Consider the following premises. q_10 -> q_4. ~q. q_10 or ~q_4. q <-> q_10. Can we infer q_4 from them? If possible, name the inference rules being used at each step.
 From q <-> q_10, ~q we can infer ~q_10 via biconditional elimination. From q_10 or ~q_4 we can infer q_4 -> q_10 via rewriting. From q_10 -> q_4, q_4 -> q_10 we can infer q_10 <-> q_4 via biconditional introduction. Finally, from q_10 <-> q_4, ~q_10 we can infer ~q_4 via biconditional elimination, which contradicts q_4. Therefore, the answer is no.