Consider the following premises. For all x_4, if x_4 were a scientist, then x_4 is sleeping. For all x_4, if x_4 were a scientist, then x_4 is sleeping. For all x_4, if x_4 sleeps, then x_4 is a scientist. Can we infer the following from them? If William were a scientist, then William is sleeping.
 From the fact that for all x_4, if x_4 were a scientist, then x_4 is sleeping, and that for all x_4, if x_4 sleeps, then x_4 is a scientist we can infer that for all x_4, x_4 is a scientist if and only if x_4 will sleep. From the fact that for all x_4, x_4 is a scientist if and only if x_4 will sleep we can infer that for all x_4, if x_4 sleeps, then x_4 is a scientist. From the fact that for all x_4, if x_4 were a scientist, then x_4 is sleeping, and that for all x_4, if x_4 sleeps, then x_4 is a scientist we can infer that for all x_4, x_4 is a scientist if and only if x_4 will sleep. From the fact that for all x_4, x_4 is a scientist if and only if x_4 will sleep we can infer that William is a scientist if and only if William is sleeping. Finally, from the fact that William is a scientist if and only if William is sleeping we can infer that if William were a scientist, then William is sleeping. Therefore, the answer is yes.