Consider the following premises. For all x_4, x_4 is an artist if and only if x_4 is a server. For all x_4, x_4 is not a server. There is at least one x_4 for which x_4 will write a letter if and only if x_4 is an artist. Can we infer the following from them? There is at least one x_4 for which x_4 will not write a letter.
 From the fact that for all x_4, x_4 is an artist if and only if x_4 is a server, and that for all x_4, x_4 is not a server we can infer that for all x_4, x_4 is not an artist. Finally, from the fact that there is at least one x_4 for which x_4 will write a letter if and only if x_4 is an artist, and that for all x_4, x_4 is not an artist we can infer that there is at least one x_4 for which x_4 will not write a letter. Therefore, the answer is yes.