Consider the following premises. For all x_8, if x_8 were fast, then x_8 is excited. For all x_8, x_8 will read a book or x_8 is fast. There is at least one x_8 for which x_8 is excited or x_8 will not sleep. For all x_8, if x_8 reads a book, then x_8 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not excited.
 From the fact that there is at least one x_8 for which x_8 is excited or x_8 will not sleep we can infer that there is at least one x_8 for which if x_8 sleeps, then x_8 is excited via existential rewriting. From the fact that for all x_8, if x_8 reads a book, then x_8 is sleeping, and that there is at least one x_8 for which if x_8 sleeps, then x_8 is excited we can infer that there is at least one x_8 for which if x_8 reads a book, then x_8 is excited via existential transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 reads a book, then x_8 is excited, that for all x_8, if x_8 were fast, then x_8 is excited, and that for all x_8, x_8 will read a book or x_8 is fast we can infer that there is at least one x_8 for which x_8 is excited via existential disjunction elimination, which contradicts that For all x_8, x_8 is not excited. Therefore, the answer is no.