Consider the following premises. For all x, x will not climb a mountain. There is at least one x for which if x climbs a mountain, then x is playing tennis. For all x, if x plays tennis, then x is climbing a mountain. Can we infer the following from them? There is at least one x for which x will not play tennis.
 From the fact that there is at least one x for which if x climbs a mountain, then x is playing tennis, and that for all x, if x plays tennis, then x is climbing a mountain we can infer that there is at least one x for which x will climb a mountain if and only if x will play tennis. Finally, from the fact that there is at least one x for which x will climb a mountain if and only if x will play tennis, and that for all x, x will not climb a mountain we can infer that there is at least one x for which x will not play tennis. Therefore, the answer is yes.