Consider the following premises. For all x, x will not read a book. There is at least one x for which if x reads a book, then x is a janitor. For all x, if x were a janitor, then x is reading a book. Can we infer the following from them? If we can, name the inference rule being used: For all x, x is a janitor.
 From the fact that for all x, if x were a janitor, then x is reading a book, and that there is at least one x for which if x reads a book, then x is a janitor we can infer that there is at least one x for which x is a janitor if and only if x will read a book via existential biconditional introduction. From the fact that there is at least one x for which x is a janitor if and only if x will read a book we can infer that there is at least one x for which if x were a janitor, then x is reading a book via existential biconditional elimination. Finally, from the fact that there is at least one x for which if x were a janitor, then x is reading a book, and that for all x, x will not read a book we can infer that there is at least one x for which x is not a janitor via existential modus tollens, which contradicts that For all x, x is a janitor. Therefore, the answer is no.