Consider the following premises. forall y: S(y) or T(y). exists y: ~S(y) or Q_1(y). forall y: R(y). forall y: Q_1(y) -> W_3(y). forall y: T(y) -> W_3(y). Can we infer exists y: R(y) and W_3(y) from them?
 From forall y: S(y) or T(y), exists y: ~S(y) or Q_1(y) we can infer exists y: T(y) or Q_1(y). From forall y: T(y) -> W_3(y), forall y: Q_1(y) -> W_3(y), exists y: T(y) or Q_1(y) we can infer exists y: W_3(y). Finally, from forall y: R(y), exists y: W_3(y) we can infer exists y: R(y) and W_3(y). Therefore, the answer is yes.