%   ORIGINAL: h4/defCNF/UNIQUE__def_c3
% 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/sum/sum__case__def_c0: !x f1 f. h4/sum/sum__CASE (h4/sum/INL x) f f1 = f x
% Assm: h4/sum/sum__case__def_c1: !y f1 f. h4/sum/sum__CASE (h4/sum/INR y) f f1 = f1 y
% 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/defCNF/UNIQUE__tupled__primitive__def: h4/defCNF/UNIQUE__tupled = h4/relation/WFREC (h4/min/_40 (\R. h4/relation/WF R)) (\UNIQUE__tupled a_27. h4/pair/pair__CASE a_27 (\v v2. h4/pair/pair__CASE v2 (\n v4. h4/pair/pair__CASE v4 (\conn v6. h4/pair/pair__CASE v6 (\v7 v8. h4/sum/sum__CASE v7 (\i. h4/sum/sum__CASE v8 (\j. h4/combin/I (v n <=> conn (v i) (v j))) (\b. h4/combin/I (v n <=> conn (v i) b))) (\a. h4/sum/sum__CASE v8 (\j_27. h4/combin/I (v n <=> conn a (v j_27))) (\b_27. h4/combin/I (v n <=> conn a b_27))))))))
% Assm: h4/defCNF/UNIQUE__curried__def: !x2 x1 x. h4/defCNF/UNIQUE x x1 x2 <=> h4/defCNF/UNIQUE__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !v n conn b a. h4/defCNF/UNIQUE v n (h4/pair/_2C conn (h4/pair/_2C (h4/sum/INR a) (h4/sum/INR b))) <=> v n <=> conn a b
%   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_sums_sumu_u_caseu_u_defu_c0]: !x f1 f. h4/sum/sum__CASE (h4/sum/INL x) f f1 = happ f x
% Assm [h4s_sums_sumu_u_caseu_u_defu_c1]: !y f1 f. h4/sum/sum__CASE (h4/sum/INR y) f f1 = happ f1 y
% 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_defCNFs_UNIQUEu_u_tupledu_u_primitiveu_u_def]: !_16. (!v n conn a b_27. ?v. (v <=> happ v n <=> happ (happ conn a) b_27) /\ (happ (happ (happ (happ (happ _16 v) n) conn) a) b_27 <=> h4/combin/I v)) ==> (!_15. (!n conn a v j_27. ?v. (v <=> happ v n <=> happ (happ conn a) (happ v j_27)) /\ (happ (happ (happ (happ (happ _15 n) conn) a) v) j_27 <=> h4/combin/I v)) ==> (!_14. (!v8 v n conn a. happ (happ (happ (happ (happ _14 v8) v) n) conn) a <=> h4/sum/sum__CASE v8 (happ (happ (happ (happ _15 n) conn) a) v) (happ (happ (happ (happ _16 v) n) conn) a)) ==> (!_13. (!n conn v i b. ?v. (v <=> happ v n <=> happ (happ conn (happ v i)) b) /\ (happ (happ (happ (happ (happ _13 n) conn) v) i) b <=> h4/combin/I v)) ==> (!_12. (!n conn i v j. ?v. (v <=> happ v n <=> happ (happ conn (happ v i)) (happ v j)) /\ (happ (happ (happ (happ (happ _12 n) conn) i) v) j <=> h4/combin/I v)) ==> (!_11. (!v8 n conn v i. happ (happ (happ (happ (happ _11 v8) n) conn) v) i <=> h4/sum/sum__CASE v8 (happ (happ (happ (happ _12 n) conn) i) v) (happ (happ (happ (happ _13 n) conn) v) i)) ==> (!_10. (!v7 v n conn v8. happ (happ (happ (happ (happ _10 v7) v) n) conn) v8 <=> h4/sum/sum__CASE v7 (happ (happ (happ (happ _11 v8) n) conn) v) (happ (happ (happ (happ _14 v8) v) n) conn)) ==> (!_9. (!v n conn v7. happ (happ (happ (happ _9 v) n) conn) v7 = happ (happ (happ (happ _10 v7) v) n) conn) ==> (!_8. (!v n conn v6. happ (happ (happ (happ _8 v) n) conn) v6 <=> h4/pair/pair__CASE v6 (happ (happ (happ _9 v) n) conn)) ==> (!_7. (!v n conn. happ (happ (happ _7 v) n) conn = happ (happ (happ _8 v) n) conn) ==> (!_6. (!v n v4. happ (happ (happ _6 v) n) v4 <=> h4/pair/pair__CASE v4 (happ (happ _7 v) n)) ==> (!_5. (!v n. happ (happ _5 v) n = happ (happ _6 v) n) ==> (!_4. (!v v2. happ (happ _4 v) v2 <=> h4/pair/pair__CASE v2 (happ _5 v)) ==> (!_3. (!v. happ _3 v = happ _4 v) ==> (!_2. (!a_27. happ _2 a_27 <=> h4/pair/pair__CASE a_27 _3) ==> (!_1. (!UNIQUE__tupled. happ _1 UNIQUE__tupled = _2) ==> (!_0. (!R. happ _0 R <=> h4/relation/WF R) ==> h4/defCNF/UNIQUE__tupled = h4/relation/WFREC (h4/min/_40 _0) _1))))))))))))))))
% Assm [h4s_defCNFs_UNIQUEu_u_curriedu_u_def]: !x2 x1 x. h4/defCNF/UNIQUE x x1 x2 <=> happ h4/defCNF/UNIQUE__tupled (h4/pair/_2C x (h4/pair/_2C x1 x2))
% Goal: !v n conn b a. h4/defCNF/UNIQUE v n (h4/pair/_2C conn (h4/pair/_2C (h4/sum/INR a) (h4/sum/INR b))) <=> happ v n <=> happ (happ conn a) b
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_Q172075,TV_Q172071]: ![V_f, V_g]: (![V_x]: s(TV_Q172071,happ(s(t_fun(TV_Q172075,TV_Q172071),V_f),s(TV_Q172075,V_x))) = s(TV_Q172071,happ(s(t_fun(TV_Q172075,TV_Q172071),V_g),s(TV_Q172075,V_x))) => s(t_fun(TV_Q172075,TV_Q172071),V_f) = s(t_fun(TV_Q172075,TV_Q172071),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_sums_sumu_u_caseu_u_defu_c0, axiom, ![TV_u_27b,TV_u_27c,TV_u_27a]: ![V_x, V_f1, V_f]: s(TV_u_27c,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inl(s(TV_u_27a,V_x))),s(t_fun(TV_u_27a,TV_u_27c),V_f),s(t_fun(TV_u_27b,TV_u_27c),V_f1))) = s(TV_u_27c,happ(s(t_fun(TV_u_27a,TV_u_27c),V_f),s(TV_u_27a,V_x)))).
