Consider the following premises. For all x_8, x_8 will play a game or x_8 is a janitor. For all x_8, if x_8 plays a game, then x_8 is running. There is at least one x_8 for which x_8 is a janitor if and only if x_8 is happy. For all x_8, if x_8 goes running, then x_8 is happy. Can we infer the following from them? There is at least one x_8 for which x_8 is happy.
 From the fact that there is at least one x_8 for which x_8 is a janitor if and only if x_8 is happy we can infer that there is at least one x_8 for which if x_8 were a janitor, then x_8 is happy. From the fact that for all x_8, if x_8 plays a game, then x_8 is running, and that for all x_8, if x_8 goes running, then x_8 is happy we can infer that for all x_8, if x_8 plays a game, then x_8 is happy. Finally, from the fact that for all x_8, if x_8 plays a game, then x_8 is happy, that there is at least one x_8 for which if x_8 were a janitor, then x_8 is happy, and that for all x_8, x_8 will play a game or x_8 is a janitor we can infer that there is at least one x_8 for which x_8 is happy. Therefore, the answer is yes.