%   ORIGINAL: h4/enumeral/OWL__bt__to__ol
% 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/TRUTH: T
% Assm: h4/bool/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/enumeral/ol__set: !t cmp. h4/enumeral/ENUMERAL cmp t = h4/list/LIST__TO__SET (h4/enumeral/bt__to__ol cmp t)
% Assm: h4/enumeral/OL__bt__to__ol: !t cmp. h4/enumeral/OL cmp (h4/enumeral/bt__to__ol cmp t)
% Assm: h4/enumeral/OWL0: !s l cmp. h4/enumeral/OWL cmp s l <=> s = h4/list/LIST__TO__SET l /\ h4/enumeral/OL cmp l
% Goal: !t cmp. h4/enumeral/OWL cmp (h4/enumeral/ENUMERAL cmp t) (h4/enumeral/bt__to__ol cmp t)
%   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_TRUTH]: T
% Assm [h4s_bools_ANDu_u_CLAUSESu_c0]: !t. T /\ 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_enumerals_olu_u_set]: !t cmp. h4/enumeral/ENUMERAL cmp t = h4/list/LIST__TO__SET (h4/enumeral/bt__to__ol cmp t)
% Assm [h4s_enumerals_OLu_u_btu_u_tou_u_ol]: !t cmp. h4/enumeral/OL cmp (h4/enumeral/bt__to__ol cmp t)
% Assm [h4s_enumerals_OWL0]: !s l cmp. h4/enumeral/OWL cmp s l <=> s = h4/list/LIST__TO__SET l /\ h4/enumeral/OL cmp l
% Goal: !t cmp. h4/enumeral/OWL cmp (h4/enumeral/ENUMERAL cmp t) (h4/enumeral/bt__to__ol cmp t)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t0))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) | s(t_bool,V_t) = s(t_bool,f))).
fof(aHLu_EXT, axiom, ![TV_Q333715,TV_Q333711]: ![V_f, V_g]: (![V_x]: s(TV_Q333711,happ(s(t_fun(TV_Q333715,TV_Q333711),V_f),s(TV_Q333715,V_x))) = s(TV_Q333711,happ(s(t_fun(TV_Q333715,TV_Q333711),V_g),s(TV_Q333715,V_x))) => s(t_fun(TV_Q333715,TV_Q333711),V_f) = s(t_fun(TV_Q333715,TV_Q333711),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,t0))).
fof(ah4s_bools_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t0)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_t)))).
fof(ah4s_bools_REFLu_u_CLAUSE, axiom, ![TV_u_27a]: ![V_x]: (s(TV_u_27a,V_x) = s(TV_u_27a,V_x) <=> p(s(t_bool,t0)))).
fof(ah4s_bools_EQu_u_CLAUSESu_c1, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t0) <=> p(s(t_bool,V_t)))).
fof(ah4s_enumerals_olu_u_set, axiom, ![TV_u_27a]: ![V_t, V_cmp]: s(t_fun(TV_u_27a,t_bool),h4s_enumerals_enumeral(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t)))))).
fof(ah4s_enumerals_OLu_u_btu_u_tou_u_ol, axiom, ![TV_u_27a]: ![V_t, V_cmp]: p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))))))).
fof(ah4s_enumerals_OWL0, axiom, ![TV_u_27a]: ![V_s, V_l, V_cmp]: (p(s(t_bool,h4s_enumerals_owl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),V_s),s(t_h4s_lists_list(TV_u_27a),V_l)))) <=> (s(t_fun(TV_u_27a,t_bool),V_s) = s(t_fun(TV_u_27a,t_bool),h4s_lists_listu_u_tou_u_set(s(t_h4s_lists_list(TV_u_27a),V_l))) & p(s(t_bool,h4s_enumerals_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_lists_list(TV_u_27a),V_l))))))).
fof(ch4s_enumerals_OWLu_u_btu_u_tou_u_ol, conjecture, ![TV_u_27a]: ![V_t, V_cmp]: p(s(t_bool,h4s_enumerals_owl(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_fun(TV_u_27a,t_bool),h4s_enumerals_enumeral(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))),s(t_h4s_lists_list(TV_u_27a),h4s_enumerals_btu_u_tou_u_ol(s(t_h4s_totos_toto(TV_u_27a),V_cmp),s(t_h4s_enumerals_bt(TV_u_27a),V_t))))))).
