Consider the following premises. For all z, if z were a writer, then z is a police officer. For all z, z is a writer. For all z, z will write a letter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which z is not a police officer.
 From the fact that for all z, if z were a writer, then z is a police officer, and that for all z, z is a writer we can infer that for all z, z is a police officer via universal modus ponens. From the fact that for all z, z will write a letter, and that for all z, z is a police officer we can infer that for all z, z will write a letter and z is a police officer via universal conjunction. Finally, from the fact that for all z, z will write a letter and z is a police officer we can infer that for all z, z will write a letter via universal simplification, which contradicts that There is at least one z for which z is not a police officer. Therefore, the answer is no.