%   ORIGINAL: h4/transc/ATN__BOUNDS_c0
% 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/AND__CLAUSES_c0: !t. T /\ t <=> t
% Assm: h4/bool/EQ__CLAUSES_c1: !t. (t <=> T) <=> t
% Assm: h4/transc/ATN_c0: !y. h4/realax/real__lt (h4/realax/real__neg (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/transc/atn y)
% Assm: h4/transc/ATN_c1: !y. h4/realax/real__lt (h4/transc/atn y) (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Goal: !y. h4/realax/real__lt (h4/realax/real__neg (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/transc/atn 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_ANDu_u_CLAUSESu_c0]: !t. T /\ t <=> t
% Assm [h4s_bools_EQu_u_CLAUSESu_c1]: !t. (t <=> T) <=> t
% Assm [h4s_transcs_ATNu_c0]: !y. h4/realax/real__lt (h4/realax/real__neg (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/transc/atn y)
% Assm [h4s_transcs_ATNu_c1]: !y. h4/realax/real__lt (h4/transc/atn y) (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))
% Goal: !y. h4/realax/real__lt (h4/realax/real__neg (h4/real/_2F h4/transc/pi (h4/real/real__of__num (h4/arithmetic/NUMERAL (h4/arithmetic/BIT2 h4/arithmetic/ZERO))))) (h4/transc/atn 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_Q195536,TV_Q195532]: ![V_f, V_g]: (![V_x]: s(TV_Q195532,happ(s(t_fun(TV_Q195536,TV_Q195532),V_f),s(TV_Q195536,V_x))) = s(TV_Q195532,happ(s(t_fun(TV_Q195536,TV_Q195532),V_g),s(TV_Q195536,V_x))) => s(t_fun(TV_Q195536,TV_Q195532),V_f) = s(t_fun(TV_Q195536,TV_Q195532),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_ANDu_u_CLAUSESu_c0, axiom, ![V_t]: ((p(s(t_bool,t)) & p(s(t_bool,V_t))) <=> p(s(t_bool,V_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_transcs_ATNu_c0, axiom, ![V_y]: p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),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_atn(s(t_h4s_realaxs_real,V_y))))))).
fof(ah4s_transcs_ATNu_c1, axiom, ![V_y]: p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_transcs_atn(s(t_h4s_realaxs_real,V_y))),s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),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))))))))))))).
fof(ch4s_transcs_ATNu_u_BOUNDSu_c0, conjecture, ![V_y]: p(s(t_bool,h4s_realaxs_realu_u_lt(s(t_h4s_realaxs_real,h4s_realaxs_realu_u_neg(s(t_h4s_realaxs_real,h4s_reals_u_2f(s(t_h4s_realaxs_real,h4s_transcs_pi),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_atn(s(t_h4s_realaxs_real,V_y))))))).
