Consider the following premises. For all z, z is fast or z is not a writer. For all z, z is a writer or z is not fast. There is at least one z for which z is not fast. Can we infer the following from them? If we can, name the inference rule being used: For all z, z is a writer.
 From the fact that for all z, z is a writer or z is not fast we can infer that for all z, if z were fast, then z is a writer via universal rewriting. From the fact that for all z, z is fast or z is not a writer we can infer that for all z, if z were a writer, then z is fast via universal rewriting. From the fact that for all z, if z were a writer, then z is fast, and that for all z, if z were fast, then z is a writer we can infer that for all z, z is a writer if and only if z is fast via universal biconditional introduction. Finally, from the fact that for all z, z is a writer if and only if z is fast, and that there is at least one z for which z is not fast we can infer that there is at least one z for which z is not a writer via existential biconditional elimination, which contradicts that For all z, z is a writer. Therefore, the answer is no.