Consider the following premises. p_4 <-> q_1. ~r_3. p_4 <-> p. u_1 <-> r_3. u_1 <-> q_1. Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From u_1 <-> r_3, ~r_3 we can infer ~u_1 via biconditional elimination. From u_1 <-> q_1, ~u_1 we can infer ~q_1 via biconditional elimination. From p_4 <-> q_1, ~q_1 we can infer ~p_4 via biconditional elimination. Finally, from p_4 <-> p, ~p_4 we can infer ~p via biconditional elimination. Therefore, the answer is yes.