Consider the following premises. For all x_11, x_11 will play squash. For all x_11, if x_11 reads a book, then x_11 is a nurse. For all x_11, if x_11 were excited, then x_11 is a nurse. There is at least one x_11 for which x_11 will read a book or x_11 is excited. 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 play squash.
 From the fact that for all x_11, if x_11 reads a book, then x_11 is a nurse, that for all x_11, if x_11 were excited, then x_11 is a nurse, and that there is at least one x_11 for which x_11 will read a book or x_11 is excited we can infer that there is at least one x_11 for which x_11 is a nurse via existential disjunction elimination. From the fact that there is at least one x_11 for which x_11 is a nurse, and that for all x_11, x_11 will play squash we can infer that some nurses will play squash via existential conjunction. Finally, from the fact that some nurses will play squash we can infer that there is at least one x_11 for which x_11 will play squash via existential simplification. Therefore, the answer is yes.