Consider the following premises. For all x_7, if x_7 reads a book, then x_7 is fast. There is at least one x_7 for which x_7 will read a book. For all x_7, x_7 will read a book or x_7 is not fast. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is not fast.
 From the fact that for all x_7, x_7 will read a book or x_7 is not fast we can infer that for all x_7, if x_7 were fast, then x_7 is reading a book via universal rewriting. From the fact that for all x_7, if x_7 reads a book, then x_7 is fast, and that for all x_7, if x_7 were fast, then x_7 is reading a book we can infer that for all x_7, x_7 will read a book if and only if x_7 is fast via universal biconditional introduction. From the fact that for all x_7, x_7 will read a book if and only if x_7 is fast we can infer that for all x_7, if x_7 reads a book, then x_7 is fast via universal biconditional elimination. Finally, from the fact that for all x_7, if x_7 reads a book, then x_7 is fast, and that there is at least one x_7 for which x_7 will read a book we can infer that there is at least one x_7 for which x_7 is fast via existential modus ponens, which contradicts that For all x_7, x_7 is not fast. Therefore, the answer is no.