Consider the following premises. u or ~r. p -> r. ~p. u -> p. Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From u or ~r we can infer r -> u via rewriting. From r -> u, u -> p we can infer r -> p via transitivity. From r -> p, p -> r we can infer r <-> p via biconditional introduction. Finally, from r <-> p, ~p we can infer ~r via biconditional elimination. Therefore, the answer is yes.