Consider the following premises. For all x_4, x_4 is a janitor if and only if x_4 will cook. There is at least one x_4 for which x_4 will cook or x_4 is excited. For all x_4, if x_4 were excited, then x_4 is a janitor. Can we infer the following from them? There is at least one x_4 for which x_4 is a janitor.
 From the fact that for all x_4, x_4 is a janitor if and only if x_4 will cook we can infer that for all x_4, if x_4 cooks, then x_4 is a janitor. Finally, from the fact that for all x_4, if x_4 cooks, then x_4 is a janitor, that for all x_4, if x_4 were excited, then x_4 is a janitor, and that there is at least one x_4 for which x_4 will cook or x_4 is excited we can infer that there is at least one x_4 for which x_4 is a janitor. Therefore, the answer is yes.