Consider the following premises. For all x_6, x_6 is a carpenter. There is at least one x_6 for which if x_6 reads a book, then x_6 is not an office clerk. For all x_6, x_6 is an office clerk or x_6 is not a carpenter. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not read a book.
 From the fact that for all x_6, x_6 is an office clerk or x_6 is not a carpenter we can infer that for all x_6, if x_6 were a carpenter, then x_6 is an office clerk via universal rewriting. From the fact that for all x_6, if x_6 were a carpenter, then x_6 is an office clerk, and that for all x_6, x_6 is a carpenter we can infer that for all x_6, x_6 is an office clerk via universal modus ponens. Finally, from the fact that there is at least one x_6 for which if x_6 reads a book, then x_6 is not an office clerk, and that for all x_6, x_6 is an office clerk we can infer that there is at least one x_6 for which x_6 will not read a book via existential modus tollens. Therefore, the answer is yes.