%   ORIGINAL: h4/sptree/inter__LN_c1
% 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/TRUTH: T
% Assm: h4/bool/IMP__ANTISYM__AX: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/IMP__CLAUSES_c3: !t. t ==> t <=> T
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% 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/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/inter__def_c0: !t. h4/sptree/inter h4/sptree/LN t = h4/sptree/LN
% Assm: h4/sptree/inter__def_c1: !t a. h4/sptree/inter (h4/sptree/LS a) t = h4/sptree/spt__CASE t h4/sptree/LN (\b. h4/sptree/LS a) (\t1 t2. h4/sptree/LN) (\t1_27 v4 t2_27. h4/sptree/LS a)
% Assm: h4/sptree/inter__def_c2: !t2 t1 t. h4/sptree/inter (h4/sptree/BN t1 t2) t = h4/sptree/spt__CASE t h4/sptree/LN (\a. h4/sptree/LN) (\t1_27 t2_27. h4/sptree/mk__BN (h4/sptree/inter t1 t1_27) (h4/sptree/inter t2 t2_27)) (\t1_27_27 a_27 t2_27_27. h4/sptree/mk__BN (h4/sptree/inter t1 t1_27_27) (h4/sptree/inter t2 t2_27_27))
% Assm: h4/sptree/inter__def_c3: !t2 t1 t a. h4/sptree/inter (h4/sptree/BS t1 a t2) t = h4/sptree/spt__CASE t h4/sptree/LN (\a_27. h4/sptree/LS a) (\t1_27 t2_27. h4/sptree/mk__BN (h4/sptree/inter t1 t1_27) (h4/sptree/inter t2 t2_27)) (\t1_27_27 a_27_27 t2_27_27. h4/sptree/mk__BS (h4/sptree/inter t1 t1_27_27) a (h4/sptree/inter t2 t2_27_27))
% Goal: !t. h4/sptree/inter h4/sptree/LN t = h4/sptree/LN
%   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_TRUTH]: T
% Assm [h4s_bools_IMPu_u_ANTISYMu_u_AX]: !t2 t1. (t1 ==> t2) ==> (t2 ==> t1) ==> (t1 <=> t2)
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> T
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% 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_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_interu_u_defu_c0]: !t. h4/sptree/inter h4/sptree/LN t = h4/sptree/LN
% Assm [h4s_sptrees_interu_u_defu_c1]: !_5. (!a t2_27. happ (happ _5 a) t2_27 = happ h4/sptree/LS a) ==> (!_4. (!a v4. happ (happ _4 a) v4 = happ _5 a) ==> (!_3. (!a t1_27. happ (happ _3 a) t1_27 = happ _4 a) ==> (!_2. (!t2. happ _2 t2 = h4/sptree/LN) ==> (!_1. (!t1. happ _1 t1 = _2) ==> (!_0. (!a b. happ (happ _0 a) b = happ h4/sptree/LS a) ==> (!t a. h4/sptree/inter (happ h4/sptree/LS a) t = h4/sptree/spt__CASE t h4/sptree/LN (happ _0 a) _1 (happ _3 a)))))))
% Assm [h4s_sptrees_interu_u_defu_c2]: !_4. (!_2 t1 t1_27_27 t2 a_27. happ (happ (happ (happ (happ _4 _2) t1) t1_27_27) t2) a_27 = happ (happ (happ _2 t1) t1_27_27) t2) ==> (!_3. (!_2 t1 t2 t1_27_27. happ (happ (happ (happ _3 _2) t1) t2) t1_27_27 = happ (happ (happ (happ _4 _2) t1) t1_27_27) t2) ==> (!_2. (!t1 t1_27 t2 t2_27. happ (happ (happ (happ _2 t1) t1_27) t2) t2_27 = h4/sptree/mk__BN (h4/sptree/inter t1 t1_27) (h4/sptree/inter t2 t2_27)) ==> (!_1. (!t1 t2 t1_27. happ (happ (happ _1 t1) t2) t1_27 = happ (happ (happ _2 t1) t1_27) t2) ==> (!_0. (!a. happ _0 a = h4/sptree/LN) ==> (!t2 t1 t. h4/sptree/inter (happ (happ h4/sptree/BN t1) t2) t = h4/sptree/spt__CASE t h4/sptree/LN _0 (happ (happ _1 t1) t2) (happ (happ (happ _3 _2) t1) t2))))))
