Consider the following premises. For all y_3, if y_3 climbs a mountain, then y_3 is cooking. For all y_3, y_3 will climb a mountain or y_3 will not go running. There is at least one y_3 for which y_3 will go running or y_3 will not cook. Can we infer the following from them? There is at least one y_3 for which if y_3 cooks, then y_3 is climbing a mountain.
 From the fact that for all y_3, y_3 will climb a mountain or y_3 will not go running we can infer that for all y_3, if y_3 goes running, then y_3 is climbing a mountain. From the fact that there is at least one y_3 for which y_3 will go running or y_3 will not cook we can infer that there is at least one y_3 for which if y_3 cooks, then y_3 is running. Finally, from the fact that there is at least one y_3 for which if y_3 cooks, then y_3 is running, and that for all y_3, if y_3 goes running, then y_3 is climbing a mountain we can infer that there is at least one y_3 for which if y_3 cooks, then y_3 is climbing a mountain. Therefore, the answer is yes.