Consider the following premises. ~p. q_8 -> p. p -> q_8. p -> q_8. Can we infer q_8 from them? If possible, name the inference rules being used at each step.
 From p -> q_8, q_8 -> p we can infer p <-> q_8 via biconditional introduction. From p <-> q_8 we can infer q_8 -> p via biconditional elimination. From q_8 -> p, p -> q_8 we can infer q_8 <-> p via biconditional introduction. Finally, from q_8 <-> p, ~p we can infer ~q_8 via biconditional elimination, which contradicts q_8. Therefore, the answer is no.