Consider the following premises. q_4 or q_7. p_7 or ~q_7. p_7 <-> q_4. Can we infer ~p_7 from them? If possible, name the inference rules being used at each step.
 From p_7 or ~q_7 we can infer q_7 -> p_7 via rewriting. From p_7 <-> q_4 we can infer q_4 -> p_7 via biconditional elimination. Finally, from q_4 -> p_7, q_7 -> p_7, q_4 or q_7 we can infer p_7 via disjunction elimination, which contradicts ~p_7. Therefore, the answer is no.