%   ORIGINAL: h4/rich__list/REVERSE__FLAT
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/list/FLAT0_c0: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm: h4/list/FLAT0_c1: !t h. h4/list/FLAT (h4/list/CONS h t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm: h4/list/MAP0_c0: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm: h4/list/MAP0_c1: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (f h) (h4/list/MAP f t)
% Assm: h4/list/list__INDUCT: !P. P h4/list/NIL /\ (!t. P t ==> (!h. P (h4/list/CONS h t))) ==> (!l. P l)
% Assm: h4/list/REVERSE__APPEND: !l2 l1. h4/list/REVERSE (h4/list/APPEND l1 l2) = h4/list/APPEND (h4/list/REVERSE l2) (h4/list/REVERSE l1)
% Assm: h4/list/REVERSE__SNOC__DEF_c0: h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm: h4/list/REVERSE__SNOC__DEF_c1: !x l. h4/list/REVERSE (h4/list/CONS x l) = h4/list/SNOC x (h4/list/REVERSE l)
% Assm: h4/rich__list/FLAT__SNOC: !x l. h4/list/FLAT (h4/list/SNOC x l) = h4/list/APPEND (h4/list/FLAT l) x
% Goal: !l. h4/list/REVERSE (h4/list/FLAT l) = h4/list/FLAT (h4/list/REVERSE (h4/list/MAP h4/list/REVERSE l))
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_lists_FLAT0u_c0]: h4/list/FLAT h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_FLAT0u_c1]: !t h. h4/list/FLAT (h4/list/CONS h t) = h4/list/APPEND h (h4/list/FLAT t)
% Assm [h4s_lists_MAP0u_c0]: !f. h4/list/MAP f h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_MAP0u_c1]: !t h f. h4/list/MAP f (h4/list/CONS h t) = h4/list/CONS (happ f h) (h4/list/MAP f t)
% Assm [h4s_lists_listu_u_INDUCT]: !P. happ P h4/list/NIL /\ (!t. happ P t ==> (!h. happ P (h4/list/CONS h t))) ==> (!l. happ P l)
% Assm [h4s_lists_REVERSEu_u_APPEND]: !l2 l1. happ h4/list/REVERSE (h4/list/APPEND l1 l2) = h4/list/APPEND (happ h4/list/REVERSE l2) (happ h4/list/REVERSE l1)
% Assm [h4s_lists_REVERSEu_u_SNOCu_u_DEFu_c0]: happ h4/list/REVERSE h4/list/NIL = h4/list/NIL
% Assm [h4s_lists_REVERSEu_u_SNOCu_u_DEFu_c1]: !x l. happ h4/list/REVERSE (h4/list/CONS x l) = h4/list/SNOC x (happ h4/list/REVERSE l)
% Assm [h4s_richu_u_lists_FLATu_u_SNOC]: !x l. h4/list/FLAT (h4/list/SNOC x l) = h4/list/APPEND (h4/list/FLAT l) x
% Goal: !l. happ h4/list/REVERSE (h4/list/FLAT l) = h4/list/FLAT (happ h4/list/REVERSE (h4/list/MAP h4/list/REVERSE l))
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_Q162308,TV_Q162304]: ![V_f, V_g]: (![V_x]: s(TV_Q162304,happ(s(t_fun(TV_Q162308,TV_Q162304),V_f),s(TV_Q162308,V_x))) = s(TV_Q162304,happ(s(t_fun(TV_Q162308,TV_Q162304),V_g),s(TV_Q162308,V_x))) => s(t_fun(TV_Q162308,TV_Q162304),V_f) = s(t_fun(TV_Q162308,TV_Q162304),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_FORALLu_u_SIMP, axiom, ![TV_u_27a]: ![V_t]: (![V_x]: p(s(t_bool,V_t)) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_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,t)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) <=> p(s(t_bool,V_t)))).
fof(ah4s_lists_FLAT0u_c0, axiom, ![TV_u_27a]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)).
fof(ah4s_lists_FLAT0u_c1, axiom, ![TV_u_27a]: ![V_t, V_h]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_cons(s(t_h4s_lists_list(TV_u_27a),V_h),s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_t))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_h),s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_t)))))).
fof(ah4s_lists_MAP0u_c0, axiom, ![TV_u_27a,TV_u_27b]: ![V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_MAP0u_c1, axiom, ![TV_u_27b,TV_u_27a]: ![V_t, V_h, V_f]: s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t))))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_cons(s(TV_u_27b,happ(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(TV_u_27a,V_h))),s(t_h4s_lists_list(TV_u_27b),h4s_lists_map(s(t_fun(TV_u_27a,TV_u_27b),V_f),s(t_h4s_lists_list(TV_u_27a),V_t)))))).
fof(ah4s_lists_listu_u_INDUCT, axiom, ![TV_u_27a]: ![V_P]: ((p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_nil)))) & ![V_t]: (p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_t)))) => ![V_h]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_h),s(t_h4s_lists_list(TV_u_27a),V_t)))))))) => ![V_l]: p(s(t_bool,happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_bool),V_P),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_lists_REVERSEu_u_APPEND, axiom, ![TV_u_27a]: ![V_l2, V_l1]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),V_l1),s(t_h4s_lists_list(TV_u_27a),V_l2))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),V_l2))),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),V_l1)))))).
fof(ah4s_lists_REVERSEu_u_SNOCu_u_DEFu_c0, axiom, ![TV_u_27b]: s(t_h4s_lists_list(TV_u_27b),happ(s(t_fun(t_h4s_lists_list(TV_u_27b),t_h4s_lists_list(TV_u_27b)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil))) = s(t_h4s_lists_list(TV_u_27b),h4s_lists_nil)).
fof(ah4s_lists_REVERSEu_u_SNOCu_u_DEFu_c1, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),h4s_lists_cons(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_snoc(s(TV_u_27a,V_x),s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),V_l)))))).
fof(ah4s_richu_u_lists_FLATu_u_SNOC, axiom, ![TV_u_27a]: ![V_x, V_l]: s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_snoc(s(t_h4s_lists_list(TV_u_27a),V_x),s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_append(s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l))),s(t_h4s_lists_list(TV_u_27a),V_x)))).
fof(ch4s_richu_u_lists_REVERSEu_u_FLAT, conjecture, ![TV_u_27a]: ![V_l]: s(t_h4s_lists_list(TV_u_27a),happ(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l))))) = s(t_h4s_lists_list(TV_u_27a),h4s_lists_flat(s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),happ(s(t_fun(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),t_h4s_lists_list(t_h4s_lists_list(TV_u_27a))),h4s_lists_reverse),s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),h4s_lists_map(s(t_fun(t_h4s_lists_list(TV_u_27a),t_h4s_lists_list(TV_u_27a)),h4s_lists_reverse),s(t_h4s_lists_list(t_h4s_lists_list(TV_u_27a)),V_l)))))))).
