Consider the following premises. For all x_6, x_6 will make tea. For all x_6, if x_6 plays squash, then x_6 is reading a book. For all x_6, if x_6 makes tea, then x_6 is a writer. There is at least one x_6 for which if x_6 were a writer, then x_6 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not read a book.
 From the fact that there is at least one x_6 for which if x_6 were a writer, then x_6 is playing squash, and that for all x_6, if x_6 plays squash, then x_6 is reading a book we can infer that there is at least one x_6 for which if x_6 were a writer, then x_6 is reading a book via existential transitivity. From the fact that for all x_6, if x_6 makes tea, then x_6 is a writer, and that there is at least one x_6 for which if x_6 were a writer, then x_6 is reading a book we can infer that there is at least one x_6 for which if x_6 makes tea, then x_6 is reading a book via existential transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 makes tea, then x_6 is reading a book, and that for all x_6, x_6 will make tea we can infer that there is at least one x_6 for which x_6 will read a book via existential modus ponens, which contradicts that For all x_6, x_6 will not read a book. Therefore, the answer is no.