Consider the following premises. For all x_4, if x_4 were rich, then x_4 is driving a car. For all x_4, if x_4 drives a car, then x_4 is excited. There is at least one x_4 for which x_4 is rich. For all x_4, if x_4 takes a plane, then x_4 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is not excited.
 From the fact that for all x_4, if x_4 were rich, then x_4 is driving a car, and that for all x_4, if x_4 drives a car, then x_4 is excited we can infer that for all x_4, if x_4 were rich, then x_4 is excited via universal transitivity. From the fact that there is at least one x_4 for which x_4 is rich we can infer that there is at least one x_4 for which x_4 is rich or x_4 will take a plane via existential addition. Finally, from the fact that for all x_4, if x_4 were rich, then x_4 is excited, that for all x_4, if x_4 takes a plane, then x_4 is excited, and that there is at least one x_4 for which x_4 is rich or x_4 will take a plane we can infer that there is at least one x_4 for which x_4 is excited via existential disjunction elimination, which contradicts that For all x_4, x_4 is not excited. Therefore, the answer is no.