Consider the following premises. There is at least one x_2 for which if x_2 were a politician, then x_2 is not excited. For all x_2, x_2 is not a soldier. For all x_2, x_2 is a soldier or x_2 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is a politician.
 From the fact that for all x_2, x_2 is a soldier or x_2 is excited, and that for all x_2, x_2 is not a soldier we can infer that for all x_2, x_2 is excited via universal disjunctive syllogism. Finally, from the fact that there is at least one x_2 for which if x_2 were a politician, then x_2 is not excited, and that for all x_2, x_2 is excited we can infer that there is at least one x_2 for which x_2 is not a politician via existential modus tollens, which contradicts that For all x_2, x_2 is a politician. Therefore, the answer is no.