fof(ah4s_sums_sumu_u_caseu_u_defu_c1, axiom, ![TV_u_27a,TV_u_27c,TV_u_27b]: ![V_y, V_f1, V_f]: s(TV_u_27c,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(TV_u_27a,TV_u_27b),h4s_sums_inr(s(TV_u_27b,V_y))),s(t_fun(TV_u_27a,TV_u_27c),V_f),s(t_fun(TV_u_27b,TV_u_27c),V_f1))) = s(TV_u_27c,happ(s(t_fun(TV_u_27b,TV_u_27c),V_f1),s(TV_u_27b,V_y)))).
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_defCNFs_UNIQUEu_u_tupledu_u_primitiveu_u_def, axiom, ![V_uu_16]: (![V_v, V_n, V_conn, V_a, V_bu_27]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_bool,V_a))),s(t_bool,V_bu_27)))) & s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool))))),V_uu_16),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_bool,V_a))),s(t_bool,V_bu_27))) = s(t_bool,h4s_combins_i(s(t_bool,V_v0)))) => ![V_uu_15]: (![V_n, V_conn, V_a, V_v, V_ju_27]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_bool,V_a))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_ju_27)))))) & s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_15),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_bool,V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_ju_27))) = s(t_bool,h4s_combins_i(s(t_bool,V_v0)))) => ![V_uu_14]: (![V_v8, V_v, V_n, V_conn, V_a]: s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool))))),V_uu_14),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_bool,V_a))) = s(t_bool,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_15),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_bool,V_a))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_fun(t_bool,t_bool))))),V_uu_16),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_bool,V_a))))) => ![V_uu_13]: (![V_n, V_conn, V_v, V_i, V_b]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_i))))),s(t_bool,V_b)))) & s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))))),V_uu_13),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_i))),s(t_bool,V_b))) = s(t_bool,h4s_combins_i(s(t_bool,V_v0)))) => ![V_uu_12]: (![V_n, V_conn, V_i, V_v, V_j]: ?[V_v0]: ((p(s(t_bool,V_v0)) <=> s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_i))))),s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_j)))))) & s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_12),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_h4s_nums_num,V_i))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_j))) = s(t_bool,h4s_combins_i(s(t_bool,V_v0)))) => ![V_uu_11]: (![V_v8, V_n, V_conn, V_v, V_i]: s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_11),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_i))) = s(t_bool,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_12),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_h4s_nums_num,V_i))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_fun(t_bool,t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_bool,t_bool))))),V_uu_13),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_i))))) => ![V_uu_10]: (![V_v7, V_v, V_n, V_conn, V_v8]: s(t_bool,happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))))),V_uu_10),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v7))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8))) = s(t_bool,h4s_sums_sumu_u_case(s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v7),s(t_fun(t_h4s_nums_num,t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_bool))))),V_uu_11),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_fun(t_bool,t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_bool,t_bool))))),V_uu_14),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v8))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))))) => ![V_uu_9]: (![V_v, V_n, V_conn, V_v7]: s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))))),V_uu_9),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v7))) = s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)))),happ(s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))))),V_uu_10),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),V_v7))),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))) => ![V_uu_8]: (![V_v, V_n, V_conn, V_v6]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)))),V_uu_8),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))),s(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),V_v6))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),V_v6),s(t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool)))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_fun(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_bool))))),V_uu_9),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))))) => ![V_uu_7]: (![V_v, V_n, V_conn]: