Consider the following premises. For all x_5, x_5 will work or x_5 will cook. For all x_5, if x_5 works, then x_5 is sleeping. For all x_5, if x_5 cooks, then x_5 is sleeping. Can we infer the following from them? There is at least one z for which z will sleep.
 From the fact that for all x_5, if x_5 works, then x_5 is sleeping, that for all x_5, if x_5 cooks, then x_5 is sleeping, and that for all x_5, x_5 will work or x_5 will cook we can infer that for all x_5, x_5 will sleep. From the fact that for all x_5, x_5 will sleep we can infer that Richard is sleeping. Finally, from the fact that Richard is sleeping we can infer that there is at least one z for which z will sleep. Therefore, the answer is yes.