Consider the following premises. For all x_11, x_11 is poor or x_11 will not cook. There is at least one x_11 for which x_11 is a scientist or x_11 will cook. For all x_11, if x_11 plays squash, then x_11 is not poor. For all x_11, if x_11 were a scientist, then x_11 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 will not play squash.
 From the fact that for all x_11, x_11 is poor or x_11 will not cook we can infer that for all x_11, if x_11 cooks, then x_11 is poor via universal rewriting. From the fact that for all x_11, if x_11 were a scientist, then x_11 is poor, that for all x_11, if x_11 cooks, then x_11 is poor, and that there is at least one x_11 for which x_11 is a scientist or x_11 will cook we can infer that there is at least one x_11 for which x_11 is poor via existential disjunction elimination. Finally, from the fact that for all x_11, if x_11 plays squash, then x_11 is not poor, and that there is at least one x_11 for which x_11 is poor we can infer that there is at least one x_11 for which x_11 will not play squash via existential modus tollens. Therefore, the answer is yes.