%   ORIGINAL: h4/sptree/wf__mk__wf
% 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/ETA__AX: !t. (\x. t x) = t
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/FALSITY: !t. F ==> t
% Assm: h4/bool/BETA__THM: !y f. (\x. f x) y = f y
% Assm: h4/bool/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/IMP__F: !t. (t ==> F) ==> ~t
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/AND__CLAUSES_c1: !t. t /\ T <=> t
% Assm: h4/bool/AND__CLAUSES_c2: !t. F /\ t <=> F
% Assm: h4/bool/AND__CLAUSES_c4: !t. t /\ t <=> t
% Assm: h4/bool/OR__CLAUSES_c0: !t. T \/ t <=> T
% Assm: h4/bool/OR__CLAUSES_c2: !t. F \/ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/NOT__CLAUSES_c0: !t. ~ ~t <=> t
% Assm: h4/bool/NOT__CLAUSES_c1: ~T <=> F
% Assm: h4/bool/NOT__CLAUSES_c2: ~F <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% Assm: h4/bool/EQ__CLAUSES_c0: !t. (T <=> t) <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/bool/EQ__CLAUSES_c2: !t. (F <=> t) <=> ~t
% Assm: h4/bool/EQ__CLAUSES_c3: !t. (t <=> F) <=> ~t
% Assm: h4/bool/DE__MORGAN__THM_c0: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm: h4/bool/MONO__AND: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm: h4/bool/MONO__OR: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm: h4/bool/MONO__EXISTS: !Q P. (!x. P x ==> Q x) ==> (?x. P x) ==> (?x. Q x)
% Assm: h4/bool/JRH__INDUCT__UTIL: !t P. (!x. x = t ==> P x) ==> $exists P
% Assm: h4/combin/I__THM: !x. h4/combin/I x = x
% Assm: h4/relation/WF__EMPTY__REL: h4/relation/WF h4/relation/EMPTY__REL
% 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/pair/pair__case__thm: !y x f. h4/pair/pair__CASE (h4/pair/_2C x y) f = f x 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/ind__type/FCONS0_c1: !n f a. h4/ind__type/FCONS a f (h4/num/SUC n) = f n
% Assm: h4/sptree/spt__repfns_c0: !a. h4/sptree/_20_40ind__typesptree4 (h4/sptree/_20_40ind__typesptree5 a) = a
% Assm: h4/sptree/spt__repfns_c1: !r. (\a0_27. !_27spt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a0_270 = (\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (\n. h4/ind__type/BOTTOM)) a) \/ (?a0 a1. a0_270 = (\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) a0 a1 /\ _27spt_27 a0 /\ _27spt_27 a1) \/ (?a0 a1 a2. a0_270 = (\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) a0 a1 a2 /\ _27spt_27 a0 /\ _27spt_27 a2) ==> _27spt_27 a0_270) ==> _27spt_27 a0_27) r <=> h4/sptree/_20_40ind__typesptree5 (h4/sptree/_20_40ind__typesptree4 r) = r
% Assm: h4/sptree/hidden____20__40ind____typesptree0____def: h4/sptree/_20_40ind__typesptree0 = h4/sptree/_20_40ind__typesptree4 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/sptree/hidden____20__40ind____typesptree1____def: h4/sptree/_20_40ind__typesptree1 = (\a. h4/sptree/_20_40ind__typesptree4 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a0 (\n. h4/ind__type/BOTTOM)) a))
% Assm: h4/sptree/hidden____20__40ind____typesptree2____def: h4/sptree/_20_40ind__typesptree2 = (\a0 a1. h4/sptree/_20_40ind__typesptree4 ((\a00 a10. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a10 (\n. h4/ind__type/BOTTOM)))) (h4/sptree/_20_40ind__typesptree5 a0) (h4/sptree/_20_40ind__typesptree5 a1)))
% Assm: h4/sptree/hidden____20__40ind____typesptree3____def: h4/sptree/_20_40ind__typesptree3 = (\a0 a1 a2. h4/sptree/_20_40ind__typesptree4 ((\a00 a10 a20. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) a10 (h4/ind__type/FCONS a00 (h4/ind__type/FCONS a20 (\n. h4/ind__type/BOTTOM)))) (h4/sptree/_20_40ind__typesptree5 a0) a1 (h4/sptree/_20_40ind__typesptree5 a2)))
% Assm: h4/sptree/LN0: h4/sptree/LN = h4/sptree/_20_40ind__typesptree0
% Assm: h4/sptree/LS0: h4/sptree/LS = h4/sptree/_20_40ind__typesptree1
