Consider the following premises. For all x_3, x_3 is rich if and only if x_3 will sleep. For all x_3, x_3 will drive a car or x_3 is rich. For all x_3, if x_3 were a writer, then x_3 is sleeping. For all x_3, if x_3 drives a car, then x_3 is a writer. Can we infer the following from them? For all x_3, x_3 will sleep.
 From the fact that for all x_3, if x_3 drives a car, then x_3 is a writer, and that for all x_3, if x_3 were a writer, then x_3 is sleeping we can infer that for all x_3, if x_3 drives a car, then x_3 is sleeping. From the fact that for all x_3, x_3 is rich if and only if x_3 will sleep we can infer that for all x_3, if x_3 were rich, then x_3 is sleeping. Finally, from the fact that for all x_3, if x_3 drives a car, then x_3 is sleeping, that for all x_3, if x_3 were rich, then x_3 is sleeping, and that for all x_3, x_3 will drive a car or x_3 is rich we can infer that for all x_3, x_3 will sleep. Therefore, the answer is yes.