Consider the following premises. ~r_3. t <-> w. t -> r_3. r_3 -> w. Can we infer ~w from them?
 From t <-> w we can infer w -> t. From w -> t, t -> r_3 we can infer w -> r_3. From r_3 -> w, w -> r_3 we can infer r_3 <-> w. Finally, from r_3 <-> w, ~r_3 we can infer ~w. Therefore, the answer is yes.