Consider the following premises. Karen is not a lawyer. For all x_20, if x_20 were a carpenter, then x_20 is playing tennis. For all y_2, if y_2 climbs a mountain, then y_2 is a lawyer. Karen is climbing a mountain if and only if Robert is playing tennis. Can we infer the following from them? If we can, name the inference rule being used: Robert is not a carpenter.
 From the fact that for all x_20, if x_20 were a carpenter, then x_20 is playing tennis we can infer that if Robert were a carpenter, then Robert is playing tennis via universal instantiation. From the fact that for all y_2, if y_2 climbs a mountain, then y_2 is a lawyer we can infer that if Karen climbs a mountain, then Karen is a lawyer via universal instantiation. From the fact that if Karen climbs a mountain, then Karen is a lawyer, and that Karen is not a lawyer we can infer that Karen is not climbing a mountain via modus tollens. From the fact that Karen is climbing a mountain if and only if Robert is playing tennis, and that Karen is not climbing a mountain we can infer that Robert is not playing tennis via biconditional elimination. Finally, from the fact that if Robert were a carpenter, then Robert is playing tennis, and that Robert is not playing tennis we can infer that Robert is not a carpenter via modus tollens. Therefore, the answer is yes.