Consider the following premises. If it is overcast, then Barbara is running. For all x_10, if x_10 climbs a mountain, then x_10 is running. Barbara is climbing a mountain or it is overcast. For all x_10, if x_10 goes running, then x_10 is climbing a mountain. Can we infer the following from them? Barbara is not running.
 From the fact that for all x_10, if x_10 climbs a mountain, then x_10 is running, and that for all x_10, if x_10 goes running, then x_10 is climbing a mountain we can infer that for all x_10, x_10 will climb a mountain if and only if x_10 will go running. From the fact that for all x_10, x_10 will climb a mountain if and only if x_10 will go running we can infer that for all x_10, if x_10 climbs a mountain, then x_10 is running. From the fact that for all x_10, if x_10 climbs a mountain, then x_10 is running we can infer that if Barbara climbs a mountain, then Barbara is running. Finally, from the fact that if Barbara climbs a mountain, then Barbara is running, that if it is overcast, then Barbara is running, and that Barbara is climbing a mountain or it is overcast we can infer that Barbara is running, which contradicts that Barbara is not running. Therefore, the answer is no.