%   ORIGINAL: h4/patricia/ADD__def_c2
% 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/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__CLAUSES_c1: !t. t ==> T <=> T
% 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/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/IMP__F__EQ__F: !t. t ==> F <=> t <=> F
% Assm: h4/bool/AND__IMP__INTRO: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm: h4/bool/IMP__CONG: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm: h4/bool/COND__CONG: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/inv__image__def: !f R. h4/relation/inv__image R f = (\x y. R (f x) (f y))
% Assm: h4/relation/WF__inv__image: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% Assm: h4/relation/RESTRICT__LEMMA: !z y f R. R y z ==> h4/relation/RESTRICT f R z y = f y
% 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/prim__rec/WF__LESS: h4/relation/WF h4/prim__rec/_3C
% Assm: h4/pair/PAIR: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm: h4/pair/FST0: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% Assm: h4/pair/UNCURRY__DEF: !y x f. h4/pair/UNCURRY f (h4/pair/_2C x y) = f x y
% Assm: h4/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x y
% Assm: h4/arithmetic/ADD__CLAUSES_c0: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm: h4/arithmetic/ADD__SYM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm: h4/arithmetic/ADD__COMM: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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/NOT__LESS: !n m. ~h4/prim__rec/_3C m n <=> h4/arithmetic/_3C_3D n m
% Assm: h4/arithmetic/MULT__CLAUSES_c2: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm: h4/arithmetic/LESS__EQ__TRANS: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm: h4/arithmetic/ZERO__LESS__EQ: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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/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/numeral/numeral__lte_c1: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% Assm: h4/patricia/ptree__case__def_c0: !v f1 f. h4/patricia/ptree__CASE h4/patricia/Empty v f f1 = v
% 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/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__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/patricia/ADD__tupled__primitive__def: h4/patricia/ADD__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R /\ (!l e r p k m. h4/bit/MOD__2EXP__EQ m k p /\ ~h4/bit/BIT m k ==> R (h4/pair/_2C r (h4/pair/_2C k e)) (h4/pair/_2C (h4/patricia/Branch p m l r) (h4/pair/_2C k e))) /\ (!r e l p k m. h4/bit/MOD__2EXP__EQ m k p /\ h4/bit/BIT m k ==> R (h4/pair/_2C l (h4/pair/_2C k e)) (h4/pair/_2C (h4/patricia/Branch p m l r) (h4/pair/_2C k e))))) (\ADD__tupled a. h4/pair/pair__CASE a (\v v1. h4/pair/pair__CASE v1 (\k e. h4/patricia/ptree__CASE v (h4/combin/I (h4/patricia/Leaf k e)) (\j d. h4/combin/I (h4/bool/COND (j = k) (h4/patricia/Leaf k e) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C j (h4/patricia/Leaf j d))))))) (\p m l r. h4/combin/I (h4/bool/COND (h4/bit/MOD__2EXP__EQ m k p) (h4/bool/COND (h4/bit/BIT m k) (h4/patricia/Branch p m (ADD__tupled (h4/pair/_2C l (h4/pair/_2C k e))) r) (h4/patricia/Branch p m l (ADD__tupled (h4/pair/_2C r (h4/pair/_2C k e))))) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C p (h4/patricia/Branch p m l r))))))))))
