Consider the following premises. For all y_2, y_2 will write a letter if and only if y_2 is a server. There is at least one y_2 for which if y_2 writes a letter, then y_2 is a server. For all y_2, if y_2 sleeps, then y_2 is a server. Can we infer the following from them? There is at least one y_2 for which if y_2 sleeps, then y_2 is writing a letter.
 From the fact that for all y_2, y_2 will write a letter if and only if y_2 is a server we can infer that for all y_2, if y_2 were a server, then y_2 is writing a letter. From the fact that there is at least one y_2 for which if y_2 writes a letter, then y_2 is a server, and that for all y_2, if y_2 were a server, then y_2 is writing a letter we can infer that there is at least one y_2 for which y_2 will write a letter if and only if y_2 is a server. From the fact that there is at least one y_2 for which y_2 will write a letter if and only if y_2 is a server we can infer that there is at least one y_2 for which if y_2 were a server, then y_2 is writing a letter. Finally, from the fact that for all y_2, if y_2 sleeps, then y_2 is a server, and that there is at least one y_2 for which if y_2 were a server, then y_2 is writing a letter we can infer that there is at least one y_2 for which if y_2 sleeps, then y_2 is writing a letter. Therefore, the answer is yes.