Consider the following premises. For all x_2, x_2 is not a server. There is at least one x_2 for which if x_2 were a server, then x_2 is writing a letter. For all x_2, if x_2 writes a letter, then x_2 is a bartender. For all x_2, if x_2 were a bartender, then x_2 is a server. Can we infer the following from them? There is at least one x_2 for which x_2 is not a bartender.
 From the fact that there is at least one x_2 for which if x_2 were a server, then x_2 is writing a letter, and that for all x_2, if x_2 writes a letter, then x_2 is a bartender we can infer that there is at least one x_2 for which if x_2 were a server, then x_2 is a bartender. From the fact that for all x_2, if x_2 were a bartender, then x_2 is a server, and that there is at least one x_2 for which if x_2 were a server, then x_2 is a bartender we can infer that there is at least one x_2 for which x_2 is a bartender if and only if x_2 is a server. Finally, from the fact that there is at least one x_2 for which x_2 is a bartender if and only if x_2 is a server, and that for all x_2, x_2 is not a server we can infer that there is at least one x_2 for which x_2 is not a bartender. Therefore, the answer is yes.