Consider the following premises. For all x_6, if x_6 reads a book, then x_6 is a police officer. For all x_6, x_6 is not a police officer. For all x_6, if x_6 were a cashier, then x_6 is reading a book. There is at least one x_6 for which if x_6 reads a book, then x_6 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is not a cashier.
 From the fact that for all x_6, if x_6 were a cashier, then x_6 is reading a book, and that there is at least one x_6 for which if x_6 reads a book, then x_6 is a cashier we can infer that there is at least one x_6 for which x_6 is a cashier if and only if x_6 will read a book via existential biconditional introduction. From the fact that for all x_6, if x_6 reads a book, then x_6 is a police officer, and that for all x_6, x_6 is not a police officer we can infer that for all x_6, x_6 will not read a book via universal modus tollens. Finally, from the fact that there is at least one x_6 for which x_6 is a cashier if and only if x_6 will read a book, and that for all x_6, x_6 will not read a book we can infer that there is at least one x_6 for which x_6 is not a cashier via existential biconditional elimination. Therefore, the answer is yes.