Consider the following premises. There is at least one x_5 for which if x_5 reads a book, then x_5 is a poet. For all x_5, x_5 is not a cashier. For all x_5, if x_5 were a poet, then x_5 is a cashier. For all x_5, if x_5 were a cashier, then x_5 is a poet. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will read a book.
 From the fact that for all x_5, if x_5 were a cashier, then x_5 is a poet, and that for all x_5, if x_5 were a poet, then x_5 is a cashier we can infer that for all x_5, x_5 is a cashier if and only if x_5 is a poet via universal biconditional introduction. From the fact that for all x_5, x_5 is a cashier if and only if x_5 is a poet, and that for all x_5, x_5 is not a cashier we can infer that for all x_5, x_5 is not a poet via universal biconditional elimination. Finally, from the fact that there is at least one x_5 for which if x_5 reads a book, then x_5 is a poet, and that for all x_5, x_5 is not a poet we can infer that there is at least one x_5 for which x_5 will not read a book via existential modus tollens, which contradicts that For all x_5, x_5 will read a book. Therefore, the answer is no.