% Assm: h4/sptree/BN0: h4/sptree/BN = h4/sptree/_20_40ind__typesptree2
% Assm: h4/sptree/BS0: h4/sptree/BS = h4/sptree/_20_40ind__typesptree3
% Assm: h4/sptree/spt__case__def_c0: !v f2 f1 f. h4/sptree/spt__CASE h4/sptree/LN v f f1 f2 = v
% Assm: h4/sptree/spt__case__def_c1: !v f2 f1 f a. h4/sptree/spt__CASE (h4/sptree/LS a) v f f1 f2 = f a
% Assm: h4/sptree/spt__case__def_c2: !v f2 f1 f a1 a0. h4/sptree/spt__CASE (h4/sptree/BN a0 a1) v f f1 f2 = f1 a0 a1
% Assm: h4/sptree/spt__case__def_c3: !v f2 f1 f a2 a1 a0. h4/sptree/spt__CASE (h4/sptree/BS a0 a1 a2) v f f1 f2 = f2 a0 a1 a2
% Assm: h4/sptree/wf__def_c0: h4/sptree/wf h4/sptree/LN <=> T
% Assm: h4/sptree/wf__def_c1: !a. h4/sptree/wf (h4/sptree/LS a) <=> T
% Assm: h4/sptree/wf__def_c2: !t2 t1. h4/sptree/wf (h4/sptree/BN t1 t2) <=> h4/sptree/wf t1 /\ h4/sptree/wf t2 /\ ~(t1 = h4/sptree/LN /\ t2 = h4/sptree/LN)
% Assm: h4/sptree/wf__def_c3: !t2 t1 a. h4/sptree/wf (h4/sptree/BS t1 a t2) <=> h4/sptree/wf t1 /\ h4/sptree/wf t2 /\ ~(t1 = h4/sptree/LN /\ t2 = h4/sptree/LN)
% Assm: h4/sptree/mk__BN__tupled__primitive__def: h4/sptree/mk__BN__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\mk__BN__tupled a. h4/pair/pair__CASE a (\v v1. h4/sptree/spt__CASE v (h4/sptree/spt__CASE v1 (h4/combin/I h4/sptree/LN) (\v20. h4/combin/I (h4/sptree/BN h4/sptree/LN (h4/sptree/LS v20))) (\v21 v22. h4/combin/I (h4/sptree/BN h4/sptree/LN (h4/sptree/BN v21 v22))) (\v23 v24 v25. h4/combin/I (h4/sptree/BN h4/sptree/LN (h4/sptree/BS v23 v24 v25)))) (\v8. h4/combin/I (h4/sptree/BN (h4/sptree/LS v8) v1)) (\v9 v10. h4/combin/I (h4/sptree/BN (h4/sptree/BN v9 v10) v1)) (\v11 v12 v13. h4/combin/I (h4/sptree/BN (h4/sptree/BS v11 v12 v13) v1))))
% Assm: h4/sptree/mk__BN__curried__def: !x1 x. h4/sptree/mk__BN x x1 = h4/sptree/mk__BN__tupled (h4/pair/_2C x x1)
% Assm: h4/sptree/mk__BS__tupled__primitive__def: h4/sptree/mk__BS__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\mk__BS__tupled a. h4/pair/pair__CASE a (\v v1. h4/pair/pair__CASE v1 (\x v3. h4/sptree/spt__CASE v3 (h4/sptree/spt__CASE v (h4/combin/I (h4/sptree/LS x)) (\v22. h4/combin/I (h4/sptree/BS (h4/sptree/LS v22) x h4/sptree/LN)) (\v23 v24. h4/combin/I (h4/sptree/BS (h4/sptree/BN v23 v24) x h4/sptree/LN)) (\v25 v26 v27. h4/combin/I (h4/sptree/BS (h4/sptree/BS v25 v26 v27) x h4/sptree/LN))) (\v10. h4/combin/I (h4/sptree/BS v x (h4/sptree/LS v10))) (\v11 v12. h4/combin/I (h4/sptree/BS v x (h4/sptree/BN v11 v12))) (\v13 v14 v15. h4/combin/I (h4/sptree/BS v x (h4/sptree/BS v13 v14 v15))))))
% Assm: h4/sptree/mk__BS__curried__def: !x2 x1 x. h4/sptree/mk__BS x x1 x2 = h4/sptree/mk__BS__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm: h4/sptree/mk__wf__def_c0: h4/sptree/mk__wf h4/sptree/LN = h4/sptree/LN
% Assm: h4/sptree/mk__wf__def_c1: !x. h4/sptree/mk__wf (h4/sptree/LS x) = h4/sptree/LS x
% Assm: h4/sptree/mk__wf__def_c2: !t2 t1. h4/sptree/mk__wf (h4/sptree/BN t1 t2) = h4/sptree/mk__BN (h4/sptree/mk__wf t1) (h4/sptree/mk__wf t2)
% Assm: h4/sptree/mk__wf__def_c3: !x t2 t1. h4/sptree/mk__wf (h4/sptree/BS t1 x t2) = h4/sptree/mk__BS (h4/sptree/mk__wf t1) x (h4/sptree/mk__wf t2)
% Goal: !t. h4/sptree/wf (h4/sptree/mk__wf t)
%   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_ETAu_u_AX]: !t x. happ t x = happ t x
% 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_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_FALSITY]: !t. F ==> t
% Assm [h4s_bools_BETAu_u_THM]: !y f. happ f y = happ f y
% Assm [h4s_bools_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_IMPu_u_F]: !t. (t ==> F) ==> ~t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c1]: !t. t /\ T <=> t
% Assm [h4s_bools_ANDu_u_CLAUSESu_c2]: !t. F /\ t <=> F
% Assm [h4s_bools_ANDu_u_CLAUSESu_c4]: !t. t /\ t <=> t
