%   ORIGINAL: h4/toto/num__dt__case__cong
% 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/IMP__CLAUSES_c3: !t. t ==> t <=> 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/toto/num__dt__repfns_c0: !a. h4/toto/_20_40ind__typetoto3 (h4/toto/_20_40ind__typetoto4 a) = a
% Assm: h4/toto/num__dt__repfns_c1: !r. (\a0. !_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) \/ (?a. a00 = (\a1. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a1 (\n. h4/ind__type/BOTTOM))) a /\ _27num__dt_27 a) ==> _27num__dt_27 a00) ==> _27num__dt_27 a0) r <=> h4/toto/_20_40ind__typetoto4 (h4/toto/_20_40ind__typetoto3 r) = r
% Assm: h4/toto/hidden____20__40ind____typetoto0____def: h4/toto/_20_40ind__typetoto0 = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB (\n. h4/ind__type/BOTTOM))
% Assm: h4/toto/hidden____20__40ind____typetoto1____def: h4/toto/_20_40ind__typetoto1 = (\a. h4/toto/_20_40ind__typetoto3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/toto/_20_40ind__typetoto4 a)))
% Assm: h4/toto/hidden____20__40ind____typetoto2____def: h4/toto/_20_40ind__typetoto2 = (\a. h4/toto/_20_40ind__typetoto3 ((\a0. h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a0 (\n. h4/ind__type/BOTTOM))) (h4/toto/_20_40ind__typetoto4 a)))
% Assm: h4/toto/zer0: h4/toto/zer = h4/toto/_20_40ind__typetoto0
% Assm: h4/toto/bit10: h4/toto/bit1 = h4/toto/_20_40ind__typetoto1
% Assm: h4/toto/bit20: h4/toto/bit2 = h4/toto/_20_40ind__typetoto2
% Assm: h4/toto/num__dt__case__def_c0: !v f1 f. h4/toto/num__dt__CASE h4/toto/zer v f f1 = v
% Assm: h4/toto/num__dt__case__def_c1: !v f1 f a. h4/toto/num__dt__CASE (h4/toto/bit1 a) v f f1 = f a
% Assm: h4/toto/num__dt__case__def_c2: !v f1 f a. h4/toto/num__dt__CASE (h4/toto/bit2 a) v f f1 = f1 a
% Goal: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/toto/zer ==> v = v_27) /\ (!a. M_27 = h4/toto/bit1 a ==> f a = f_27 a) /\ (!a. M_27 = h4/toto/bit2 a ==> f1 a = f1_27 a) ==> h4/toto/num__dt__CASE M v f f1 = h4/toto/num__dt__CASE M_27 v_27 f_27 f1_27
%   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_IMPu_u_CLAUSESu_c3]: !t. t ==> t <=> 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_totos_numu_u_dtu_u_repfnsu_c0]: !a. h4/toto/_20_40ind__typetoto3 (h4/toto/_20_40ind__typetoto4 a) = a
% Assm [h4s_totos_numu_u_dtu_u_repfnsu_c1]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!r. (!_27num__dt_27. (!a00. a00 = h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0 \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27num__dt_27 a) \/ (?a. a00 = h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS a _0) /\ happ _27num__dt_27 a) ==> happ _27num__dt_27 a00) ==> happ _27num__dt_27 r) <=> h4/toto/_20_40ind__typetoto4 (h4/toto/_20_40ind__typetoto3 r) = r)
% Assm [h4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto0u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> h4/toto/_20_40ind__typetoto0 = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR h4/num/0 h4/bool/ARB _0)
% Assm [h4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto1u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/toto/_20_40ind__typetoto1 x = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR (h4/num/SUC h4/num/0) h4/bool/ARB (h4/ind__type/FCONS (h4/toto/_20_40ind__typetoto4 x) _0)))
% Assm [h4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto2u_u_u_u_def]: !_0. (!n. happ _0 n = h4/ind__type/BOTTOM) ==> (!x. happ h4/toto/_20_40ind__typetoto2 x = h4/toto/_20_40ind__typetoto3 (h4/ind__type/CONSTR (h4/num/SUC (h4/num/SUC h4/num/0)) h4/bool/ARB (h4/ind__type/FCONS (h4/toto/_20_40ind__typetoto4 x) _0)))
% Assm [h4s_totos_zer0]: h4/toto/zer = h4/toto/_20_40ind__typetoto0
% Assm [h4s_totos_bit10]: h4/toto/bit1 = h4/toto/_20_40ind__typetoto1
% Assm [h4s_totos_bit20]: h4/toto/bit2 = h4/toto/_20_40ind__typetoto2
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c0]: !v f1 f. h4/toto/num__dt__CASE h4/toto/zer v f f1 = v
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c1]: !v f1 f a. h4/toto/num__dt__CASE (happ h4/toto/bit1 a) v f f1 = happ f a
% Assm [h4s_totos_numu_u_dtu_u_caseu_u_defu_c2]: !v f1 f a. h4/toto/num__dt__CASE (happ h4/toto/bit2 a) v f f1 = happ f1 a
% Goal: !v_27 v f1_27 f1 f_27 f M_27 M. M = M_27 /\ (M_27 = h4/toto/zer ==> v = v_27) /\ (!a. M_27 = happ h4/toto/bit1 a ==> happ f a = happ f_27 a) /\ (!a. M_27 = happ h4/toto/bit2 a ==> happ f1 a = happ f1_27 a) ==> h4/toto/num__dt__CASE M v f f1 = h4/toto/num__dt__CASE M_27 v_27 f_27 f1_27
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q252057,TV_Q252053]: ![V_f, V_g]: (![V_x]: s(TV_Q252053,happ(s(t_fun(TV_Q252057,TV_Q252053),V_f),s(TV_Q252057,V_x))) = s(TV_Q252053,happ(s(t_fun(TV_Q252057,TV_Q252053),V_g),s(TV_Q252057,V_x))) => s(t_fun(TV_Q252057,TV_Q252053),V_f) = s(t_fun(TV_Q252057,TV_Q252053),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,t))).
