Consider the following premises. For all x_8, x_8 will go running if and only if x_8 will drive a car. For all x_8, if x_8 sleeps, then x_8 is running. For all x_8, if x_8 drives a car, then x_8 is sleeping. There is at least one x_8 for which x_8 will not sleep. 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 not go running.
 From the fact that for all x_8, x_8 will go running if and only if x_8 will drive a car we can infer that for all x_8, if x_8 goes running, then x_8 is driving a car via universal biconditional elimination. From the fact that for all x_8, if x_8 goes running, then x_8 is driving a car, and that for all x_8, if x_8 drives a car, then x_8 is sleeping we can infer that for all x_8, if x_8 goes running, then x_8 is sleeping via universal transitivity. From the fact that for all x_8, if x_8 goes running, then x_8 is sleeping, and that for all x_8, if x_8 sleeps, then x_8 is running we can infer that for all x_8, x_8 will go running if and only if x_8 will sleep via universal biconditional introduction. Finally, from the fact that for all x_8, x_8 will go running if and only if x_8 will sleep, and that there is at least one x_8 for which x_8 will not sleep we can infer that there is at least one x_8 for which x_8 will not go running via existential biconditional elimination. Therefore, the answer is yes.