Consider the following premises. For all z, z is not a police officer. William is a police officer or Joseph is not sleeping. Can we infer the following from them? If we can, name the inference rule being used: Joseph is not sleeping.
 From the fact that for all z, z is not a police officer we can infer that William is not a police officer via universal instantiation. From the fact that William is a police officer or Joseph is not sleeping we can infer that if Joseph sleeps, then William is a police officer via rewriting. Finally, from the fact that if Joseph sleeps, then William is a police officer, and that William is not a police officer we can infer that Joseph is not sleeping via modus tollens. Therefore, the answer is yes.