%   ORIGINAL: h4/transc/ATN__TAN
% 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/FORALL__SIMP: !t. (!x. t) <=> t
% Assm: h4/bool/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/transc/ATN_c2: !y. h4/transc/tan (h4/transc/atn y) = y
% Goal: !y. h4/transc/tan (h4/transc/atn y) = y
%   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_FORALLu_u_SIMP]: !t. (!x. t) <=> t
% Assm [h4s_bools_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_transcs_ATNu_c2]: !y. h4/transc/tan (h4/transc/atn y) = y
% Goal: !y. h4/transc/tan (h4/transc/atn y) = y
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_Q195511,TV_Q195507]: ![V_f, V_g]: (![V_x]: s(TV_Q195507,happ(s(t_fun(TV_Q195511,TV_Q195507),V_f),s(TV_Q195511,V_x))) = s(TV_Q195507,happ(s(t_fun(TV_Q195511,TV_Q195507),V_g),s(TV_Q195511,V_x))) => s(t_fun(TV_Q195511,TV_Q195507),V_f) = s(t_fun(TV_Q195511,TV_Q195507),V_g))).
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_transcs_ATNu_c2, axiom, ![V_y]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,h4s_transcs_atn(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,V_y)).
fof(ch4s_transcs_ATNu_u_TAN, conjecture, ![V_y]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,h4s_transcs_atn(s(t_h4s_realaxs_real,V_y))))) = s(t_h4s_realaxs_real,V_y)).
