%   ORIGINAL: h4/numeral__bit/NUMERAL__BITWISE_c1
% 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/REFL__CLAUSE: !x. x = x <=> T
% Assm: h4/arithmetic/NUMERAL__DEF: !x. h4/arithmetic/NUMERAL x = x
% Assm: h4/numeral__bit/iBITWISE__def: h4/numeral__bit/iBITWISE = h4/bit/BITWISE
% Goal: !x f a. h4/bit/BITWISE x f (h4/arithmetic/NUMERAL a) h4/num/0 = h4/arithmetic/NUMERAL (h4/numeral__bit/iBITWISE x f (h4/arithmetic/NUMERAL a) h4/num/0)
%   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_REFLu_u_CLAUSE]: !x. x = x <=> T
% Assm [h4s_arithmetics_NUMERALu_u_DEF]: !x. h4/arithmetic/NUMERAL x = x
% Assm [h4s_numeralu_u_bits_iBITWISEu_u_def]: h4/numeral__bit/iBITWISE = h4/bit/BITWISE
% Goal: !x f a. happ (happ (happ (happ h4/bit/BITWISE x) f) (h4/arithmetic/NUMERAL a)) h4/num/0 = h4/arithmetic/NUMERAL (happ (happ (happ (happ h4/numeral__bit/iBITWISE x) f) (h4/arithmetic/NUMERAL a)) h4/num/0)
fof(aHLu_TRUTH, axiom, p(s(t_bool,t))).
fof(aHLu_FALSITY, axiom, ~ (p(s(t_bool,f0)))).
fof(aHLu_BOOLu_CASES, axiom, ![V_t]: (s(t_bool,V_t) = s(t_bool,t) | s(t_bool,V_t) = s(t_bool,f0))).
fof(aHLu_EXT, axiom, ![TV_Q15777,TV_Q15773]: ![V_f, V_g]: (![V_x]: s(TV_Q15773,happ(s(t_fun(TV_Q15777,TV_Q15773),V_f),s(TV_Q15777,V_x))) = s(TV_Q15773,happ(s(t_fun(TV_Q15777,TV_Q15773),V_g),s(TV_Q15777,V_x))) => s(t_fun(TV_Q15777,TV_Q15773),V_f) = s(t_fun(TV_Q15777,TV_Q15773),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_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_arithmetics_NUMERALu_u_DEF, axiom, ![V_x]: s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_x))) = s(t_h4s_nums_num,V_x)).
fof(ah4s_numeralu_u_bits_iBITWISEu_u_def, axiom, s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise) = s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_bits_bitwise)).
fof(ch4s_numeralu_u_bits_NUMERALu_u_BITWISEu_c1, conjecture, ![V_x, V_f, V_a]: s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_bits_bitwise),s(t_h4s_nums_num,V_x))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_a))))),s(t_h4s_nums_num,h4s_nums_0))) = s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),happ(s(t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)),happ(s(t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num))),happ(s(t_fun(t_h4s_nums_num,t_fun(t_fun(t_bool,t_fun(t_bool,t_bool)),t_fun(t_h4s_nums_num,t_fun(t_h4s_nums_num,t_h4s_nums_num)))),h4s_numeralu_u_bits_ibitwise),s(t_h4s_nums_num,V_x))),s(t_fun(t_bool,t_fun(t_bool,t_bool)),V_f))),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,V_a))))),s(t_h4s_nums_num,h4s_nums_0)))))).
