Consider the following premises. For all x_10, x_10 will not play squash. There is at least one x_10 for which if x_10 reads a book, then x_10 is playing squash. For all x_10, x_10 will read a book or x_10 will cook. For all x_10, if x_10 plays squash, then x_10 is reading a book. 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 cook.
 From the fact that for all x_10, if x_10 plays squash, then x_10 is reading a book, and that there is at least one x_10 for which if x_10 reads a book, then x_10 is playing squash we can infer that there is at least one x_10 for which x_10 will play squash if and only if x_10 will read a book via existential biconditional introduction. From the fact that there is at least one x_10 for which x_10 will play squash if and only if x_10 will read a book, and that for all x_10, x_10 will not play squash we can infer that there is at least one x_10 for which x_10 will not read a book via existential biconditional elimination. Finally, from the fact that for all x_10, x_10 will read a book or x_10 will cook, and that there is at least one x_10 for which x_10 will not read a book we can infer that there is at least one x_10 for which x_10 will cook via existential disjunctive syllogism. Therefore, the answer is yes.