Consider the following premises. ~p_7 or t_4. p_2 or ~t_4. p_7 or u_3. u_3 <-> p_2. Can we infer ~p_2 from them? If possible, name the inference rules being used at each step.
 From u_3 <-> p_2 we can infer u_3 -> p_2 via biconditional elimination. From p_7 or u_3, ~p_7 or t_4 we can infer u_3 or t_4 via resolution. From p_2 or ~t_4 we can infer t_4 -> p_2 via rewriting. Finally, from u_3 -> p_2, t_4 -> p_2, u_3 or t_4 we can infer p_2 via disjunction elimination, which contradicts ~p_2. Therefore, the answer is no.