Consider the following premises. There is at least one x_14 for which if x_14 were a carpenter, then x_14 is playing tennis. For all x_14, x_14 will read a book. For all x_14, if x_14 reads a book, then x_14 is a writer. For all x_14, if x_14 were a police officer, then x_14 is playing tennis. For all x_14, x_14 is a writer if and only if x_14 is a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_14 for which x_14 will play tennis.
 From the fact that for all x_14, x_14 is a writer if and only if x_14 is a carpenter we can infer that for all x_14, if x_14 were a writer, then x_14 is a carpenter via universal biconditional elimination. From the fact that for all x_14, if x_14 reads a book, then x_14 is a writer, and that for all x_14, if x_14 were a writer, then x_14 is a carpenter we can infer that for all x_14, if x_14 reads a book, then x_14 is a carpenter via universal transitivity. From the fact that for all x_14, if x_14 reads a book, then x_14 is a carpenter, and that there is at least one x_14 for which if x_14 were a carpenter, then x_14 is playing tennis we can infer that there is at least one x_14 for which if x_14 reads a book, then x_14 is playing tennis via existential transitivity. From the fact that for all x_14, x_14 will read a book we can infer that for all x_14, x_14 will read a book or x_14 is a police officer via universal addition. Finally, from the fact that there is at least one x_14 for which if x_14 reads a book, then x_14 is playing tennis, that for all x_14, if x_14 were a police officer, then x_14 is playing tennis, and that for all x_14, x_14 will read a book or x_14 is a police officer we can infer that there is at least one x_14 for which x_14 will play tennis via existential disjunction elimination. Therefore, the answer is yes.