# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))))=>p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),X1),s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,X2)))))))=>![X3]:p(s(t_bool,happ(s(t_fun(t_h4s_strings_char,t_bool),X1),s(t_h4s_strings_char,X3))))),file('i/f/string/CHAR__INDUCT__THM', ch4s_strings_CHARu_u_INDUCTu_u_THM)).
fof(2, axiom,p(s(t_bool,t)),file('i/f/string/CHAR__INDUCT__THM', aHLu_TRUTH)).
fof(3, axiom,~(p(s(t_bool,f))),file('i/f/string/CHAR__INDUCT__THM', aHLu_FALSITY)).
fof(6, axiom,![X5]:?[X6]:(s(t_h4s_strings_char,X5)=s(t_h4s_strings_char,h4s_strings_chr(s(t_h4s_nums_num,X6)))&p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X6),s(t_h4s_nums_num,h4s_arithmetics_numeral(s(t_h4s_nums_num,h4s_arithmetics_bit2(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_bit1(s(t_h4s_nums_num,h4s_arithmetics_zero))))))))))))))))))))))),file('i/f/string/CHAR__INDUCT__THM', ah4s_strings_CHRu_u_ONTO)).
fof(7, axiom,![X4]:(s(t_bool,X4)=s(t_bool,t)|s(t_bool,X4)=s(t_bool,f)),file('i/f/string/CHAR__INDUCT__THM', aHLu_BOOLu_CASES)).
# SZS output end CNFRefutation
