Consider the following premises. There is at least one x_5 for which if x_5 were a police officer, then x_5 is sleeping. For all x_5, if x_5 were excited, then x_5 is sleeping. For all x_5, x_5 is excited and x_5 will play a game. 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 will sleep.
 From the fact that for all x_5, x_5 is excited and x_5 will play a game we can infer that for all x_5, x_5 is excited via universal simplification. From the fact that for all x_5, x_5 is excited we can infer that for all x_5, x_5 is excited or x_5 is a police officer via universal addition. Finally, from the fact that for all x_5, if x_5 were excited, then x_5 is sleeping, that there is at least one x_5 for which if x_5 were a police officer, then x_5 is sleeping, and that for all x_5, x_5 is excited or x_5 is a police officer we can infer that there is at least one x_5 for which x_5 will sleep via existential disjunction elimination. Therefore, the answer is yes.