Consider the following premises. For all x_10, x_10 will go running. There is at least one x_10 for which x_10 will play squash. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 will play squash or x_10 will climb a mountain.
 From the fact that there is at least one x_10 for which x_10 will play squash, and that for all x_10, x_10 will go running we can infer that there is at least one x_10 for which x_10 will play squash and x_10 will go running via existential conjunction. From the fact that there is at least one x_10 for which x_10 will play squash and x_10 will go running we can infer that there is at least one x_10 for which x_10 will play squash via existential simplification. Finally, from the fact that there is at least one x_10 for which x_10 will play squash we can infer that there is at least one x_10 for which x_10 will play squash or x_10 will climb a mountain via existential addition. Therefore, the answer is yes.