Consider the following premises. For all x_5, x_5 is a janitor or x_5 is not a police officer. For all x_5, if x_5 sleeps, then x_5 is a police officer. There is at least one x_5 for which if x_5 plays tennis, then x_5 is sleeping. 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 if x_5 plays tennis, then x_5 is a janitor.
 From the fact that there is at least one x_5 for which if x_5 plays tennis, then x_5 is sleeping, and that for all x_5, if x_5 sleeps, then x_5 is a police officer we can infer that there is at least one x_5 for which if x_5 plays tennis, then x_5 is a police officer via existential transitivity. From the fact that for all x_5, x_5 is a janitor or x_5 is not a police officer we can infer that for all x_5, if x_5 were a police officer, then x_5 is a janitor via universal rewriting. Finally, from the fact that there is at least one x_5 for which if x_5 plays tennis, then x_5 is a police officer, and that for all x_5, if x_5 were a police officer, then x_5 is a janitor we can infer that there is at least one x_5 for which if x_5 plays tennis, then x_5 is a janitor via existential transitivity. Therefore, the answer is yes.