% Assm [h4s_sptrees_interu_u_defu_c3]: !_5. (!t1 t1_27_27 a t2 t2_27_27. happ (happ (happ (happ (happ _5 t1) t1_27_27) a) t2) t2_27_27 = h4/sptree/mk__BS (h4/sptree/inter t1 t1_27_27) a (h4/sptree/inter t2 t2_27_27)) ==> (!_4. (!t1 t1_27_27 a t2 a_27_27. happ (happ (happ (happ (happ _4 t1) t1_27_27) a) t2) a_27_27 = happ (happ (happ (happ _5 t1) t1_27_27) a) t2) ==> (!_3. (!t1 a t2 t1_27_27. happ (happ (happ (happ _3 t1) a) t2) t1_27_27 = happ (happ (happ (happ _4 t1) t1_27_27) a) t2) ==> (!_2. (!t1 t1_27 t2 t2_27. happ (happ (happ (happ _2 t1) t1_27) t2) t2_27 = h4/sptree/mk__BN (h4/sptree/inter t1 t1_27) (h4/sptree/inter t2 t2_27)) ==> (!_1. (!t1 t2 t1_27. happ (happ (happ _1 t1) t2) t1_27 = happ (happ (happ _2 t1) t1_27) t2) ==> (!_0. (!a a_27. happ (happ _0 a) a_27 = happ h4/sptree/LS a) ==> (!t2 t1 t a. h4/sptree/inter (happ (happ (happ h4/sptree/BS t1) a) t2) t = h4/sptree/spt__CASE t h4/sptree/LN (happ _0 a) (happ (happ _1 t1) t2) (happ (happ (happ _3 t1) a) t2)))))))
% Goal: !t. h4/sptree/inter h4/sptree/LN t = h4/sptree/LN
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_Q82847,TV_Q82843]: ![V_f, V_g]: (![V_x]: s(TV_Q82843,happ(s(t_fun(TV_Q82847,TV_Q82843),V_f),s(TV_Q82847,V_x))) = s(TV_Q82843,happ(s(t_fun(TV_Q82847,TV_Q82843),V_g),s(TV_Q82847,V_x))) => s(t_fun(TV_Q82847,TV_Q82843),V_f) = s(t_fun(TV_Q82847,TV_Q82843),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_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_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_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_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_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_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_interu_u_defu_c0, axiom, ![TV_u_27b,TV_u_27a]: ![V_t]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln),s(t_h4s_sptrees_spt(TV_u_27b),V_t))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln)).
fof(ah4s_sptrees_interu_u_defu_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_5]: (![V_a, V_t2u_27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),V_uu_5),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27))) = 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))) => ![V_uu_4]: (![V_a, V_v4]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_4),s(TV_u_27a,V_a))),s(TV_u_27b,V_v4))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),V_uu_5),s(TV_u_27a,V_a))) => ![V_uu_3]: (![V_a, V_t1u_27]: s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_3),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))) = s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),V_uu_4),s(TV_u_27a,V_a))) => ![V_uu_2]: (![V_t2]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27b),V_t2))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln) => ![V_uu_1]: (![V_t1]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1),s(t_h4s_sptrees_spt(TV_u_27b),V_t1))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),V_uu_2) => ![V_uu_0]: (![V_a, V_b]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a))),V_uu_0),s(TV_u_27a,V_a))),s(TV_u_27b,V_b))) = 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))) => ![V_t, V_a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(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_h4s_sptrees_spt(TV_u_27b),V_t))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27b),V_t),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln),s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a))),V_uu_0),s(TV_u_27a,V_a))),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),V_uu_1),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_3),s(TV_u_27a,V_a)))))))))))).
