Consider the following premises. There is at least one y for which y will write a letter. For all y, y will write a letter or y will not sleep. For all y, if y writes a letter, then y is sleeping. Can we infer the following from them? For all y, y will not sleep.
 From the fact that for all y, y will write a letter or y will not sleep we can infer that for all y, if y sleeps, then y is writing a letter. From the fact that for all y, if y writes a letter, then y is sleeping, and that for all y, if y sleeps, then y is writing a letter we can infer that for all y, y will write a letter if and only if y will sleep. From the fact that for all y, y will write a letter if and only if y will sleep we can infer that for all y, if y writes a letter, then y is sleeping. Finally, from the fact that for all y, if y writes a letter, then y is sleeping, and that there is at least one y for which y will write a letter we can infer that there is at least one y for which y will sleep, which contradicts that For all y, y will not sleep. Therefore, the answer is no.