Consider the following premises. p_12 or ~u. w_1 <-> p_12. ~w_1. u <-> p. Can we infer p from them? If possible, name the inference rules being used at each step.
 From p_12 or ~u we can infer u -> p_12 via rewriting. From w_1 <-> p_12, ~w_1 we can infer ~p_12 via biconditional elimination. From u -> p_12, ~p_12 we can infer ~u via modus tollens. Finally, from u <-> p, ~u we can infer ~p via biconditional elimination, which contradicts p. Therefore, the answer is no.