% Assm [h4s_bools_ORu_u_CLAUSESu_c0]: !t. T \/ t <=> T
% Assm [h4s_bools_ORu_u_CLAUSESu_c2]: !t. F \/ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_NOTu_u_CLAUSESu_c0]: !t. ~ ~t <=> t
% Assm [h4s_bools_NOTu_u_CLAUSESu_c1]: ~T <=> F
% Assm [h4s_bools_NOTu_u_CLAUSESu_c2]: ~F <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% Assm [h4s_bools_EQu_u_CLAUSESu_c0]: !t. (T <=> t) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c2]: !t. (F <=> t) <=> ~t
% Assm [h4s_bools_EQu_u_CLAUSESu_c3]: !t. (t <=> F) <=> ~t
% Assm [h4s_bools_DEu_u_MORGANu_u_THMu_c0]: !B A. ~(A /\ B) <=> ~A \/ ~B
% Assm [h4s_bools_MONOu_u_AND]: !z y x w. (x ==> y) /\ (z ==> w) ==> x /\ z ==> y /\ w
% Assm [h4s_bools_MONOu_u_OR]: !z y x w. (x ==> y) /\ (z ==> w) ==> x \/ z ==> y \/ w
% Assm [h4s_bools_MONOu_u_EXISTS]: !Q P. (!x. happ P x ==> happ Q x) ==> (?x. happ P x) ==> (?x. happ Q x)
% Assm [h4s_bools_JRHu_u_INDUCTu_u_UTIL]: !t P. (!x. x = t ==> happ P x) ==> $exists P
% Assm [h4s_combins_Iu_u_THM]: !x. h4/combin/I x = x
% Assm [h4s_relations_WFu_u_EMPTYu_u_REL]: h4/relation/WF h4/relation/EMPTY__REL
% 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_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_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_indu_u_types_FCONS0u_c1]: !n f a. happ (h4/ind__type/FCONS a f) (h4/num/SUC n) = happ f n
% Assm [h4s_sptrees_sptu_u_repfnsu_c0]: !a. h4/sptree/_20_40ind__typesptree4 (h4/sptree/_20_40ind__typesptree5 a) = a
% Assm [h4s_sptrees_sptu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27spt_27. (!a0_270. a0_270 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a. a0_270 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) a _0) \/ (?a0 a1. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a1 _0)) /\ happ _27spt_27 a0 /\ happ _27spt_27 a1) \/ (?a0 a1 a2. a0_270 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) a1 (h4/ind__type/FCONS a0 (h4/ind__type/FCONS a2 _0)) /\ happ _27spt_27 a0 /\ happ _27spt_27 a2) ==> happ _27spt_27 a0_270) ==> happ _27spt_27 r) <=> h4/sptree/_20_40ind__typesptree5 (h4/sptree/_20_40ind__typesptree4 r) = r)
% Assm [h4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/sptree/_20_40ind__typesptree0 = h4/sptree/_20_40ind__typesptree4 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/sptree/_20_40ind__typesptree1 x = h4/sptree/_20_40ind__typesptree4 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) x _0))
% Assm [h4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x'. happ (happ h4/sptree/_20_40ind__typesptree2 x) x' = h4/sptree/_20_40ind__typesptree4 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS (h4/sptree/_20_40ind__typesptree5 x) (h4/ind__type/FCONS (h4/sptree/_20_40ind__typesptree5 x') _0))))
% Assm [h4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree3u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x x x'. happ (happ (happ h4/sptree/_20_40ind__typesptree3 x) x) x' = h4/sptree/_20_40ind__typesptree4 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC (h4/num/SUC h4/num/0))) x (h4/ind__type/FCONS (h4/sptree/_20_40ind__typesptree5 x) (h4/ind__type/FCONS (h4/sptree/_20_40ind__typesptree5 x') _0))))
% Assm [h4s_sptrees_LN0]: h4/sptree/LN = h4/sptree/_20_40ind__typesptree0
% Assm [h4s_sptrees_LS0]: h4/sptree/LS = h4/sptree/_20_40ind__typesptree1
% Assm [h4s_sptrees_BN0]: h4/sptree/BN = h4/sptree/_20_40ind__typesptree2
% Assm [h4s_sptrees_BS0]: h4/sptree/BS = h4/sptree/_20_40ind__typesptree3
% Assm [h4s_sptrees_sptu_u_caseu_u_defu_c0]: !v f2 f1 f. h4/sptree/spt__CASE h4/sptree/LN v f f1 f2 = v
% Assm [h4s_sptrees_sptu_u_caseu_u_defu_c1]: !v f2 f1 f a. h4/sptree/spt__CASE (happ h4/sptree/LS a) v f f1 f2 = happ f a
