Consider the following premises. For all x_2, if x_2 were excited, then x_2 is a scientist. For all x_2, x_2 is a scientist or x_2 is not a police officer. For all x_2, x_2 is a police officer or x_2 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 is not a scientist.
 From the fact that for all x_2, x_2 is a scientist or x_2 is not a police officer we can infer that for all x_2, if x_2 were a police officer, then x_2 is a scientist via universal rewriting. Finally, from the fact that for all x_2, if x_2 were a police officer, then x_2 is a scientist, that for all x_2, if x_2 were excited, then x_2 is a scientist, and that for all x_2, x_2 is a police officer or x_2 is excited we can infer that for all x_2, x_2 is a scientist via universal disjunction elimination, which contradicts that There is at least one x_2 for which x_2 is not a scientist. Therefore, the answer is no.