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