%   ORIGINAL: h4/sptree/mk__BS__def_c5
% Assm: HL_TRUTH: T
% Assm: HL_FALSITY: ~F
% Assm: HL_BOOL_CASES: !t. (t <=> T) \/ (t <=> F)
% Assm: HL_EXT: !f g. (!x. f x = g x) ==> f = g
% Assm: h4/bool/SELECT__AX: !x P. P x ==> P (h4/min/_40 P)
% Assm: h4/bool/EQ__SYM__EQ: !y x. x = y <=> y = x
% 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/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/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))
% Goal: !x v6 v5 t1. h4/sptree/mk__BS t1 x (h4/sptree/BN v5 v6) = h4/sptree/BS t1 x (h4/sptree/BN v5 v6)
%   PROCESSED
% Assm [HLu_TRUTH]: T
% Assm [HLu_FALSITY]: ~F
% Assm [HLu_BOOLu_CASES]: !t. (t <=> T) \/ (t <=> F)
% Assm [HLu_EXT]: !f g. (!x. happ f x = happ g x) ==> f = g
% Assm [h4s_bools_SELECTu_u_AX]: !x P. happ P x ==> happ P (h4/min/_40 P)
% Assm [h4s_bools_EQu_u_SYMu_u_EQ]: !y x. x = y <=> y = x
% 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_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 (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 (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 (h4/sptree/BS a0 a1 a2) v f f1 f2 = happ (happ (happ f2 a0) a1) a2
% 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 (h4/sptree/BS v x (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 (h4/sptree/BS v x (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 (h4/sptree/BS v x (h4/sptree/LS v10))) ==> (!_12. (!v25 v26 x v27. happ (happ (happ (happ _12 v25) v26) x) v27 = h4/combin/I (h4/sptree/BS (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 (h4/sptree/BS (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 (h4/sptree/BS (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 (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))
% Goal: !x v6 v5 t1. h4/sptree/mk__BS t1 x (h4/sptree/BN v5 v6) = h4/sptree/BS t1 x (h4/sptree/BN v5 v6)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q81425,TV_Q81421]: ![V_f, V_g]: (![V_x]: s(TV_Q81421,happ(s(t_fun(TV_Q81425,TV_Q81421),V_f),s(TV_Q81425,V_x))) = s(TV_Q81421,happ(s(t_fun(TV_Q81425,TV_Q81421),V_g),s(TV_Q81425,V_x))) => s(t_fun(TV_Q81425,TV_Q81421),V_f) = s(t_fun(TV_Q81425,TV_Q81421),V_g))).
fof(ah4s_bools_SELECTu_u_AX, axiom, ![TV_u_27a]: ![V_x, V_P]: (p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,V_x)))) => p(s(t_bool,happ(s(t_fun(TV_u_27a,t_bool),V_P),s(TV_u_27a,h4s_mins_u_40(s(t_fun(TV_u_27a,t_bool),V_P)))))))).
fof(ah4s_bools_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_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_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),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),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),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_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),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),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),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),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),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),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),h4s_sptrees_bs(s(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),h4s_sptrees_bs(s(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),h4s_sptrees_bs(s(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),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(ch4s_sptrees_mku_u_BSu_u_defu_c5, conjecture, ![TV_u_27a]: ![V_x, V_v6, V_v5, V_t1]: s(t_h4s_sptrees_spt(TV_u_27a),h4s_sptrees_mku_u_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),h4s_sptrees_bn(s(t_h4s_sptrees_spt(TV_u_27a),V_v5),s(t_h4s_sptrees_spt(TV_u_27a),V_v6))))) = s(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),h4s_sptrees_bn(s(t_h4s_sptrees_spt(TV_u_27a),V_v5),s(t_h4s_sptrees_spt(TV_u_27a),V_v6)))))).