% Assm [h4s_sptrees_sptu_u_caseu_u_defu_c2]: !v f2 f1 f a1 a0. h4/sptree/spt__CASE (happ (happ h4/sptree/BN a0) a1) v f f1 f2 = happ (happ f1 a0) a1
% Assm [h4s_sptrees_sptu_u_caseu_u_defu_c3]: !v f2 f1 f a2 a1 a0. h4/sptree/spt__CASE (happ (happ (happ h4/sptree/BS a0) a1) a2) v f f1 f2 = happ (happ (happ f2 a0) a1) a2
% Assm [h4s_sptrees_wfu_u_defu_c0]: h4/sptree/wf h4/sptree/LN <=> T
% Assm [h4s_sptrees_wfu_u_defu_c1]: !a. h4/sptree/wf (happ h4/sptree/LS a) <=> T
% Assm [h4s_sptrees_wfu_u_defu_c2]: !t2 t1. h4/sptree/wf (happ (happ h4/sptree/BN t1) t2) <=> h4/sptree/wf t1 /\ h4/sptree/wf t2 /\ ~(t1 = h4/sptree/LN /\ t2 = h4/sptree/LN)
% Assm [h4s_sptrees_wfu_u_defu_c3]: !t2 t1 a. h4/sptree/wf (happ (happ (happ h4/sptree/BS t1) a) t2) <=> h4/sptree/wf t1 /\ h4/sptree/wf t2 /\ ~(t1 = h4/sptree/LN /\ t2 = h4/sptree/LN)
% Assm [h4s_sptrees_mku_u_BNu_u_tupledu_u_primitiveu_u_def]: !_16. (!v11 v12 v1 v13. happ (happ (happ (happ _16 v11) v12) v1) v13 = h4/combin/I (happ (happ h4/sptree/BN (happ (happ (happ h4/sptree/BS v11) v12) v13)) v1)) ==> (!_15. (!v11 v1 v12. happ (happ (happ _15 v11) v1) v12 = happ (happ (happ _16 v11) v12) v1) ==> (!_14. (!v1 v11. happ (happ _14 v1) v11 = happ (happ _15 v11) v1) ==> (!_13. (!v9 v1 v10. happ (happ (happ _13 v9) v1) v10 = h4/combin/I (happ (happ h4/sptree/BN (happ (happ h4/sptree/BN v9) v10)) v1)) ==> (!_12. (!v1 v9. happ (happ _12 v1) v9 = happ (happ _13 v9) v1) ==> (!_11. (!v1 v8. happ (happ _11 v1) v8 = h4/combin/I (happ (happ h4/sptree/BN (happ h4/sptree/LS v8)) v1)) ==> (!_10. (!v23 v24 v25. happ (happ (happ _10 v23) v24) v25 = h4/combin/I (happ (happ h4/sptree/BN h4/sptree/LN) (happ (happ (happ h4/sptree/BS v23) v24) v25))) ==> (!_9. (!v23 v24. happ (happ _9 v23) v24 = happ (happ _10 v23) v24) ==> (!_8. (!v23. happ _8 v23 = happ _9 v23) ==> (!_7. (!v21 v22. happ (happ _7 v21) v22 = h4/combin/I (happ (happ h4/sptree/BN h4/sptree/LN) (happ (happ h4/sptree/BN v21) v22))) ==> (!_6. (!v21. happ _6 v21 = happ _7 v21) ==> (!_5. (!v20. happ _5 v20 = h4/combin/I (happ (happ h4/sptree/BN h4/sptree/LN) (happ h4/sptree/LS v20))) ==> (!_4. (!v v1. happ (happ _4 v) v1 = h4/sptree/spt__CASE v (h4/sptree/spt__CASE v1 (h4/combin/I h4/sptree/LN) _5 _6 _8) (happ _11 v1) (happ _12 v1) (happ _14 v1)) ==> (!_3. (!v. happ _3 v = happ _4 v) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!mk__BN__tupled. happ _1 mk__BN__tupled = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/sptree/mk__BN__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))))
% Assm [h4s_sptrees_mku_u_BNu_u_curriedu_u_def]: !x1 x. h4/sptree/mk__BN x x1 = happ h4/sptree/mk__BN__tupled (h4/pair/_2C x x1)
% Assm [h4s_sptrees_mku_u_BSu_u_tupledu_u_primitiveu_u_def]: !_18. (!v x v13 v14 v15. happ (happ (happ (happ (happ _18 v) x) v13) v14) v15 = h4/combin/I (happ (happ (happ h4/sptree/BS v) x) (happ (happ (happ h4/sptree/BS v13) v14) v15))) ==> (!_17. (!v x v13 v14. happ (happ (happ (happ _17 v) x) v13) v14 = happ (happ (happ (happ _18 v) x) v13) v14) ==> (!_16. (!v x v13. happ (happ (happ _16 v) x) v13 = happ (happ (happ _17 v) x) v13) ==> (!_15. (!v x v11 v12. happ (happ (happ (happ _15 v) x) v11) v12 = h4/combin/I (happ (happ (happ h4/sptree/BS v) x) (happ (happ h4/sptree/BN v11) v12))) ==> (!_14. (!v x v11. happ (happ (happ _14 v) x) v11 = happ (happ (happ _15 v) x) v11) ==> (!_13. (!v x v10. happ (happ (happ _13 v) x) v10 = h4/combin/I (happ (happ (happ h4/sptree/BS v) x) (happ h4/sptree/LS v10))) ==> (!_12. (!v25 v26 x v27. happ (happ (happ (happ _12 v25) v26) x) v27 = h4/combin/I (happ (happ (happ h4/sptree/BS (happ (happ (happ h4/sptree/BS v25) v26) v27)) x) h4/sptree/LN)) ==> (!_11. (!v25 x v26. happ (happ (happ _11 v25) x) v26 = happ (happ (happ _12 v25) v26) x) ==> (!