Consider the following premises. u or ~q_7. ~t. t <-> u. Can we infer q_7 from them? If possible, name the inference rules being used at each step.
 From u or ~q_7 we can infer q_7 -> u via rewriting. From t <-> u, ~t we can infer ~u via biconditional elimination. Finally, from q_7 -> u, ~u we can infer ~q_7 via modus tollens, which contradicts q_7. Therefore, the answer is no.