Consider the following premises. For all x_5, x_5 will play tennis. There is at least one x_5 for which x_5 is a server. For all x_5, if x_5 plays tennis, then x_5 is excited. For all x_5, if x_5 were excited, then x_5 is a bartender. Can we infer the following from them? If we can, name the inference rule being used: Some bartenders are servers.
 From the fact that for all x_5, if x_5 plays tennis, then x_5 is excited, and that for all x_5, x_5 will play tennis we can infer that for all x_5, x_5 is excited via universal modus ponens. From the fact that for all x_5, if x_5 were excited, then x_5 is a bartender, and that for all x_5, x_5 is excited we can infer that for all x_5, x_5 is a bartender via universal modus ponens. Finally, from the fact that for all x_5, x_5 is a bartender, and that there is at least one x_5 for which x_5 is a server we can infer that some bartenders are servers via existential conjunction. Therefore, the answer is yes.