Consider the following premises. For all x_8, x_8 is a lawyer or x_8 will play a game. For all x_8, x_8 is a lawyer if and only if x_8 is a politician. For all x_8, if x_8 plays a game, then x_8 is driving a car. There is at least one x_8 for which if x_8 drives a car, then x_8 is a politician. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not a politician.
 From the fact that for all x_8, x_8 is a lawyer if and only if x_8 is a politician we can infer that for all x_8, if x_8 were a lawyer, then x_8 is a politician via universal biconditional elimination. From the fact that for all x_8, if x_8 plays a game, then x_8 is driving a car, and that there is at least one x_8 for which if x_8 drives a car, then x_8 is a politician we can infer that there is at least one x_8 for which if x_8 plays a game, then x_8 is a politician via existential transitivity. Finally, from the fact that for all x_8, if x_8 were a lawyer, then x_8 is a politician, that there is at least one x_8 for which if x_8 plays a game, then x_8 is a politician, and that for all x_8, x_8 is a lawyer or x_8 will play a game we can infer that there is at least one x_8 for which x_8 is a politician via existential disjunction elimination, which contradicts that For all x_8, x_8 is not a politician. Therefore, the answer is no.