% Assm: h4/patricia/ADD__curried__def: !x1 x. h4/patricia/ADD x x1 = h4/patricia/ADD__tupled (h4/pair/_2C x x1)
% Goal: !r p m l k e. h4/patricia/ADD (h4/patricia/Branch p m l r) (h4/pair/_2C k e) = h4/bool/COND (h4/bit/MOD__2EXP__EQ m k p) (h4/bool/COND (h4/bit/BIT m k) (h4/patricia/Branch p m (h4/patricia/ADD l (h4/pair/_2C k e)) r) (h4/patricia/Branch p m l (h4/patricia/ADD r (h4/pair/_2C k e)))) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C p (h4/patricia/Branch p m l r)))))
%   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_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_TRUTH]: T
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c1]: !t. t ==> T <=> T
% 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_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_IMPu_u_Fu_u_EQu_u_F]: !t. t ==> F <=> t <=> F
% Assm [h4s_bools_ANDu_u_IMPu_u_INTRO]: !t3 t2 t1. t1 ==> t2 ==> t3 <=> t1 /\ t2 ==> t3
% Assm [h4s_bools_IMPu_u_CONG]: !y_27 y x_27 x. (x <=> x_27) /\ (x_27 ==> (y <=> y_27)) ==> (x ==> y <=> x_27 ==> y_27)
% Assm [h4s_bools_CONDu_u_CONG]: !y_27 y x_27 x Q P. (P <=> Q) /\ (Q ==> x = x_27) /\ (~Q ==> y = y_27) ==> h4/bool/COND P x y = h4/bool/COND Q x_27 y_27
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% 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_relations_WFu_u_invu_u_image]: !f R. h4/relation/WF R ==> h4/relation/WF (h4/relation/inv__image R f)
% 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_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_primu_u_recs_WFu_u_LESS]: h4/relation/WF h4/prim__rec/_3C
% Assm [h4s_pairs_PAIR]: !x. h4/pair/_2C (h4/pair/FST x) (h4/pair/SND x) = x
% Assm [h4s_pairs_FST0]: !y x. h4/pair/FST (h4/pair/_2C x y) = x
% 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_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_arithmetics_ADDu_u_CLAUSESu_c0]: !m. h4/arithmetic/_2B h4/num/0 m = m
% Assm [h4s_arithmetics_ADDu_u_SYM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% Assm [h4s_arithmetics_ADDu_u_COMM]: !n m. h4/arithmetic/_2B m n = h4/arithmetic/_2B n m
% 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_NOTu_u_LESS]: !n m. ~happ (happ h4/prim__rec/_3C m) n <=> h4/arithmetic/_3C_3D n m
% Assm [h4s_arithmetics_MULTu_u_CLAUSESu_c2]: !m. h4/arithmetic/_2A (h4/arithmetic/NUMERAL (h4/arithmetic/BIT1 h4/arithmetic/ZERO)) m = m
% Assm [h4s_arithmetics_LESSu_u_EQu_u_TRANS]: !p n m. h4/arithmetic/_3C_3D m n /\ h4/arithmetic/_3C_3D n p ==> h4/arithmetic/_3C_3D m p
% Assm [h4s_arithmetics_ZEROu_u_LESSu_u_EQ]: !n. h4/arithmetic/_3C_3D h4/num/0 n
% 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_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_numerals_numeralu_u_lteu_c1]: !n. h4/arithmetic/_3C_3D (h4/arithmetic/BIT1 n) h4/arithmetic/ZERO <=> F
% 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_patricias_ptreeu_u_caseu_u_defu_c1]: !v f1 f a1 a0. h4/patricia/ptree__CASE (h4/patricia/Leaf a0 a1) v f f1 = happ (happ f a0) a1
% Assm [h4s_patricias_ptreeu_u_caseu_u_defu_c2]: !v f1 f a3 a2 a1 a0. h4/patricia/ptree__CASE (h4/patricia/Branch a0 a1 a2 a3) v f f1 = happ (happ (happ (happ f1 a0) a1) a2) a3
