Consider the following premises. There is at least one x_4 for which x_4 will not play a game or x_4 will take a plane. For all x_4, if x_4 goes running, then x_4 is a police officer. For all x_4, x_4 will play a game or x_4 will go running. For all x_4, x_4 is not a police officer. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will not take a plane.
 From the fact that for all x_4, if x_4 goes running, then x_4 is a police officer, and that for all x_4, x_4 is not a police officer we can infer that for all x_4, x_4 will not go running via universal modus tollens. From the fact that for all x_4, x_4 will play a game or x_4 will go running, and that there is at least one x_4 for which x_4 will not play a game or x_4 will take a plane we can infer that there is at least one x_4 for which x_4 will go running or x_4 will take a plane via existential resolution. Finally, from the fact that there is at least one x_4 for which x_4 will go running or x_4 will take a plane, and that for all x_4, x_4 will not go running we can infer that there is at least one x_4 for which x_4 will take a plane via existential disjunctive syllogism, which contradicts that For all x_4, x_4 will not take a plane. Therefore, the answer is no.