Consider the following premises. forall x_3: T(x_3) -> Q_3(x_3). exists x_3: W(x_3) -> T(x_3). forall x_3: Q_3(x_3) -> W(x_3). forall x_3: ~T(x_3). Can we infer exists x_3: ~W(x_3) from them?
 From forall x_3: T(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> W(x_3) we can infer forall x_3: T(x_3) -> W(x_3). From exists x_3: W(x_3) -> T(x_3), forall x_3: T(x_3) -> W(x_3) we can infer exists x_3: W(x_3) <-> T(x_3). Finally, from exists x_3: W(x_3) <-> T(x_3), forall x_3: ~T(x_3) we can infer exists x_3: ~W(x_3). Therefore, the answer is yes.