Consider the following premises. For all x_9, if x_9 plays a game, then x_9 is working. For all x_9, x_9 will work or x_9 will go running. There is at least one x_9 for which x_9 will not play a game. For all x_9, if x_9 works, then x_9 is playing a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will go running.
 From the fact that for all x_9, if x_9 works, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is working we can infer that for all x_9, x_9 will work if and only if x_9 will play a game via universal biconditional introduction. From the fact that for all x_9, x_9 will work if and only if x_9 will play a game, and that there is at least one x_9 for which x_9 will not play a game we can infer that there is at least one x_9 for which x_9 will not work via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will work or x_9 will go running, and that there is at least one x_9 for which x_9 will not work we can infer that there is at least one x_9 for which x_9 will go running via existential disjunctive syllogism. Therefore, the answer is yes.