Consider the following premises. For all x_9, x_9 will play tennis or x_9 is not a cashier. For all x_9, x_9 is not a cashier. There is at least one x_9 for which if x_9 were a cashier, then x_9 is playing tennis. For all x_9, if x_9 plays tennis, then x_9 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will play tennis.
 From the fact that for all x_9, x_9 will play tennis or x_9 is not a cashier we can infer that for all x_9, if x_9 were a cashier, then x_9 is playing tennis via universal rewriting. From the fact that for all x_9, if x_9 were a cashier, then x_9 is playing tennis, and that for all x_9, if x_9 plays tennis, then x_9 is a cashier we can infer that for all x_9, x_9 is a cashier if and only if x_9 will play tennis via universal biconditional introduction. From the fact that for all x_9, x_9 is a cashier if and only if x_9 will play tennis we can infer that for all x_9, if x_9 plays tennis, then x_9 is a cashier via universal biconditional elimination. From the fact that for all x_9, if x_9 plays tennis, then x_9 is a cashier, and that there is at least one x_9 for which if x_9 were a cashier, then x_9 is playing tennis we can infer that there is at least one x_9 for which x_9 will play tennis if and only if x_9 is a cashier via existential biconditional introduction. Finally, from the fact that there is at least one x_9 for which x_9 will play tennis if and only if x_9 is a cashier, and that for all x_9, x_9 is not a cashier we can infer that there is at least one x_9 for which x_9 will not play tennis via existential biconditional elimination, which contradicts that For all x_9, x_9 will play tennis. Therefore, the answer is no.