Consider the following premises. For all x_5, if x_5 drives a car, then x_5 is cooking. For all x_5, x_5 is bored if and only if x_5 will drive a car. For all x_5, if x_5 goes running, then x_5 is bored. For all x_5, x_5 will not cook. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not go running.
 From the fact that for all x_5, if x_5 drives a car, then x_5 is cooking, and that for all x_5, x_5 will not cook we can infer that for all x_5, x_5 will not drive a car via universal modus tollens. From the fact that for all x_5, x_5 is bored if and only if x_5 will drive a car, and that for all x_5, x_5 will not drive a car we can infer that for all x_5, x_5 is not bored via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 goes running, then x_5 is bored, and that for all x_5, x_5 is not bored we can infer that for all x_5, x_5 will not go running via universal modus tollens. Therefore, the answer is yes.