_10. (!x v25. happ (happ _10 x) v25 = happ (happ _11 v25) x) ==> (!_9. (!v23 x v24. happ (happ (happ _9 v23) x) v24 = h4/combin/I (happ (happ (happ h4/sptree/BS (happ (happ h4/sptree/BN v23) v24)) x) h4/sptree/LN)) ==> (!_8. (!x v23. happ (happ _8 x) v23 = happ (happ _9 v23) x) ==> (!_7. (!x v22. happ (happ _7 x) v22 = h4/combin/I (happ (happ (happ h4/sptree/BS (happ h4/sptree/LS v22)) x) h4/sptree/LN)) ==> (!_6. (!v x v3. happ (happ (happ _6 v) x) v3 = h4/sptree/spt__CASE v3 (h4/sptree/spt__CASE v (h4/combin/I (happ h4/sptree/LS x)) (happ _7 x) (happ _8 x) (happ _10 x)) (happ (happ _13 v) x) (happ (happ _14 v) x) (happ (happ _16 v) x)) ==> (!_5. (!v x. happ (happ _5 v) x = happ (happ _6 v) x) ==> (!_4. (!v v1. happ (happ _4 v) v1 = h4/pair/pair__CASE v1 (happ _5 v)) ==> (!_3. (!v. happ _3 v = happ _4 v) ==> (!_2. (!a. happ _2 a = h4/pair/pair__CASE a _3) ==> (!_1. (!mk__BS__tupled. happ _1 mk__BS__tupled = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/sptree/mk__BS__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))))))
% Assm [h4s_sptrees_mku_u_BSu_u_curriedu_u_def]: !x2 x1 x. h4/sptree/mk__BS x x1 x2 = happ h4/sptree/mk__BS__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Assm [h4s_sptrees_mku_u_wfu_u_defu_c0]: h4/sptree/mk__wf h4/sptree/LN = h4/sptree/LN
% Assm [h4s_sptrees_mku_u_wfu_u_defu_c1]: !x. h4/sptree/mk__wf (happ h4/sptree/LS x) = happ h4/sptree/LS x
% Assm [h4s_sptrees_mku_u_wfu_u_defu_c2]: !t2 t1. h4/sptree/mk__wf (happ (happ h4/sptree/BN t1) t2) = h4/sptree/mk__BN (h4/sptree/mk__wf t1) (h4/sptree/mk__wf t2)
% Assm [h4s_sptrees_mku_u_wfu_u_defu_c3]: !x t2 t1. h4/sptree/mk__wf (happ (happ (happ h4/sptree/BS t1) x) t2) = h4/sptree/mk__BS (h4/sptree/mk__wf t1) x (h4/sptree/mk__wf t2)
% Goal: !t. h4/sptree/wf (h4/sptree/mk__wf t)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q82502,TV_Q82498]: ![V_f, V_g]: (![V_x]: s(TV_Q82498,happ(s(t_fun(TV_Q82502,TV_Q82498),V_f),s(TV_Q82502,V_x))) = s(TV_Q82498,happ(s(t_fun(TV_Q82502,TV_Q82498),V_g),s(TV_Q82502,V_x))) => s(t_fun(TV_Q82502,TV_Q82498),V_f) = s(t_fun(TV_Q82502,TV_Q82498),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_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,t0))).
fof(ah4s_bools_IMPu_u_ANTISYMu_u_AX, axiom, ![V_t2, V_t1]: ((p(s(t_bool,V_t1)) => p(s(t_bool,V_t2))) => ((p(s(t_bool,V_t2)) => p(s(t_bool,V_t1))) => s(t_bool,V_t1) = s(t_bool,V_t2)))).
fof(ah4s_bools_FALSITY, axiom, ![V_t]: (p(s(t_bool,f)) => 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_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_F, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,f))) => ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c1, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,t0))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) & p(s(t_bool,V_t))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c4, axiom, ![V_t]: ((p(s(t_bool,V_t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) | p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_ORu_u_CLAUSESu_c2, axiom, ![V_t]: ((p(s(t_bool,f)) | p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c0, axiom, ![V_t]: (~ (~ (p(s(t_bool,V_t)))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c1, axiom, (~ (p(s(t_bool,t0))) <=> p(s(t_bool,f)))).
fof(ah4s_bools_NOTu_u_CLAUSESu_c2, axiom, (~ (p(s(t_bool,f))) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_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_c0, axiom, ![V_t]: (s(t_bool,t0) = s(t_bool,V_t) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c2, axiom, ![V_t]: (s(t_bool,f) = s(t_bool,V_t) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_EQu_u_CLAUSESu_c3, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,f) <=> ~ (p(s(t_bool,V_t))))).
