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