Consider the following premises. For all x_16, x_16 will sleep. There is at least one x_16 for which if x_16 goes running, then x_16 is not a nurse. For all x_16, x_16 is a nurse if and only if x_16 will sleep. For all x_16, if x_16 were a janitor, then x_16 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_16 for which x_16 is not a janitor.
 From the fact that for all x_16, x_16 is a nurse if and only if x_16 will sleep we can infer that for all x_16, if x_16 sleeps, then x_16 is a nurse via universal biconditional elimination. From the fact that for all x_16, if x_16 sleeps, then x_16 is a nurse, and that for all x_16, x_16 will sleep we can infer that for all x_16, x_16 is a nurse via universal modus ponens. From the fact that there is at least one x_16 for which if x_16 goes running, then x_16 is not a nurse, and that for all x_16, x_16 is a nurse we can infer that there is at least one x_16 for which x_16 will not go running via existential modus tollens. Finally, from the fact that for all x_16, if x_16 were a janitor, then x_16 is running, and that there is at least one x_16 for which x_16 will not go running we can infer that there is at least one x_16 for which x_16 is not a janitor via existential modus tollens. Therefore, the answer is yes.