Consider the following premises. There is at least one x_3 for which x_3 will drive a car or x_3 is a janitor. For all x_3, x_3 is a janitor if and only if x_3 will go running. For all x_3, if x_3 drives a car, then x_3 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 will go running.
 From the fact that for all x_3, x_3 is a janitor if and only if x_3 will go running we can infer that for all x_3, if x_3 were a janitor, then x_3 is running via universal biconditional elimination. Finally, from the fact that for all x_3, if x_3 drives a car, then x_3 is running, that for all x_3, if x_3 were a janitor, then x_3 is running, and that there is at least one x_3 for which x_3 will drive a car or x_3 is a janitor we can infer that there is at least one x_3 for which x_3 will go running via existential disjunction elimination. Therefore, the answer is yes.