Consider the following premises. For all x_6, x_6 is a lawyer or x_6 will play a game. There is at least one x_6 for which x_6 is not a cashier. For all x_6, x_6 is a cashier if and only if x_6 is a lawyer. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not play a game.
 From the fact that for all x_6, x_6 is a cashier if and only if x_6 is a lawyer, and that there is at least one x_6 for which x_6 is not a cashier we can infer that there is at least one x_6 for which x_6 is not a lawyer via existential biconditional elimination. Finally, from the fact that for all x_6, x_6 is a lawyer or x_6 will play a game, and that there is at least one x_6 for which x_6 is not a lawyer we can infer that there is at least one x_6 for which x_6 will play a game via existential disjunctive syllogism, which contradicts that For all x_6, x_6 will not play a game. Therefore, the answer is no.