Consider the following premises. u_2 -> w. u_2 <-> w_4. ~q_6. w_4 -> q_6. w -> u_2. Can we infer ~w from them?
 From w -> u_2, u_2 -> w we can infer w <-> u_2. From w_4 -> q_6, ~q_6 we can infer ~w_4. From u_2 <-> w_4, ~w_4 we can infer ~u_2. Finally, from w <-> u_2, ~u_2 we can infer ~w. Therefore, the answer is yes.