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