Consider the following premises. For all z, z is a server or z will not work. For all z, if z were a server, then z is working. There is at least one z for which z is a server or z will not work. Can we infer the following from them? For all z, if is not true that z is a server if and only if z will work.
 From the fact that there is at least one z for which z is a server or z will not work we can infer that there is at least one z for which if z works, then z is a server. From the fact that for all z, z is a server or z will not work we can infer that for all z, if z works, then z is a server. Finally, from the fact that for all z, if z were a server, then z is working, and that for all z, if z works, then z is a server we can infer that for all z, z is a server if and only if z will work, which contradicts that For all z, if is not true that z is a server if and only if z will work. Therefore, the answer is no.