Consider the following premises. For all x, x is fast. For all x, x is excited or x is not fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x is not excited.
 From the fact that for all x, x is excited or x is not fast we can infer that for all x, if x were fast, then x is excited via universal rewriting. Finally, from the fact that for all x, if x were fast, then x is excited, and that for all x, x is fast we can infer that for all x, x is excited via universal modus ponens, which contradicts that There is at least one x for which x is not excited. Therefore, the answer is no.