Consider the following premises. For all x_6, x_6 is happy if and only if x_6 is a server. For all x_6, x_6 is not a server. There is at least one x_6 for which if x_6 were happy, then x_6 is writing a letter. For all x_6, if x_6 writes a letter, then x_6 is happy. Can we infer the following from them? There is at least one x_6 for which x_6 will not write a letter.
 From the fact that for all x_6, x_6 is happy if and only if x_6 is a server, and that for all x_6, x_6 is not a server we can infer that for all x_6, x_6 is not happy. From the fact that there is at least one x_6 for which if x_6 were happy, then x_6 is writing a letter, and that for all x_6, if x_6 writes a letter, then x_6 is happy we can infer that there is at least one x_6 for which x_6 is happy if and only if x_6 will write a letter. Finally, from the fact that there is at least one x_6 for which x_6 is happy if and only if x_6 will write a letter, and that for all x_6, x_6 is not happy we can infer that there is at least one x_6 for which x_6 will not write a letter. Therefore, the answer is yes.