Consider the following premises. q <-> q_4. r -> q. p_4 -> r. ~q_4. q -> p_4. Can we infer r from them? If possible, name the inference rules being used at each step.
 From q -> p_4, p_4 -> r we can infer q -> r via transitivity. From q -> r, r -> q we can infer q <-> r via biconditional introduction. From q <-> q_4, ~q_4 we can infer ~q via biconditional elimination. Finally, from q <-> r, ~q we can infer ~r via biconditional elimination, which contradicts r. Therefore, the answer is no.