Consider the following premises. There is at least one x_7 for which if x_7 were a mechanic, then x_7 is making tea. For all x_7, if x_7 were a server, then x_7 is making tea. For all x_7, x_7 is a mechanic or x_7 is a server. For all x_7, if x_7 were an artist, then x_7 is not making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not an artist.
 From the fact that there is at least one x_7 for which if x_7 were a mechanic, then x_7 is making tea, that for all x_7, if x_7 were a server, then x_7 is making tea, and that for all x_7, x_7 is a mechanic or x_7 is a server we can infer that there is at least one x_7 for which x_7 will make tea via existential disjunction elimination. Finally, from the fact that for all x_7, if x_7 were an artist, then x_7 is not making tea, and that there is at least one x_7 for which x_7 will make tea we can infer that there is at least one x_7 for which x_7 is not an artist via existential modus tollens. Therefore, the answer is yes.