Consider the following premises. q_4 <-> r. s_3 -> u. s_3. ~r. Can we infer q_4 from them? If possible, name the inference rules being used at each step.
 From s_3 -> u, s_3 we can infer u via modus ponens. Finally, from q_4 <-> r, ~r we can infer ~q_4 via biconditional elimination, which contradicts q_4. Therefore, the answer is no.