Consider the following premises. q_11 -> r. ~r. q_11 <-> s_4. r -> q_11. Can we infer s_4 from them? If possible, name the inference rules being used at each step.
 From r -> q_11, q_11 -> r we can infer r <-> q_11 via biconditional introduction. From r <-> q_11 we can infer q_11 -> r via biconditional elimination. From q_11 -> r, ~r we can infer ~q_11 via modus tollens. Finally, from q_11 <-> s_4, ~q_11 we can infer ~s_4 via biconditional elimination, which contradicts s_4. Therefore, the answer is no.