% Assm [h4s_patricias_ptreeu_u_sizeu_u_defu_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 [h4s_patricias_ADDu_u_tupledu_u_primitiveu_u_def]: !_12. (!ADD__tupled k e p m l r. happ (happ (happ (happ (happ (happ (happ _12 ADD__tupled) k) e) p) m) l) r = h4/combin/I (h4/bool/COND (h4/bit/MOD__2EXP__EQ m k p) (h4/bool/COND (h4/bit/BIT m k) (h4/patricia/Branch p m (happ ADD__tupled (h4/pair/_2C l (h4/pair/_2C k e))) r) (h4/patricia/Branch p m l (happ ADD__tupled (h4/pair/_2C r (h4/pair/_2C k e))))) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C p (h4/patricia/Branch p m l r))))))) ==> (!_11. (!ADD__tupled k e p m l. happ (happ (happ (happ (happ (happ _11 ADD__tupled) k) e) p) m) l = happ (happ (happ (happ (happ (happ _12 ADD__tupled) k) e) p) m) l) ==> (!_10. (!ADD__tupled k e p m. happ (happ (happ (happ (happ _10 ADD__tupled) k) e) p) m = happ (happ (happ (happ (happ _11 ADD__tupled) k) e) p) m) ==> (!_9. (!ADD__tupled k e p. happ (happ (happ (happ _9 ADD__tupled) k) e) p = happ (happ (happ (happ _10 ADD__tupled) k) e) p) ==> (!_8. (!k e j d. ?v. (v <=> j = k) /\ happ (happ (happ (happ _8 k) e) j) d = h4/combin/I (h4/bool/COND v (h4/patricia/Leaf k e) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C j (h4/patricia/Leaf j d))))))) ==> (!_7. (!k e j. happ (happ (happ _7 k) e) j = happ (happ (happ _8 k) e) j) ==> (!_6. (!v ADD__tupled k e. happ (happ (happ (happ _6 v) ADD__tupled) k) e = h4/patricia/ptree__CASE v (h4/combin/I (h4/patricia/Leaf k e)) (happ (happ _7 k) e) (happ (happ (happ _9 ADD__tupled) k) e)) ==> (!_5. (!v ADD__tupled k. happ (happ (happ _5 v) ADD__tupled) k = happ (happ (happ _6 v) ADD__tupled) k) ==> (!_4. (!v ADD__tupled v1. happ (happ (happ _4 v) ADD__tupled) v1 = h4/pair/pair__CASE v1 (happ (happ _5 v) ADD__tupled)) ==> (!_3. (!ADD__tupled v. happ (happ _3 ADD__tupled) v = happ (happ _4 v) ADD__tupled) ==> (!_2. (!ADD__tupled a. happ (happ _2 ADD__tupled) a = h4/pair/pair__CASE a (happ _3 ADD__tupled)) ==> (!_1. (!ADD__tupled. happ _1 ADD__tupled = happ _2 ADD__tupled) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R /\ (!l e r p k m. h4/bit/MOD__2EXP__EQ m k p /\ ~h4/bit/BIT m k ==> happ (happ R (h4/pair/_2C r (h4/pair/_2C k e))) (h4/pair/_2C (h4/patricia/Branch p m l r) (h4/pair/_2C k e))) /\ (!r e l p k m. h4/bit/MOD__2EXP__EQ m k p /\ h4/bit/BIT m k ==> happ (happ R (h4/pair/_2C l (h4/pair/_2C k e))) (h4/pair/_2C (h4/patricia/Branch p m l r) (h4/pair/_2C k e)))) ==> h4/patricia/ADD__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))
% Assm [h4s_patricias_ADDu_u_curriedu_u_def]: !x1 x. h4/patricia/ADD x x1 = happ h4/patricia/ADD__tupled (h4/pair/_2C x x1)
% Goal: !r p m l k e. h4/patricia/ADD (h4/patricia/Branch p m l r) (h4/pair/_2C k e) = h4/bool/COND (h4/bit/MOD__2EXP__EQ m k p) (h4/bool/COND (h4/bit/BIT m k) (h4/patricia/Branch p m (h4/patricia/ADD l (h4/pair/_2C k e)) r) (h4/patricia/Branch p m l (h4/patricia/ADD r (h4/pair/_2C k e)))) (h4/patricia/JOIN (h4/pair/_2C k (h4/pair/_2C (h4/patricia/Leaf k e) (h4/pair/_2C p (h4/patricia/Branch p m l r)))))
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q285483,TV_Q285479]: ![V_f, V_g]: (![V_x]: s(TV_Q285479,happ(s(t_fun(TV_Q285483,TV_Q285479),V_f),s(TV_Q285483,V_x))) = s(TV_Q285479,happ(s(t_fun(TV_Q285483,TV_Q285479),V_g),s(TV_Q285483,V_x))) => s(t_fun(TV_Q285483,TV_Q285479),V_f) = s(t_fun(TV_Q285483,TV_Q285479),V_g))).
