Consider the following premises. For all y, if y reads a book, then y is a server. For all y, if y were a server, then y is a doctor. There is at least one y for which y is not a server. For all y, if y were a doctor, then y is reading a book. Can we infer the following from them? There is at least one y for which y is not a doctor.
 From the fact that for all y, if y were a doctor, then y is reading a book, and that for all y, if y reads a book, then y is a server we can infer that for all y, if y were a doctor, then y is a server. From the fact that for all y, if y were a doctor, then y is a server, and that for all y, if y were a server, then y is a doctor we can infer that for all y, y is a doctor if and only if y is a server. Finally, from the fact that for all y, y is a doctor if and only if y is a server, and that there is at least one y for which y is not a server we can infer that there is at least one y for which y is not a doctor. Therefore, the answer is yes.