Consider the following premises. For all x_8, x_8 is poor if and only if x_8 will play a game. There is at least one x_8 for which if x_8 goes running, then x_8 is playing a game. For all x_8, x_8 is poor or x_8 is a janitor. For all x_8, if x_8 were a janitor, then x_8 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will play a game.
 From the fact that for all x_8, x_8 is poor if and only if x_8 will play a game we can infer that for all x_8, if x_8 were poor, then x_8 is playing a game via universal biconditional elimination. From the fact that for all x_8, if x_8 were a janitor, then x_8 is running, and that there is at least one x_8 for which if x_8 goes running, then x_8 is playing a game we can infer that there is at least one x_8 for which if x_8 were a janitor, then x_8 is playing a game via existential transitivity. Finally, from the fact that for all x_8, if x_8 were poor, then x_8 is playing a game, that there is at least one x_8 for which if x_8 were a janitor, then x_8 is playing a game, and that for all x_8, x_8 is poor or x_8 is a janitor we can infer that there is at least one x_8 for which x_8 will play a game via existential disjunction elimination. Therefore, the answer is yes.