Consider the following premises. For all x_3, x_3 will cook or x_3 will play tennis. For all x_3, x_3 will not cook or x_3 will take a plane. For all x_3, if x_3 takes a plane, then x_3 is running. For all x_3, if x_3 goes running, then x_3 is sleeping. There is at least one x_3 for which if x_3 plays tennis, then x_3 is sleeping. Can we infer the following from them? There is at least one x_3 for which x_3 will sleep.
 From the fact that for all x_3, if x_3 takes a plane, then x_3 is running, and that for all x_3, if x_3 goes running, then x_3 is sleeping we can infer that for all x_3, if x_3 takes a plane, then x_3 is sleeping. From the fact that for all x_3, x_3 will cook or x_3 will play tennis, and that for all x_3, x_3 will not cook or x_3 will take a plane we can infer that for all x_3, x_3 will play tennis or x_3 will take a plane. Finally, from the fact that there is at least one x_3 for which if x_3 plays tennis, then x_3 is sleeping, that for all x_3, if x_3 takes a plane, then x_3 is sleeping, and that for all x_3, x_3 will play tennis or x_3 will take a plane we can infer that there is at least one x_3 for which x_3 will sleep. Therefore, the answer is yes.