Consider the following premises. For all x_8, if x_8 makes tea, then x_8 is a janitor. For all x_8, x_8 is a police officer. There is at least one x_8 for which x_8 will make tea or x_8 is not a police officer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is a janitor.
 From the fact that there is at least one x_8 for which x_8 will make tea or x_8 is not a police officer we can infer that there is at least one x_8 for which if x_8 were a police officer, then x_8 is making tea via existential rewriting. From the fact that there is at least one x_8 for which if x_8 were a police officer, then x_8 is making tea, and that for all x_8, if x_8 makes tea, then x_8 is a janitor we can infer that there is at least one x_8 for which if x_8 were a police officer, then x_8 is a janitor via existential transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 were a police officer, then x_8 is a janitor, and that for all x_8, x_8 is a police officer we can infer that there is at least one x_8 for which x_8 is a janitor via existential modus ponens. Therefore, the answer is yes.