s(t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)))),V_uu_7),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))) = s(t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)))),V_uu_8),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn))) => ![V_uu_6]: (![V_v, V_n, V_v4]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool))),V_uu_6),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))),s(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),V_v4))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),V_v4),s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool))),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),t_bool)))),V_uu_7),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))))) => ![V_uu_5]: (![V_v, V_n]: s(t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool))),V_uu_5),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool))),V_uu_6),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_nums_num,V_n))) => ![V_uu_4]: (![V_v, V_v2]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool)),V_uu_4),s(t_fun(t_h4s_nums_num,t_bool),V_v))),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),V_v2))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),V_v2),s(t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool)),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_nums_num,t_fun(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),t_bool))),V_uu_5),s(t_fun(t_h4s_nums_num,t_bool),V_v))))) => ![V_uu_3]: (![V_v]: s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool)),V_uu_3),s(t_fun(t_h4s_nums_num,t_bool),V_v))) = s(t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool),happ(s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool)),V_uu_4),s(t_fun(t_h4s_nums_num,t_bool),V_v))) => ![V_uu_2]: (![V_au_27]: s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),V_uu_2),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),V_au_27))) = s(t_bool,h4s_pairs_pairu_u_case(s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),V_au_27),s(t_fun(t_fun(t_h4s_nums_num,t_bool),t_fun(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),t_bool)),V_uu_3))) => ![V_uu_1]: (![V_UNIQUEu_u_tupled]: s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),V_uu_1),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),V_UNIQUEu_u_tupled))) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),V_uu_2) => ![V_uu_0]: (![V_R]: s(t_bool,happ(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),t_bool),V_uu_0),s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),V_R))) = s(t_bool,h4s_relations_wf(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),V_R))) => s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),h4s_defcnfs_uniqueu_u_tupled) = s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),h4s_relations_wfrec(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),h4s_mins_u_40(s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),t_bool),V_uu_0))),s(t_fun(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool)),V_uu_1))))))))))))))))))))).
fof(ah4s_defCNFs_UNIQUEu_u_curriedu_u_def, axiom, ![V_x2, V_x1, V_x]: s(t_bool,h4s_defcnfs_unique(s(t_fun(t_h4s_nums_num,t_bool),V_x),s(t_h4s_nums_num,V_x1),s(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),V_x2))) = s(t_bool,happ(s(t_fun(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),t_bool),h4s_defcnfs_uniqueu_u_tupled),s(t_h4s_pairs_prod(t_fun(t_h4s_nums_num,t_bool),t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))))),h4s_pairs_u_2c(s(t_fun(t_h4s_nums_num,t_bool),V_x),s(t_h4s_pairs_prod(t_h4s_nums_num,t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)))),h4s_pairs_u_2c(s(t_h4s_nums_num,V_x1),s(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),V_x2)))))))).
fof(ch4s_defCNFs_UNIQUEu_u_defu_c3, conjecture, ![V_v, V_n, V_conn, V_b, V_a]: (p(s(t_bool,h4s_defcnfs_unique(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n),s(t_h4s_pairs_prod(t_fun(t_bool,t_fun(t_bool,t_bool)),t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool))),h4s_pairs_u_2c(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_h4s_pairs_prod(t_h4s_sums_sum(t_h4s_nums_num,t_bool),t_h4s_sums_sum(t_h4s_nums_num,t_bool)),h4s_pairs_u_2c(s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),h4s_sums_inr(s(t_bool,V_a))),s(t_h4s_sums_sum(t_h4s_nums_num,t_bool),h4s_sums_inr(s(t_bool,V_b)))))))))) <=> s(t_bool,happ(s(t_fun(t_h4s_nums_num,t_bool),V_v),s(t_h4s_nums_num,V_n))) = s(t_bool,happ(s(t_fun(t_bool,t_bool),happ(s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_conn),s(t_bool,V_a))),s(t_bool,V_b))))).
