Consider the following premises. For all x, if x drives a car, then x is a cashier. There is at least one x for which if x were a cashier, then x is driving a car. For all x, x is not a cashier. For all x, if x plays a game, then x is driving a car. For all x, if x drives a car, then x is playing a game. Can we infer the following from them? For all x, x will play a game.
 From the fact that for all x, if x plays a game, then x is driving a car, and that for all x, if x drives a car, then x is playing a game we can infer that for all x, x will play a game if and only if x will drive a car. From the fact that there is at least one x for which if x were a cashier, then x is driving a car, and that for all x, if x drives a car, then x is a cashier we can infer that there is at least one x for which x is a cashier if and only if x will drive a car. From the fact that there is at least one x for which x is a cashier if and only if x will drive a car, and that for all x, x is not a cashier we can infer that there is at least one x for which x will not drive a car. Finally, from the fact that for all x, x will play a game if and only if x will drive a car, and that there is at least one x for which x will not drive a car we can infer that there is at least one x for which x will not play a game, which contradicts that For all x, x will play a game. Therefore, the answer is no.