Consider the following premises. For all x_6, x_6 is not a cashier. For all x_6, if x_6 plays tennis, then x_6 is a lawyer. For all x_6, if x_6 listens to a song, then x_6 is playing tennis. For all x_6, if x_6 were a lawyer, then x_6 is listening to a song. For all x_6, if x_6 plays tennis, then x_6 is a cashier. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is a lawyer.
 From the fact that for all x_6, if x_6 were a lawyer, then x_6 is listening to a song, and that for all x_6, if x_6 listens to a song, then x_6 is playing tennis we can infer that for all x_6, if x_6 were a lawyer, then x_6 is playing tennis via universal transitivity. From the fact that for all x_6, if x_6 plays tennis, then x_6 is a cashier, and that for all x_6, x_6 is not a cashier we can infer that for all x_6, x_6 will not play tennis via universal modus tollens. From the fact that for all x_6, if x_6 were a lawyer, then x_6 is playing tennis, and that for all x_6, if x_6 plays tennis, then x_6 is a lawyer we can infer that for all x_6, x_6 is a lawyer if and only if x_6 will play tennis via universal biconditional introduction. Finally, from the fact that for all x_6, x_6 is a lawyer if and only if x_6 will play tennis, and that for all x_6, x_6 will not play tennis we can infer that for all x_6, x_6 is not a lawyer via universal biconditional elimination, which contradicts that There is at least one x_6 for which x_6 is a lawyer. Therefore, the answer is no.