Consider the following premises. There is at least one x_5 for which if x_5 plays tennis, then x_5 is cooking. For all x_5, if x_5 plays tennis, then x_5 is working. For all x_5, if x_5 works, then x_5 is playing tennis. Can we infer the following from them? There is at least one x_5 for which if x_5 works, then x_5 is cooking.
 From the fact that for all x_5, if x_5 plays tennis, then x_5 is working, and that for all x_5, if x_5 works, then x_5 is playing tennis we can infer that for all x_5, x_5 will play tennis if and only if x_5 will work. From the fact that for all x_5, x_5 will play tennis if and only if x_5 will work we can infer that for all x_5, if x_5 works, then x_5 is playing tennis. Finally, from the fact that for all x_5, if x_5 works, then x_5 is playing tennis, and that there is at least one x_5 for which if x_5 plays tennis, then x_5 is cooking we can infer that there is at least one x_5 for which if x_5 works, then x_5 is cooking. Therefore, the answer is yes.