Consider the following premises. There is at least one x_9 for which if x_9 sleeps, then x_9 is not writing a letter. For all x_9, if x_9 reads a book, then x_9 is writing a letter. For all x_9, x_9 will drink water if and only if x_9 will write a letter. For all x_9, x_9 will drink water. Can we infer the following from them? There is at least one x_9 for which x_9 will not sleep.
 From the fact that for all x_9, x_9 will drink water if and only if x_9 will write a letter we can infer that for all x_9, if x_9 drinks water, then x_9 is writing a letter. From the fact that for all x_9, x_9 will drink water we can infer that for all x_9, x_9 will drink water or x_9 will read a book. From the fact that for all x_9, if x_9 drinks water, then x_9 is writing a letter, that for all x_9, if x_9 reads a book, then x_9 is writing a letter, and that for all x_9, x_9 will drink water or x_9 will read a book we can infer that for all x_9, x_9 will write a letter. Finally, from the fact that there is at least one x_9 for which if x_9 sleeps, then x_9 is not writing a letter, and that for all x_9, x_9 will write a letter we can infer that there is at least one x_9 for which x_9 will not sleep. Therefore, the answer is yes.