Consider the following premises. For all x_10, x_10 will not sleep. There is at least one x_10 for which if x_10 reads a book, then x_10 is taking a plane. For all x_10, x_10 will sleep if and only if x_10 will read a book. For all x_10, if x_10 takes a plane, 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 not take a plane.
 From the fact that for all x_10, x_10 will sleep if and only if x_10 will read a book, and that for all x_10, x_10 will not sleep we can infer that for all x_10, x_10 will not read a book via universal biconditional elimination. From the fact that there is at least one x_10 for which if x_10 reads a book, then x_10 is taking a plane, and that for all x_10, if x_10 takes a plane, then x_10 is reading a book we can infer that there is at least one x_10 for which x_10 will read a book if and only if x_10 will take a plane via existential biconditional introduction. From the fact that there is at least one x_10 for which x_10 will read a book if and only if x_10 will take a plane we can infer that there is at least one x_10 for which if x_10 takes a plane, then x_10 is reading a book via existential biconditional elimination. Finally, from the fact that there is at least one x_10 for which if x_10 takes a plane, then x_10 is reading a book, and that for all x_10, x_10 will not read a book we can infer that there is at least one x_10 for which x_10 will not take a plane via existential modus tollens. Therefore, the answer is yes.