fof(ah4s_bools_DEu_u_MORGANu_u_THMu_c0, axiom, ![V_B, V_A]: (~ ((p(s(t_bool,V_A)) & p(s(t_bool,V_B)))) <=> (~ (p(s(t_bool,V_A))) | ~ (p(s(t_bool,V_B)))))).
fof(ah4s_bools_MONOu_u_AND, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) & p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) & p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_OR, axiom, ![V_z, V_y, V_x, V_w]: (((p(s(t_bool,V_x)) => p(s(t_bool,V_y))) & (p(s(t_bool,V_z)) => p(s(t_bool,V_w)))) => ((p(s(t_bool,V_x)) | p(s(t_bool,V_z))) => (p(s(t_bool,V_y)) | p(s(t_bool,V_w)))))).
fof(ah4s_bools_MONOu_u_EXISTS, axiom, ![TV_u_27a]: ![V_Q, V_P]: (![V_x]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))) => (?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => ?[V_x]: p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_Q),s(TV_u_27a,V_x))))))).
fof(ah4s_bools_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_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_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_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_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_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_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_sptrees_sptu_u_repfnsu_c0, axiom, ![TV_u_27a]: ![V_a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),V_a))))) = s(t_h4s_sptrees_spt(TV_u_27a),V_a)).
fof(ah4s_sptrees_sptu_u_repfnsu_c1, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27sptu_27]: (![V_a0u_270]: ((s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | (?[V_a]: s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))) | (?[V_a0, V_a1]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a1)))))) | ?[V_a0, V_a1, V_a2]: (s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(TV_u_27a,V_a1),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))) & (p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0)))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a2))))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_a0u_270))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(TV_u_27a),t_bool),V_uu_27sptu_27),s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) <=> s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r))))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),V_r)))).
fof(ah4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree0u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree0) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree1u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_u_20u_40indu_u_typesptree1),s(TV_u_27a,V_x))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(TV_u_27a,V_x),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))).
fof(ah4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree2u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_xi_]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_u_20u_40indu_u_typesptree2),s(t_h4s_sptrees_spt(TV_u_27a),V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_xi_))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))),s(TV_u_27a,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))))).
fof(ah4s_sptrees_hiddenu_u_u_u_20u_u_40indu_u_u_u_typesptree3u_u_u_u_def, axiom, ![TV_u_27a]: ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(TV_u_27a),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_bottom) => ![V_x, V_x0, V_xi_]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_u_20u_40indu_u_typesptree3),s(t_h4s_sptrees_spt(TV_u_27a),V_x))),s(TV_u_27a,V_x0))),s(t_h4s_sptrees_spt(TV_u_27a),V_xi_))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree4(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))))))),s(TV_u_27a,V_x0),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree5(s(t_h4s_sptrees_spt(TV_u_27a),V_xi_))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(TV_u_27a)),V_uu_0))))))))))).
fof(ah4s_sptrees_LN0, axiom, ![TV_u_27a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_u_20u_40indu_u_typesptree0)).
fof(ah4s_sptrees_LS0, axiom, ![TV_u_27a]: s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls) = s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_u_20u_40indu_u_typesptree1)).
fof(ah4s_sptrees_BN0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_u_20u_40indu_u_typesptree2)).
fof(ah4s_sptrees_BS0, axiom, ![TV_u_27a]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_u_20u_40indu_u_typesptree3)).
fof(ah4s_sptrees_sptu_u_caseu_u_defu_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_v, V_f2, V_f1, V_f]: s(TV_u_27b,h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),V_f1),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b))),V_f2))) = s(TV_u_27b,V_v)).
fof(ah4s_sptrees_sptu_u_caseu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f2, V_f1, V_f, V_a]: s(TV_u_27b,h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_a))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),V_f1),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b))),V_f2))) = s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_a)))).
fof(ah4s_sptrees_sptu_u_caseu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f2, V_f1, V_f, V_a1, V_a0]: s(TV_u_27b,h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_a0))),s(t_h4s_sptrees_spt(TV_u_27a),V_a1))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),V_f1),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b))),V_f2))) = s(TV_u_27b,happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),V_f1),s(t_h4s_sptrees_spt(TV_u_27a),V_a0))),s(t_h4s_sptrees_spt(TV_u_27a),V_a1)))).
fof(ah4s_sptrees_sptu_u_caseu_u_defu_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_v, V_f2, V_f1, V_f, V_a2, V_a1, V_a0]: s(TV_u_27b,h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_sptrees_spt(TV_u_27a),V_a2))),s(TV_u_27b,V_v),s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),V_f1),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b))),V_f2))) = s(TV_u_27b,happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),TV_u_27b))),V_f2),s(t_h4s_sptrees_spt(TV_u_27a),V_a0))),s(TV_u_27a,V_a1))),s(t_h4s_sptrees_spt(TV_u_27a),V_a2)))).
