Consider the following premises. For all x_15, if x_15 cooks, then x_15 is playing squash. For all x_15, x_15 is a cashier or x_15 will sleep. For all x_15, if x_15 were a cashier, then x_15 is cooking. For all x_15, if x_15 sleeps, then x_15 is playing squash. For all x_15, if x_15 plays squash, then x_15 is playing a game. For all x_15, x_15 will play a game if and only if x_15 will work. Can we infer the following from them? For all x_15, x_15 will work.
 From the fact that for all x_15, x_15 will play a game if and only if x_15 will work we can infer that for all x_15, if x_15 plays a game, then x_15 is working. From the fact that for all x_15, if x_15 were a cashier, then x_15 is cooking, and that for all x_15, if x_15 cooks, then x_15 is playing squash we can infer that for all x_15, if x_15 were a cashier, then x_15 is playing squash. From the fact that for all x_15, if x_15 were a cashier, then x_15 is playing squash, that for all x_15, if x_15 sleeps, then x_15 is playing squash, and that for all x_15, x_15 is a cashier or x_15 will sleep we can infer that for all x_15, x_15 will play squash. From the fact that for all x_15, if x_15 plays squash, then x_15 is playing a game, and that for all x_15, x_15 will play squash we can infer that for all x_15, x_15 will play a game. Finally, from the fact that for all x_15, if x_15 plays a game, then x_15 is working, and that for all x_15, x_15 will play a game we can infer that for all x_15, x_15 will work. Therefore, the answer is yes.