Consider the following premises. For all x_2, x_2 will go running if and only if x_2 will climb a mountain. For all x_2, if x_2 goes running, then x_2 is playing tennis. There is at least one x_2 for which if x_2 plays tennis, then x_2 is climbing a mountain. Can we infer the following from them? For all x_2, the fact that x_2 goes running does not imply that x_2 is climbing a mountain.
That contradicts the premises. Therefore the answer is no.