Consider the following premises. For all x, x is a server if and only if x will write a letter. There is at least one x for which x will write a letter if and only if x is a server. Can we infer the following from them? If we can, name the inference rule being used: For all x, if is not true that x will write a letter if and only if x is a server.
That contradicts the premises. Therefore the answer is no.