Consider the following premises. For all z, z will not go running. For all z, if z goes running, then z is reading a book. For all z, if z reads a book, then z is a police officer. For all z, if z reads a book, then z is running. For all z, if z were a police officer, then z is reading a book. 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 a police officer.
 From the fact that for all z, if z reads a book, then z is a police officer, and that for all z, if z were a police officer, then z is reading a book we can infer that for all z, z will read a book if and only if z is a police officer via universal biconditional introduction. From the fact that for all z, if z reads a book, then z is running, and that for all z, if z goes running, then z is reading a book we can infer that for all z, z will read a book if and only if z will go running via universal biconditional introduction. From the fact that for all z, z will read a book if and only if z will go running, and that for all z, z will not go running we can infer that for all z, z will not read a book via universal biconditional elimination. Finally, from the fact that for all z, z will read a book if and only if z is a police officer, and that for all z, z will not read a book we can infer that for all z, z is not a police officer via universal biconditional elimination, which contradicts that There is at least one z for which z is a police officer. Therefore, the answer is no.