Consider the following premises. For all x_3, x_3 will not climb a mountain or x_3 will cook. For all x_3, x_3 will climb a mountain. There is at least one x_3 for which if x_3 plays squash, then x_3 is sad. For all x_3, if x_3 cooks, then x_3 is sad. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_3 for which x_3 is sad.
 From the fact that for all x_3, x_3 will climb a mountain we can infer that for all x_3, x_3 will climb a mountain or x_3 will play squash via universal addition. From the fact that for all x_3, x_3 will climb a mountain or x_3 will play squash, and that for all x_3, x_3 will not climb a mountain or x_3 will cook we can infer that for all x_3, x_3 will play squash or x_3 will cook via universal resolution. Finally, from the fact that there is at least one x_3 for which if x_3 plays squash, then x_3 is sad, that for all x_3, if x_3 cooks, then x_3 is sad, and that for all x_3, x_3 will play squash or x_3 will cook we can infer that there is at least one x_3 for which x_3 is sad via existential disjunction elimination. Therefore, the answer is yes.