Consider the following premises. For all x_4, x_4 is fast or x_4 is a writer. There is at least one x_4 for which x_4 is not fast or x_4 will read a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, neither x_4 is a writer nor x_4 will read a book.
That contradicts the premises. Therefore the answer is no.