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_IMPu_u_CLAUSESu_c3, axiom, ![V_t]: ((p(s(t_bool,V_t)) => p(s(t_bool,V_t))) <=> p(s(t_bool,t)))).
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_totos_numu_u_dtu_u_repfnsu_c0, axiom, ![V_a]: s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_a))))) = s(t_h4s_totos_numu_u_dt,V_a)).
fof(ah4s_totos_numu_u_dtu_u_repfnsu_c1, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_r]: (![V_uu_27numu_u_dtu_27]: (![V_a00]: ((s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))) | (?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))) | ?[V_a]: (s(t_h4s_indu_u_types_recspace(t_bool),V_a00) = s(t_h4s_indu_u_types_recspace(t_bool),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(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),V_a),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))) & p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a))))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_a00))))) => p(s(t_bool,happ(s(t_fun(t_h4s_indu_u_types_recspace(t_bool),t_bool),V_uu_27numu_u_dtu_27),s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) <=> s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),V_r))))) = s(t_h4s_indu_u_types_recspace(t_bool),V_r)))).
fof(ah4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto0u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto0) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_0),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))).
fof(ah4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto1u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto1),s(t_h4s_totos_numu_u_dt,V_x))) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_constr(s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,h4s_nums_0))),s(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_totos_hiddenu_u_u_u_20u_u_40indu_u_u_u_typetoto2u_u_u_u_def, axiom, ![V_uu_0]: (![V_n]: s(t_h4s_indu_u_types_recspace(t_bool),happ(s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0),s(t_h4s_nums_num,V_n))) = s(t_h4s_indu_u_types_recspace(t_bool),h4s_indu_u_types_bottom) => ![V_x]: s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto2),s(t_h4s_totos_numu_u_dt,V_x))) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto3(s(t_h4s_indu_u_types_recspace(t_bool),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(t_bool,h4s_bools_arb),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),h4s_indu_u_types_fcons(s(t_h4s_indu_u_types_recspace(t_bool),h4s_totos_u_20u_40indu_u_typetoto4(s(t_h4s_totos_numu_u_dt,V_x))),s(t_fun(t_h4s_nums_num,t_h4s_indu_u_types_recspace(t_bool)),V_uu_0))))))))).
fof(ah4s_totos_zer0, axiom, s(t_h4s_totos_numu_u_dt,h4s_totos_zer) = s(t_h4s_totos_numu_u_dt,h4s_totos_u_20u_40indu_u_typetoto0)).
fof(ah4s_totos_bit10, axiom, s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1) = s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto1)).
fof(ah4s_totos_bit20, axiom, s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2) = s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_u_20u_40indu_u_typetoto2)).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_defu_c0, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,h4s_totos_zer),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,V_v)).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_defu_c1, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_h4s_totos_numu_u_dt,V_a)))).
fof(ah4s_totos_numu_u_dtu_u_caseu_u_defu_c2, axiom, ![TV_u_27a]: ![V_v, V_f1, V_f, V_a]: s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1),s(t_h4s_totos_numu_u_dt,V_a)))).
fof(ch4s_totos_numu_u_dtu_u_caseu_u_cong, conjecture, ![TV_u_27a]: ![V_vu_27, V_v, V_f1u_27, V_f1, V_fu_27, V_f, V_Mu_27, V_M]: ((s(t_h4s_totos_numu_u_dt,V_M) = s(t_h4s_totos_numu_u_dt,V_Mu_27) & ((s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,h4s_totos_zer) => s(TV_u_27a,V_v) = s(TV_u_27a,V_vu_27)) & (![V_a]: (s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit1),s(t_h4s_totos_numu_u_dt,V_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_h4s_totos_numu_u_dt,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fu_27),s(t_h4s_totos_numu_u_dt,V_a)))) & ![V_a]: (s(t_h4s_totos_numu_u_dt,V_Mu_27) = s(t_h4s_totos_numu_u_dt,happ(s(t_fun(t_h4s_totos_numu_u_dt,t_h4s_totos_numu_u_dt),h4s_totos_bit2),s(t_h4s_totos_numu_u_dt,V_a))) => s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1),s(t_h4s_totos_numu_u_dt,V_a))) = s(TV_u_27a,happ(s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1u_27),s(t_h4s_totos_numu_u_dt,V_a))))))) => s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_M),s(TV_u_27a,V_v),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1))) = s(TV_u_27a,h4s_totos_numu_u_dtu_u_case(s(t_h4s_totos_numu_u_dt,V_Mu_27),s(TV_u_27a,V_vu_27),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_fu_27),s(t_fun(t_h4s_totos_numu_u_dt,TV_u_27a),V_f1u_27))))).
