Consider the following premises. For all x_8, x_8 is a janitor and x_8 will drink water. For all x_8, x_8 is rich. There is at least one x_8 for which if x_8 makes tea, then x_8 is not a janitor. 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 will not make tea.
 From the fact that for all x_8, x_8 is a janitor and x_8 will drink water we can infer that for all x_8, x_8 is a janitor via universal simplification. From the fact that for all x_8, x_8 is a janitor, and that for all x_8, x_8 is rich we can infer that for all x_8, x_8 is a janitor and x_8 is rich via universal conjunction. From the fact that for all x_8, x_8 is a janitor and x_8 is rich we can infer that for all x_8, x_8 is a janitor via universal simplification. Finally, from the fact that there is at least one x_8 for which if x_8 makes tea, then x_8 is not a janitor, and that for all x_8, x_8 is a janitor we can infer that there is at least one x_8 for which x_8 will not make tea via existential modus tollens. Therefore, the answer is yes.