Consider the following premises. forall y_2: ~T(y_2). q_1 <-> T(d_1). q_1 or w. Can we infer ~w from them?
 From forall y_2: ~T(y_2) we can infer ~T(d_1). From q_1 <-> T(d_1), ~T(d_1) we can infer ~q_1. Finally, from q_1 or w, ~q_1 we can infer w, which contradicts ~w. Therefore, the answer is no.