fof(ah4s_sptrees_wfu_u_defu_c0, axiom, ![TV_u_27a]: s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))) = s(t_bool,t0)).
fof(ah4s_sptrees_wfu_u_defu_c1, axiom, ![TV_u_27a]: ![V_a]: s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_a))))) = s(t_bool,t0)).
fof(ah4s_sptrees_wfu_u_defu_c2, axiom, ![TV_u_27a]: ![V_t2, V_t1]: (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))))) <=> (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t1)))) & (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))) & ~ ((s(t_h4s_sptrees_spt(TV_u_27a),V_t1) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln) & s(t_h4s_sptrees_spt(TV_u_27a),V_t2) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))))))).
fof(ah4s_sptrees_wfu_u_defu_c3, axiom, ![TV_u_27a]: ![V_t2, V_t1, V_a]: (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))))) <=> (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t1)))) & (p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))) & ~ ((s(t_h4s_sptrees_spt(TV_u_27a),V_t1) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln) & s(t_h4s_sptrees_spt(TV_u_27a),V_t2) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))))))).
fof(ah4s_sptrees_mku_u_BNu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_16]: (![V_v11, V_v12, V_v1, V_v13]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_16),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(TV_u_27a,V_v12))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(TV_u_27a,V_v12))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))))) => ![V_uu_15]: (![V_v11, V_v1, V_v12]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_15),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(TV_u_27a,V_v12))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_16),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(TV_u_27a,V_v12))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))) => ![V_uu_14]: (![V_v1, V_v11]: s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_14),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))) = s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_15),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))) => ![V_uu_13]: (![V_v9, V_v1, V_v10]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_13),s(t_h4s_sptrees_spt(TV_u_27a),V_v9))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_h4s_sptrees_spt(TV_u_27a),V_v10))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_v9))),s(t_h4s_sptrees_spt(TV_u_27a),V_v10))))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))))) => ![V_uu_12]: (![V_v1, V_v9]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_12),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_h4s_sptrees_spt(TV_u_27a),V_v9))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_13),s(t_h4s_sptrees_spt(TV_u_27a),V_v9))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))) => ![V_uu_11]: (![V_v1, V_v8]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_uu_11),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(TV_u_27a,V_v8))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_v8))))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))))) => ![V_uu_10]: (![V_v23, V_v24, V_v25]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_10),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_v24))),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_v24))),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))))))) => ![V_uu_9]: (![V_v23, V_v24]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_9),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_v24))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_10),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_v24))) => ![V_uu_8]: (![V_v23]: s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_8),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))) = s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_9),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))) => ![V_uu_7]: (![V_v21, V_v22]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_7),s(t_h4s_sptrees_spt(TV_u_27a),V_v21))),s(t_h4s_sptrees_spt(TV_u_27a),V_v22))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_v21))),s(t_h4s_sptrees_spt(TV_u_27a),V_v22))))))) => ![V_uu_6]: (![V_v21]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_6),s(t_h4s_sptrees_spt(TV_u_27a),V_v21))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_7),s(t_h4s_sptrees_spt(TV_u_27a),V_v21))) => ![V_uu_5]: (![V_v20]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),V_uu_5),s(TV_u_27a,V_v20))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_v20))))))) => ![V_uu_4]: (![V_v, V_v1]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),V_v),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),V_v1),s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))),s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),V_uu_5),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_6),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_8))),s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_uu_11),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_12),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_14),s(t_h4s_sptrees_spt(TV_u_27a),V_v1))))) => ![V_uu_3]: (![V_v]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_3),s(t_h4s_sptrees_spt(TV_u_27a),V_v))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_v))) => ![V_uu_2]: (![V_a]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),V_a))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),V_a),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),V_uu_3))) => ![V_uu_1]: (![V_mku_u_BNu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),V_mku_u_BNu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(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_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_mku_u_bnu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1))))))))))))))))))))).
fof(ah4s_sptrees_mku_u_BNu_u_curriedu_u_def, axiom, ![TV_u_27a]: ![V_x1, V_x]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bn(s(t_h4s_sptrees_spt(TV_u_27a),V_x),s(t_h4s_sptrees_spt(TV_u_27a),V_x1))) = s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_mku_u_bnu_u_tupled),s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),h4s_pairs_u_2c(s(t_h4s_sptrees_spt(TV_u_27a),V_x),s(t_h4s_sptrees_spt(TV_u_27a),V_x1)))))).
