%   ORIGINAL: h4/transc/TAN__PERIODIC
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/transc/SIN__PERIODIC: !x. h4/transc/sin (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/sin x
% Assm: h4/transc/COS__PERIODIC: !x. h4/transc/cos (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/cos x
% Assm: h4/transc/tan0: !x. h4/transc/tan x = h4/real/_2F (h4/transc/sin x) (h4/transc/cos x)
% Goal: !x. h4/transc/tan (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/tan x
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_transcs_SINu_u_PERIODIC]: !x. h4/transc/sin (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/sin x
% Assm [h4s_transcs_COSu_u_PERIODIC]: !x. h4/transc/cos (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/cos x
% Assm [h4s_transcs_tan0]: !x. h4/transc/tan x = h4/real/_2F (h4/transc/sin x) (h4/transc/cos x)
% Goal: !x. h4/transc/tan (h4/realax/real__add x (h4/realax/real__mul (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))) h4/transc/pi)) = h4/transc/tan x
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_Q194986,TV_Q194982]: ![V_f, V_g]: (![V_x]: s(TV_Q194982,happ(s(t_fun(TV_Q194986,TV_Q194982),V_f),s(TV_Q194986,V_x))) = s(TV_Q194982,happ(s(t_fun(TV_Q194986,TV_Q194982),V_g),s(TV_Q194986,V_x))) => s(t_fun(TV_Q194986,TV_Q194982),V_f) = s(t_fun(TV_Q194986,TV_Q194982),V_g))).
fof(ah4s_bools_TRUTH, axiom, p(s(t_bool,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_SINu_u_PERIODIC, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_transcs_pi))))))) = s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_transcs_COSu_u_PERIODIC, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_transcs_pi))))))) = s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,V_x)))).
fof(ah4s_transcs_tan0, axiom, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,V_x))) = s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_sin(s(t_h4s_realaxs_real,V_x))),s(t_h4s_realaxs_real,h4s_transcs_cos(s(t_h4s_realaxs_real,V_x)))))).
fof(ch4s_transcs_TANu_u_PERIODIC, conjecture, ![V_x]: s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_add(s(t_h4s_realaxs_real,V_x),s(t_h4s_realaxs_real,h4s_realaxs_realu_u_mul(s(t_h4s_realaxs_real,h4s_reals_realu_u_ofu_u_num(s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_zero))))))),s(t_h4s_realaxs_real,h4s_transcs_pi))))))) = s(t_h4s_realaxs_real,h4s_transcs_tan(s(t_h4s_realaxs_real,V_x)))).
