Consider the following premises. ~w. w_4 <-> w_2. w <-> p_12. p_12 or ~w_4. Can we infer w_2 from them?
 From p_12 or ~w_4 we can infer w_4 -> p_12. From w <-> p_12, ~w we can infer ~p_12. From w_4 -> p_12, ~p_12 we can infer ~w_4. Finally, from w_4 <-> w_2, ~w_4 we can infer ~w_2, which contradicts w_2. Therefore, the answer is no.