Consider the following premises. Barbara is not running. For all x_12, if x_12 plays tennis, then x_12 is running. If Barbara goes running, then Barbara is playing tennis. Can we infer the following from them? Barbara is not playing tennis.
 From the fact that for all x_12, if x_12 plays tennis, then x_12 is running we can infer that if Barbara plays tennis, then Barbara is running. From the fact that if Barbara plays tennis, then Barbara is running, and that if Barbara goes running, then Barbara is playing tennis we can infer that Barbara is playing tennis if and only if Barbara is running. From the fact that Barbara is playing tennis if and only if Barbara is running we can infer that if Barbara plays tennis, then Barbara is running. Finally, from the fact that if Barbara plays tennis, then Barbara is running, and that Barbara is not running we can infer that Barbara is not playing tennis. Therefore, the answer is yes.