Consider the following premises. For all x_6, if x_6 were a police officer, then x_6 is driving a car. For all x_6, x_6 will go running or x_6 is a police officer. For all x_6, x_6 will drive a car or x_6 will not go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which neither x_6 will drive a car nor x_6 will cook.
 From the fact that for all x_6, x_6 will drive a car or x_6 will not go running we can infer that for all x_6, if x_6 goes running, then x_6 is driving a car via universal rewriting. From the fact that for all x_6, if x_6 goes running, then x_6 is driving a car, that for all x_6, if x_6 were a police officer, then x_6 is driving a car, and that for all x_6, x_6 will go running or x_6 is a police officer we can infer that for all x_6, x_6 will drive a car via universal disjunction elimination. Finally, from the fact that for all x_6, x_6 will drive a car we can infer that for all x_6, x_6 will drive a car or x_6 will cook via universal addition, which contradicts that There is at least one x_6 for which neither x_6 will drive a car nor x_6 will cook. Therefore, the answer is no.