Consider the following premises. For all y, y will not play tennis or y will go running. If Richard goes running, then James is poor. Richard is not climbing a mountain or it is cold. If it is cold, then Charles is excited. For all y, y will play tennis or y will climb a mountain. If Charles were excited, then James is poor. Can we infer the following from them? If we can, name the inference rule being used: James is poor.
 From the fact that for all y, y will play tennis or y will climb a mountain, and that for all y, y will not play tennis or y will go running we can infer that for all y, y will climb a mountain or y will go running via universal resolution. From the fact that if it is cold, then Charles is excited, and that if Charles were excited, then James is poor we can infer that if it is cold, then James is poor via transitivity. From the fact that for all y, y will climb a mountain or y will go running we can infer that Richard is climbing a mountain or Richard is running via universal instantiation. From the fact that Richard is climbing a mountain or Richard is running, and that Richard is not climbing a mountain or it is cold we can infer that Richard is running or it is cold via resolution. Finally, from the fact that if Richard goes running, then James is poor, that if it is cold, then James is poor, and that Richard is running or it is cold we can infer that James is poor via disjunction elimination. Therefore, the answer is yes.