fof(ah4s_sptrees_interu_u_defu_c2, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_4]: (![V_uu_2, V_t1, V_t1u_27u_27, V_t2, V_au_27]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_4),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2))),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(TV_u_27b,V_au_27))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_3]: (![V_uu_2, V_t1, V_t2, V_t1u_27u_27]: s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_3),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2))),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_27b),V_t1u_27u_27))) = s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_4),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2))),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_2]: (![V_t1, V_t1u_27, V_t2, V_t2u_27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bn(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t1),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t2),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27))))) => ![V_uu_1]: (![V_t1, V_t2, V_t1u_27]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_1),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_27b),V_t1u_27))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_0]: (![V_a]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),V_uu_0),s(TV_u_27b,V_a))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln) => ![V_t2, V_t1, V_t]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(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_27b),V_t))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27b),V_t),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln),s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),V_uu_0),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_1),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),happ(s(t_fun(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_3),s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2))),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))))))))))).
fof(ah4s_sptrees_interu_u_defu_c3, axiom, ![TV_u_27b,TV_u_27a]: ![V_uu_5]: (![V_t1, V_t1u_27u_27, V_a, V_t2, V_t2u_27u_27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_5),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27u_27))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bs(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t1),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(TV_u_27a,V_a),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t2),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27u_27))))) => ![V_uu_4]: (![V_t1, V_t1u_27u_27, V_a, V_t2, V_au_27u_27]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(TV_u_27b,V_au_27u_27))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a)))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)))))),V_uu_5),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_3]: (![V_t1, V_a, V_t2, V_t1u_27u_27]: s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_3),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))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))) = s(t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27a,t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_4),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27u_27))),s(TV_u_27a,V_a))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_2]: (![V_t1, V_t1u_27, V_t2, V_t2u_27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_bn(s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t1),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27a),V_t2),s(t_h4s_sptrees_spt(TV_u_27b),V_t2u_27))))) => ![V_uu_1]: (![V_t1, V_t2, V_t1u_27]: s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_1),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_27b),V_t1u_27))) = s(t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_h4s_sptrees_spt(TV_u_27a))),happ(s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27a),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_2),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27b),V_t1u_27))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))) => ![V_uu_0]: (![V_a, V_au_27]: s(t_h4s_sptrees_spt(TV_u_27a),happ(s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a))),V_uu_0),s(TV_u_27a,V_a))),s(TV_u_27b,V_au_27))) = 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))) => ![V_t2, V_t1, V_t, V_a]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_inter(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))),s(t_h4s_sptrees_spt(TV_u_27b),V_t))) = s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_sptu_u_case(s(t_h4s_sptrees_spt(TV_u_27b),V_t),s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_ln),s(t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a)),happ(s(t_fun(TV_u_27a,t_fun(TV_u_27b,t_h4s_sptrees_spt(TV_u_27a))),V_uu_0),s(TV_u_27a,V_a))),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))),V_uu_1),s(t_h4s_sptrees_spt(TV_u_27a),V_t1))),s(t_h4s_sptrees_spt(TV_u_27a),V_t2))),s(t_fun(t_h4s_sptrees_spt(TV_u_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),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_27b),t_fun(TV_u_27b,t_fun(t_h4s_sptrees_spt(TV_u_27b),t_h4s_sptrees_spt(TV_u_27a))))))),V_uu_3),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)))))))))))).
fof(ch4s_sptrees_interu_u_LNu_c1, conjecture, ![TV_u_27a,TV_u_27c]: ![V_t]: s(t_h4s_sptrees_spt(TV_u_27c),h4s_sptrees_inter(s(t_h4s_sptrees_spt(TV_u_27c),h4s_sptrees_ln),s(t_h4s_sptrees_spt(TV_u_27a),V_t))) = s(t_h4s_sptrees_spt(TV_u_27c),h4s_sptrees_ln)).
