Consider the following premises. For all x_6, if x_6 plays tennis, then x_6 is a cashier. For all x_6, if x_6 works, then x_6 is a cashier. For all x_6, if x_6 were a cashier, then x_6 is playing tennis. For all x_6, if x_6 were a cashier, then x_6 is working. For all x_6, x_6 will not play tennis. Can we infer the following from them? There is at least one x_6 for which x_6 will work.
 From the fact that for all x_6, if x_6 were a cashier, then x_6 is working, and that for all x_6, if x_6 works, then x_6 is a cashier we can infer that for all x_6, x_6 is a cashier if and only if x_6 will work. From the fact that for all x_6, if x_6 plays tennis, then x_6 is a cashier, and that for all x_6, if x_6 were a cashier, then x_6 is playing tennis we can infer that for all x_6, x_6 will play tennis if and only if x_6 is a cashier. From the fact that for all x_6, x_6 will play tennis if and only if x_6 is a cashier, and that for all x_6, x_6 will not play tennis we can infer that for all x_6, x_6 is not a cashier. Finally, from the fact that for all x_6, x_6 is a cashier if and only if x_6 will work, and that for all x_6, x_6 is not a cashier we can infer that for all x_6, x_6 will not work, which contradicts that There is at least one x_6 for which x_6 will work. Therefore, the answer is no.