b,V_y)))).
fof(ah4s_primu_u_recs_WFu_u_LESS, axiom, p(s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c))))).
fof(ah4s_relations_RESTRICTu_u_LEMMA, axiom, ![TV_u_27b,TV_u_27a]: ![V_z, V_y, V_f, V_R]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_y))),s(TV_u_27a,V_z)))) => s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),h4s_relations_restrict(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),V_R),s(TV_u_27a,V_z))),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_relations_invu_u_imageu_u_def, axiom, ![TV_u_27b,TV_u_27a]: ![V_f, V_R, V_x, V_xi_]: s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f))),s(TV_u_27a,V_x))),s(TV_u_27a,V_xi_))) = s(t_bool,happ(s(t_fun(TV_u_27b,t_bool),happ(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x))))),s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_xi_)))))).
fof(ah4s_arithmetics_LESSu_u_MONOu_u_ADDu_u_EQ, axiom, ![V_p, V_n, V_m]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p))))),s(t_h4s_nums_num,h4s_arithmetics_u_2b(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) = s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_bool)),h4s_primu_u_recs_u_3c),s(t_h4s_nums_num,V_m))),s(t_h4s_nums_num,V_n)))).
fof(ah4s_relations_WFu_u_invu_u_image, axiom, ![TV_u_27a,TV_u_27b]: ![V_f, V_R]: (p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R)))) => p(s(t_bool,h4s_relations_wf(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_bool)),h4s_relations_invu_u_image(s(t_fun(TV_u_27b,t_fun(TV_u_27b,t_bool)),V_R),s(t_fun(TV_u_27a,TV_u_27b),V_f)))))))).
fof(ah4s_options_optionu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_x, V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_some(s(TV_u_27a,V_x))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_options_optionu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f]: s(TV_u_27b,h4s_options_optionu_u_case(s(t_h4s_options_option(TV_u_27a),h4s_options_none),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f))) = s(TV_u_27b,V_v)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c1, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,f0),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t2)).
fof(ah4s_bools_boolu_u_caseu_u_thmu_c0, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(TV_u_27a,h4s_bools_cond(s(t_bool,t),s(TV_u_27a,V_t1),s(TV_u_27a,V_t2))) = s(TV_u_27a,V_t1)).
fof(ah4s_bools_IMPu_u_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f0))) <=> s(t_bool,V_t) = s(t_bool,f0))).
fof(ch4s_patriciau_u_castss_wordu_u_ptreeu_u_caseu_u_cong, conjecture, ![TV_u_27a,TV_u_27b,TV_u_27c]: ![V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_M) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_Mu_27) & ![V_a0, V_a1]: (s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_Mu_27) = s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b)),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b))),h4s_patriciau_u_castss_wordu_u_ptree),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))) => s(TV_u_27c,happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_f),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))) = s(TV_u_27c,happ(s(t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c),happ(s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_fu_27),s(t_fun(TV_u_27a,t_h4s_ones_one),V_a0))),s(t_h4s_patricias_ptree(TV_u_27b),V_a1))))) => s(TV_u_27c,h4s_patriciau_u_castss_wordu_u_ptreeu_u_case(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_M),s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_f))) = s(TV_u_27c,h4s_patriciau_u_castss_wordu_u_ptreeu_u_case(s(t_h4s_patriciau_u_castss_wordu_u_ptree(TV_u_27a,TV_u_27b),V_Mu_27),s(t_fun(t_fun(TV_u_27a,t_h4s_ones_one),t_fun(t_h4s_patricias_ptree(TV_u_27b),TV_u_27c)),V_fu_27))))).
