Consider the following premises. For all x_3, x_3 is not a cashier. Elisabeth is a cashier or John is not playing a game. Can we infer the following from them? John is playing a game.
 From the fact that for all x_3, x_3 is not a cashier we can infer that Elisabeth is not a cashier. From the fact that Elisabeth is a cashier or John is not playing a game we can infer that if John plays a game, then Elisabeth is a cashier. Finally, from the fact that if John plays a game, then Elisabeth is a cashier, and that Elisabeth is not a cashier we can infer that John is not playing a game, which contradicts that John is playing a game. Therefore, the answer is no.