Consider the following premises. For all x_12, if x_12 plays squash, then x_12 is not playing tennis. Patricia is playing a game if and only if Robert is playing squash. If James climbs a mountain, then Patricia is playing a game. For all x_12, x_12 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: James is not climbing a mountain.
 From the fact that for all x_12, if x_12 plays squash, then x_12 is not playing tennis, and that for all x_12, x_12 will play tennis we can infer that for all x_12, x_12 will not play squash via universal modus tollens. From the fact that for all x_12, x_12 will not play squash we can infer that Robert is not playing squash via universal instantiation. From the fact that Patricia is playing a game if and only if Robert is playing squash, and that Robert is not playing squash we can infer that Patricia is not playing a game via biconditional elimination. Finally, from the fact that if James climbs a mountain, then Patricia is playing a game, and that Patricia is not playing a game we can infer that James is not climbing a mountain via modus tollens. Therefore, the answer is yes.