Consider the following premises. For all x_6, x_6 is not a nurse. For all x_6, if x_6 plays tennis, then x_6 is a cashier. For all x_6, if x_6 plays a game, then x_6 is a nurse. There is at least one x_6 for which if x_6 were a cashier, then x_6 is playing a game. Can we infer the following from them? There is at least one x_6 for which x_6 will not play tennis.
 From the fact that there is at least one x_6 for which if x_6 were a cashier, then x_6 is playing a game, and that for all x_6, if x_6 plays a game, then x_6 is a nurse we can infer that there is at least one x_6 for which if x_6 were a cashier, then x_6 is a nurse. From the fact that for all x_6, if x_6 plays tennis, then x_6 is a cashier, and that there is at least one x_6 for which if x_6 were a cashier, then x_6 is a nurse we can infer that there is at least one x_6 for which if x_6 plays tennis, then x_6 is a nurse. Finally, from the fact that there is at least one x_6 for which if x_6 plays tennis, then x_6 is a nurse, and that for all x_6, x_6 is not a nurse we can infer that there is at least one x_6 for which x_6 will not play tennis. Therefore, the answer is yes.