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