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_bools_TRUTH, axiom, p(s(t_bool,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_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_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,f))) <=> 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_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_Fu_u_EQu_u_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) <=> s(t_bool,V_t) = s(t_bool,f))).
fof(ah4s_bools_ANDu_u_IMPu_u_INTRO, axiom, ![V_t3, V_t2, V_t1]: ((p(s(t_bool,V_t1)) => (p(s(t_bool,V_t2)) => p(s(t_bool,V_t3)))) <=> ((p(s(t_bool,V_t1)) & p(s(t_bool,V_t2))) => p(s(t_bool,V_t3))))).
fof(ah4s_bools_IMPu_u_CONG, axiom, ![V_yu_27, V_y, V_xu_27, V_x]: ((s(t_bool,V_x) = s(t_bool,V_xu_27) & (p(s(t_bool,V_xu_27)) => s(t_bool,V_y) = s(t_bool,V_yu_27))) => ((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) <=> (p(s(t_bool,V_xu_27)) => p(s(t_bool,V_yu_27)))))).
fof(ah4s_bools_CONDu_u_CONG, axiom, ![TV_u_27a]: ![V_yu_27, V_y, V_xu_27, V_x, V_Q, V_P]: ((s(t_bool,V_P) = s(t_bool,V_Q) & ((p(s(t_bool,V_Q)) => s(TV_u_27a,V_x) = s(TV_u_27a,V_xu_27)) & (~ (p(s(t_bool,V_Q))) => s(TV_u_27a,V_y) = s(TV_u_27a,V_yu_27)))) => s(TV_u_27a,h4s_bools_cond(s(t_bool,V_P),s(TV_u_27a,V_x),s(TV_u_27a,V_y))) = s(TV_u_27a,h4s_bools_cond(s(t_bool,V_Q),s(TV_u_27a,V_xu_27),s(TV_u_27a,V_yu_27))))).
fof(ah4s_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_MULTu_u_CLAUSESu_c2, axiom, ![V_m]: s(t_h4s_nums_num,h4s_arithmetics_u_2a(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))),s(t_h4s_nums_num,V_m))) = s(t_h4s_nums_num,V_m)).
fof(ah4s_arithmetics_LESSu_u_EQu_u_TRANS, axiom, ![V_p, V_n, V_m]: ((p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_n)))) & p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_n),s(t_h4s_nums_num,V_p))))) => p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_p)))))).
fof(ah4s_arithmetics_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_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_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_numerals_numeralu_u_lteu_c1, axiom, ![V_n]: s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,V_n))),s(t_h4s_nums_num,h4s_arithmetics_zero))) = s(t_bool,f)).
fof(ah4s_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_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),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_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),h4s_patricias_branch(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_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),h4s_patricias_branch(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_patricias_ADDu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_12]: (![V_ADDu_u_tupled, V_k, V_e, V_p, V_m, V_l, 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))))),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_12),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),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_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_p))),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),h4s_patricias_branch(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_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))),s(t_h4s_patricias_ptree(TV_u_27a),V_r))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_r),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))))))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_join(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_p),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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))))))))))))))) => ![V_uu_11]: (![V_ADDu_u_tupled, V_k, V_e, V_p, V_m, V_l]: 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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_11),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),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_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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_12),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))),s(t_h4s_patricias_ptree(TV_u_27a),V_l))) => ![V_uu_10]: (![V_ADDu_u_tupled, V_k, V_e, V_p, V_m]: 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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_10),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_p))),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_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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_11),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_p))),s(t_h4s_nums_num,V_m))) => ![V_uu_9]: (![V_ADDu_u_tupled, V_k, V_e, 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_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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_9),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),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_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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_10),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_p))) => ![V_uu_8]: (![V_k, V_e, V_j, V_d]: ?