Consider the following premises. For all x_7, x_7 is a lawyer if and only if x_7 will drive a car. For all x_7, if x_7 drives a car, then x_7 is a janitor. For all x_7, if x_7 plays tennis, then x_7 is driving a car. For all x_7, x_7 is a lawyer or x_7 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_7 for which x_7 is not a janitor.
 From the fact that for all x_7, x_7 is a lawyer if and only if x_7 will drive a car we can infer that for all x_7, if x_7 were a lawyer, then x_7 is driving a car via universal biconditional elimination. From the fact that for all x_7, if x_7 were a lawyer, then x_7 is driving a car, that for all x_7, if x_7 plays tennis, then x_7 is driving a car, and that for all x_7, x_7 is a lawyer or x_7 will play tennis we can infer that for all x_7, x_7 will drive a car via universal disjunction elimination. Finally, from the fact that for all x_7, if x_7 drives a car, then x_7 is a janitor, and that for all x_7, x_7 will drive a car we can infer that for all x_7, x_7 is a janitor via universal modus ponens, which contradicts that There is at least one x_7 for which x_7 is not a janitor. Therefore, the answer is no.