Consider the following premises. For all x_6, x_6 will play a game or x_6 is a server. For all x_6, if x_6 sleeps, then x_6 is a police officer. For all x_6, if x_6 were a server, then x_6 is a police officer. For all x_6, x_6 will not play a game or x_6 will sleep. For all x_6, if x_6 makes tea, then x_6 is not a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not make tea.
 From the fact that for all x_6, x_6 will play a game or x_6 is a server, and that for all x_6, x_6 will not play a game or x_6 will sleep we can infer that for all x_6, x_6 is a server or x_6 will sleep via universal resolution. From the fact that for all x_6, if x_6 were a server, then x_6 is a police officer, that for all x_6, if x_6 sleeps, then x_6 is a police officer, and that for all x_6, x_6 is a server or x_6 will sleep we can infer that for all x_6, x_6 is a police officer via universal disjunction elimination. Finally, from the fact that for all x_6, if x_6 makes tea, then x_6 is not a police officer, and that for all x_6, x_6 is a police officer we can infer that for all x_6, x_6 will not make tea via universal modus tollens. Therefore, the answer is yes.