Consider the following premises. There is at least one z_2 for which if z_2 cooks, then z_2 is a janitor. For all z_2, if z_2 were a janitor, then z_2 is cooking. For all z_2, z_2 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all z_2, z_2 is a janitor.
 From the fact that for all z_2, if z_2 were a janitor, then z_2 is cooking, and that there is at least one z_2 for which if z_2 cooks, then z_2 is a janitor we can infer that there is at least one z_2 for which z_2 is a janitor if and only if z_2 will cook via existential biconditional introduction. From the fact that there is at least one z_2 for which z_2 is a janitor if and only if z_2 will cook we can infer that there is at least one z_2 for which if z_2 were a janitor, then z_2 is cooking via existential biconditional elimination. Finally, from the fact that there is at least one z_2 for which if z_2 were a janitor, then z_2 is cooking, and that for all z_2, z_2 will not cook we can infer that there is at least one z_2 for which z_2 is not a janitor via existential modus tollens, which contradicts that For all z_2, z_2 is a janitor. Therefore, the answer is no.