Consider the following premises. There is at least one x_8 for which x_8 will play a game or x_8 will drive a car. For all x_8, x_8 will go running or x_8 will not drive a car. For all x_8, x_8 will go running if and only if x_8 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will not go running.
 From the fact that for all x_8, x_8 will go running if and only if x_8 will play a game we can infer that for all x_8, if x_8 plays a game, then x_8 is running via universal biconditional elimination. From the fact that for all x_8, x_8 will go running or x_8 will not drive a car we can infer that for all x_8, if x_8 drives a car, then x_8 is running via universal rewriting. Finally, from the fact that for all x_8, if x_8 plays a game, then x_8 is running, that for all x_8, if x_8 drives a car, then x_8 is running, and that there is at least one x_8 for which x_8 will play a game or x_8 will drive a car we can infer that there is at least one x_8 for which x_8 will go running via existential disjunction elimination, which contradicts that For all x_8, x_8 will not go running. Therefore, the answer is no.