Consider the following premises. For all x_4, if x_4 drives a car, then x_4 is cooking. For all x_4, x_4 will not cook. For all x_4, x_4 is poor or x_4 will drive a car. There is at least one x_4 for which x_4 is not poor or x_4 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is not a bartender.
 From the fact that for all x_4, if x_4 drives a car, then x_4 is cooking, and that for all x_4, x_4 will not cook we can infer that for all x_4, x_4 will not drive a car via universal modus tollens. From the fact that for all x_4, x_4 is poor or x_4 will drive a car, and that there is at least one x_4 for which x_4 is not poor or x_4 is a bartender we can infer that there is at least one x_4 for which x_4 will drive a car or x_4 is a bartender via existential resolution. Finally, from the fact that there is at least one x_4 for which x_4 will drive a car or x_4 is a bartender, and that for all x_4, x_4 will not drive a car we can infer that there is at least one x_4 for which x_4 is a bartender via existential disjunctive syllogism, which contradicts that For all x_4, x_4 is not a bartender. Therefore, the answer is no.