Consider the following premises. r -> p_11. r or t. p_11 -> r. p_11 or ~t. Can we infer ~p_11 from them? If possible, name the inference rules being used at each step.
 From p_11 -> r, r -> p_11 we can infer p_11 <-> r via biconditional introduction. From p_11 <-> r we can infer r -> p_11 via biconditional elimination. From p_11 or ~t we can infer t -> p_11 via rewriting. Finally, from r -> p_11, t -> p_11, r or t we can infer p_11 via disjunction elimination, which contradicts ~p_11. Therefore, the answer is no.