Consider the following premises. For all x_9, x_9 will play a game or x_9 will not work. For all x_9, if x_9 plays a game, then x_9 is playing squash. For all x_9, if x_9 were a janitor, then x_9 is cooking. For all x_9, if x_9 cooks, then x_9 is working. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, if x_9 were a janitor, then x_9 is playing squash.
 From the fact that for all x_9, if x_9 were a janitor, then x_9 is cooking, and that for all x_9, if x_9 cooks, then x_9 is working we can infer that for all x_9, if x_9 were a janitor, then x_9 is working via universal transitivity. From the fact that for all x_9, x_9 will play a game or x_9 will not work we can infer that for all x_9, if x_9 works, then x_9 is playing a game via universal rewriting. From the fact that for all x_9, if x_9 were a janitor, then x_9 is working, and that for all x_9, if x_9 works, then x_9 is playing a game we can infer that for all x_9, if x_9 were a janitor, then x_9 is playing a game via universal transitivity. Finally, from the fact that for all x_9, if x_9 were a janitor, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is playing squash we can infer that for all x_9, if x_9 were a janitor, then x_9 is playing squash via universal transitivity. Therefore, the answer is yes.