Consider the following premises. forall y: W_1(y) -> R(y). forall y: W_1(y) -> T(y). exists y: Q(y) or T_4(y). forall y: T(y) -> T_4(y). forall y: Q(y) -> R(y). forall y: T_4(y) -> W_1(y). Can we infer exists y: Q(y) or T_4(y) from them?
That is one of the premises. Therefore, the answer is yes.