Consider the following premises. For all x_18, if x_18 drives a car, then x_18 is not excited. For all x_18, if x_18 drives a car, then x_18 is taking a plane. For all x_18, x_18 is a politician or x_18 will play a game. For all x_18, if x_18 takes a plane, then x_18 is driving a car. For all x_18, if x_18 were a politician, then x_18 is excited. There is at least one x_18 for which if x_18 plays a game, then x_18 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_18 for which x_18 will not take a plane.
 From the fact that for all x_18, if x_18 takes a plane, then x_18 is driving a car, and that for all x_18, if x_18 drives a car, then x_18 is taking a plane we can infer that for all x_18, x_18 will take a plane if and only if x_18 will drive a car via universal biconditional introduction. From the fact that for all x_18, if x_18 were a politician, then x_18 is excited, that there is at least one x_18 for which if x_18 plays a game, then x_18 is excited, and that for all x_18, x_18 is a politician or x_18 will play a game we can infer that there is at least one x_18 for which x_18 is excited via existential disjunction elimination. From the fact that for all x_18, if x_18 drives a car, then x_18 is not excited, and that there is at least one x_18 for which x_18 is excited we can infer that there is at least one x_18 for which x_18 will not drive a car via existential modus tollens. Finally, from the fact that for all x_18, x_18 will take a plane if and only if x_18 will drive a car, and that there is at least one x_18 for which x_18 will not drive a car we can infer that there is at least one x_18 for which x_18 will not take a plane via existential biconditional elimination. Therefore, the answer is yes.