Consider the following premises. For all x_10, x_10 will read a book or x_10 will not make tea. For all x_10, x_10 will make tea if and only if x_10 will work. For all x_10, if x_10 reads a book, then x_10 is working. 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 if is not true that x_10 will read a book if and only if x_10 will make tea.
 From the fact that for all x_10, x_10 will read a book or x_10 will not make tea we can infer that for all x_10, if x_10 makes tea, then x_10 is reading a book via universal rewriting. From the fact that for all x_10, x_10 will make tea if and only if x_10 will work we can infer that for all x_10, if x_10 works, then x_10 is making tea via universal biconditional elimination. From the fact that for all x_10, if x_10 reads a book, then x_10 is working, and that for all x_10, if x_10 works, then x_10 is making tea we can infer that for all x_10, if x_10 reads a book, then x_10 is making tea via universal transitivity. Finally, from the fact that for all x_10, if x_10 reads a book, then x_10 is making tea, and that for all x_10, if x_10 makes tea, then x_10 is reading a book we can infer that for all x_10, x_10 will read a book if and only if x_10 will make tea via universal biconditional introduction, which contradicts that There is at least one x_10 for which if is not true that x_10 will read a book if and only if x_10 will make tea. Therefore, the answer is no.