Consider the following premises. r_2 <-> T_4(d_2). forall z: T_4(z) or W_2(z). W_2(d_2) -> r_2. Can we infer ~r_2 from them?
 From forall z: T_4(z) or W_2(z) we can infer T_4(d_2) or W_2(d_2). From r_2 <-> T_4(d_2) we can infer T_4(d_2) -> r_2. Finally, from T_4(d_2) -> r_2, W_2(d_2) -> r_2, T_4(d_2) or W_2(d_2) we can infer r_2, which contradicts ~r_2. Therefore, the answer is no.