Consider the following premises. q -> r. ~p_5. p_5 <-> r. q or ~r. Can we infer q from them? If possible, name the inference rules being used at each step.
 From q or ~r we can infer r -> q via rewriting. From p_5 <-> r, ~p_5 we can infer ~r via biconditional elimination. From q -> r, r -> q we can infer q <-> r via biconditional introduction. Finally, from q <-> r, ~r we can infer ~q via biconditional elimination, which contradicts q. Therefore, the answer is no.