Consider the following premises. q_11 -> w_3. r -> s. s -> q_11. r or ~w_3. Can we infer ~(w_3 <-> r) from them?
 From s -> q_11, q_11 -> w_3 we can infer s -> w_3. From r -> s, s -> w_3 we can infer r -> w_3. From r or ~w_3 we can infer w_3 -> r. Finally, from w_3 -> r, r -> w_3 we can infer w_3 <-> r, which contradicts ~(w_3 <-> r). Therefore, the answer is no.