Consider the following premises. u -> p. r. p or ~r. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From p or ~r we can infer r -> p via rewriting. From r we can infer r or u via addition. Finally, from r -> p, u -> p, r or u we can infer p via disjunction elimination, which contradicts ~p. Therefore, the answer is no.