[V_v]: ((p(s(t_bool,V_v)) <=> s(t_h4s_nums_num,V_j) = s(t_h4s_nums_num,V_k)) & 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))))),V_uu_8),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_j))),s(TV_u_27a,V_d))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),h4s_bools_cond(s(t_bool,V_v),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_join(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_j),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_j),s(TV_u_27a,V_d)))))))))))))))) => ![V_uu_7]: (![V_k, V_e, V_j]: 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))))),V_uu_7),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_j))) = 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))))),V_uu_8),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),s(t_h4s_nums_num,V_j))) => ![V_uu_6]: (![V_v, V_ADDu_u_tupled, V_k, V_e]: 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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_6),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_ptreeu_u_case(s(t_h4s_patricias_ptree(TV_u_27a),V_v),s(t_h4s_patricias_ptree(TV_u_27a),h4s_combins_i(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))),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))))),V_uu_7),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),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_9),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))),s(TV_u_27a,V_e))))) => ![V_uu_5]: (![V_v, V_ADDu_u_tupled, V_k]: 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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_5),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))) = 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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_6),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_nums_num,V_k))) => ![V_uu_4]: (![V_v, V_ADDu_u_tupled, V_v1]: s(t_h4s_patricias_ptree(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_nums_num,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,TV_u_27a),V_v1),s(t_fun(t_h4s_nums_num,t_fun(TV_u_27a,t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_5),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))))) => ![V_uu_3]: (![V_ADDu_u_tupled, V_v]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,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_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_patricias_ptree(TV_u_27a),V_v))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))) => ![V_uu_2]: (![V_ADDu_u_tupled, V_a]: 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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,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_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),V_a),s(t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a))),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_patricias_ptree(TV_u_27a),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),t_h4s_patricias_ptree(TV_u_27a)))),V_uu_3),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))))) => ![V_uu_1]: (![V_ADDu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),V_uu_2),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),V_ADDu_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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool)),V_R)))) & (![V_l, V_e, V_r, V_p, V_k, V_m]: ((p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_p)))) & ~ (p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k)))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_r),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))))) & ![V_r, V_e, V_l, V_p, V_k, V_m]: ((p(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_p)))) & p(s(t_bool,h4s_bits_bit(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k))))) => p(s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool)),V_R),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e)))))))))))) => s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),h4s_patricias_addu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a))),V_uu_1))))))))))))))))).
fof(ah4s_patricias_ADDu_u_curriedu_u_def, axiom, ![TV_u_27a]: ![V_x1, V_x]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_add(s(t_h4s_patricias_ptree(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),V_x1))) = 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_pairs_prod(t_h4s_nums_num,TV_u_27a)),t_h4s_patricias_ptree(TV_u_27a)),h4s_patricias_addu_u_tupled),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),V_x1)))))).
fof(ch4s_patricias_ADDu_u_defu_c2, conjecture, ![TV_u_27a]: ![V_r, V_p, V_m, V_l, V_k, V_e]: s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_add(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))) = s(t_h4s_patricias_ptree(TV_u_27a),h4s_bools_cond(s(t_bool,h4s_bits_modu_u_2expu_u_eq(s(t_h4s_nums_num,V_m),s(t_h4s_nums_num,V_k),s(t_h4s_nums_num,V_p))),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),h4s_patricias_branch(s(t_h4s_nums_num,V_p),s(t_h4s_nums_num,V_m),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_add(s(t_h4s_patricias_ptree(TV_u_27a),V_l),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))),s(t_h4s_patricias_ptree(TV_u_27a),V_r))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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),h4s_patricias_add(s(t_h4s_patricias_ptree(TV_u_27a),V_r),s(t_h4s_pairs_prod(t_h4s_nums_num,TV_u_27a),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))))))))),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_join(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_k),s(t_h4s_pairs_prod(t_h4s_patricias_ptree(TV_u_27a),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_leaf(s(t_h4s_nums_num,V_k),s(TV_u_27a,V_e))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_patricias_ptree(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_nums_num,V_p),s(t_h4s_patricias_ptree(TV_u_27a),h4s_patricias_branch(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)))))))))))))).
