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