Consider the following premises. For all x_13, x_13 will make tea or x_13 will read a book. There is at least one x_13 for which if x_13 makes tea, then x_13 is writing a letter. For all x_13, if x_13 writes a letter, then x_13 is making tea. For all x_13, x_13 will play tennis if and only if x_13 will write a letter. For all x_13, x_13 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will not read a book.
 From the fact that for all x_13, x_13 will play tennis if and only if x_13 will write a letter, and that for all x_13, x_13 will not play tennis we can infer that for all x_13, x_13 will not write a letter via universal biconditional elimination. From the fact that there is at least one x_13 for which if x_13 makes tea, then x_13 is writing a letter, and that for all x_13, if x_13 writes a letter, then x_13 is making tea we can infer that there is at least one x_13 for which x_13 will make tea if and only if x_13 will write a letter via existential biconditional introduction. From the fact that there is at least one x_13 for which x_13 will make tea if and only if x_13 will write a letter, and that for all x_13, x_13 will not write a letter we can infer that there is at least one x_13 for which x_13 will not make tea via existential biconditional elimination. Finally, from the fact that for all x_13, x_13 will make tea or x_13 will read a book, and that there is at least one x_13 for which x_13 will not make tea we can infer that there is at least one x_13 for which x_13 will read a book via existential disjunctive syllogism, which contradicts that For all x_13, x_13 will not read a book. Therefore, the answer is no.