fof(ah4s_sptrees_mku_u_BSu_u_tupledu_u_primitiveu_u_def, axiom, ![TV_u_27a]: ![V_uu_18]: (![V_v, V_x, V_v13, V_v14, V_v15]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_18),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))),s(TV_u_27a,V_v14))),s(t_h4s_sptrees_spt(TV_u_27a),V_v15))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))),s(TV_u_27a,V_v14))),s(t_h4s_sptrees_spt(TV_u_27a),V_v15))))))) => ![V_uu_17]: (![V_v, V_x, V_v13, V_v14]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_17),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))),s(TV_u_27a,V_v14))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_18),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))),s(TV_u_27a,V_v14))) => ![V_uu_16]: (![V_v, V_x, V_v13]: s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_16),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))) = s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_17),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v13))) => ![V_uu_15]: (![V_v, V_x, V_v11, V_v12]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_15),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(t_h4s_sptrees_spt(TV_u_27a),V_v12))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))),s(t_h4s_sptrees_spt(TV_u_27a),V_v12))))))) => ![V_uu_14]: (![V_v, V_x, V_v11]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_14),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_15),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v11))) => ![V_uu_13]: (![V_v, V_x, V_v10]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)))),V_uu_13),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(TV_u_27a,V_v10))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_v10))))))) => ![V_uu_12]: (![V_v25, V_v26, V_x, V_v27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_12),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))),s(TV_u_27a,V_v26))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v27))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))),s(TV_u_27a,V_v26))),s(t_h4s_sptrees_spt(TV_u_27a),V_v27))))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))))) => ![V_uu_11]: (![V_v25, V_x, V_v26]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_11),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))),s(TV_u_27a,V_x))),s(TV_u_27a,V_v26))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_12),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))),s(TV_u_27a,V_v26))),s(TV_u_27a,V_x))) => ![V_uu_10]: (![V_x, V_v25]: s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_10),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))) = s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_11),s(t_h4s_sptrees_spt(TV_u_27a),V_v25))),s(TV_u_27a,V_x))) => ![V_uu_9]: (![V_v23, V_x, V_v24]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_9),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v24))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(t_h4s_sptrees_spt(TV_u_27a),V_v24))))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))))) => ![V_uu_8]: (![V_x, V_v23]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_8),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_9),s(t_h4s_sptrees_spt(TV_u_27a),V_v23))),s(TV_u_27a,V_x))) => ![V_uu_7]: (![V_x, V_v22]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_uu_7),s(TV_u_27a,V_x))),s(TV_u_27a,V_v22))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_v22))))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))))) => ![V_uu_6]: (![V_v, V_x, V_v3]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_6),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_v3))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),V_v3),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27a),V_v),s(t_h4s_sptrees_spt(TV_u_27a),h4s_combins_i(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_x))))),s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_uu_7),s(TV_u_27a,V_x))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_8),s(TV_u_27a,V_x))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_10),s(TV_u_27a,V_x))))),s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)))),V_uu_13),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_14),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_16),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))))) => ![V_uu_5]: (![V_v, V_x]: s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_5),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_6),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(TV_u_27a,V_x))) => ![V_uu_4]: (![V_v, V_v1]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_v))),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),V_v1))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),V_v1),s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_5),s(t_h4s_sptrees_spt(TV_u_27a),V_v))))) => ![V_uu_3]: (![V_v]: s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_3),s(t_h4s_sptrees_spt(TV_u_27a),V_v))) = s(t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_v))) => ![V_uu_2]: (![V_a]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),V_uu_2),s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_a))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),V_a),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),t_h4s_sptrees_spt(TV_u_27a))),V_uu_3))) => ![V_uu_1]: (![V_mku_u_BSu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),V_mku_u_BSu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(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_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_mku_u_bsu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1))))))))))))))))))))))).
fof(ah4s_sptrees_mku_u_BSu_u_curriedu_u_def, axiom, ![TV_u_27a]: ![V_x2, V_x1, V_x]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bs(s(t_h4s_sptrees_spt(TV_u_27a),V_x),s(TV_u_27a,V_x1),s(t_h4s_sptrees_spt(TV_u_27a),V_x2))) = s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_mku_u_bsu_u_tupled),s(t_h4s_pairs_prod(t_h4s_sptrees_spt(TV_u_27a),t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a))),h4s_pairs_u_2c(s(t_h4s_sptrees_spt(TV_u_27a),V_x),s(t_h4s_pairs_prod(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_pairs_u_2c(s(TV_u_27a,V_x1),s(t_h4s_sptrees_spt(TV_u_27a),V_x2)))))))).
fof(ah4s_sptrees_mku_u_wfu_u_defu_c0, axiom, ![TV_u_27a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln)).
fof(ah4s_sptrees_mku_u_wfu_u_defu_c1, axiom, ![TV_u_27a]: ![V_x]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_x))))) = s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27a,t_h4s_sptrees_spt(TV_u_27a)),h4s_sptrees_ls),s(TV_u_27a,V_x)))).
fof(ah4s_sptrees_mku_u_wfu_u_defu_c2, axiom, ![TV_u_27a]: ![V_t2, V_t1]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),h4s_sptrees_bn),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bn(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))))).
fof(ah4s_sptrees_mku_u_wfu_u_defu_c3, axiom, ![TV_u_27a]: ![V_x, V_t2, V_t1]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_h4s_sptrees_spt(TV_u_27a)))),h4s_sptrees_bs),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(TV_u_27a,V_x))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bs(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(TV_u_27a,V_x),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t2)))))).
fof(ch4s_sptrees_wfu_u_mku_u_wf, conjecture, ![TV_u_27a]: ![V_t]: p(s(t_bool,h4s_sptrees_wf(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_wf(s(t_h4s_sptrees_spt(TV_u_27a),V_t))))))).
