Consider the following premises. For all x_11, x_11 will not read a book or x_11 will play squash. For all x_11, if x_11 were a nurse, then x_11 is not playing squash. There is at least one x_11 for which x_11 will read a book or x_11 will cook. For all x_11, x_11 will not cook. 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 is not a nurse.
 From the fact that there is at least one x_11 for which x_11 will read a book or x_11 will cook, and that for all x_11, x_11 will not read a book or x_11 will play squash we can infer that there is at least one x_11 for which x_11 will cook or x_11 will play squash via existential resolution. From the fact that there is at least one x_11 for which x_11 will cook or x_11 will play squash, and that for all x_11, x_11 will not cook we can infer that there is at least one x_11 for which x_11 will play squash via existential disjunctive syllogism. Finally, from the fact that for all x_11, if x_11 were a nurse, then x_11 is not playing squash, and that there is at least one x_11 for which x_11 will play squash we can infer that there is at least one x_11 for which x_11 is not a nurse via existential modus tollens. Therefore, the answer is yes.