Consider the following premises. forall x_3: Q_3(x_3) -> S_2(x_3). forall x_3: S_2(x_3) -> W(x_3). exists x_3: W(x_3) -> Q_3(x_3). forall x_3: ~W(x_3). Can we infer exists x_3: ~S_2(x_3) from them?
 From exists x_3: W(x_3) -> Q_3(x_3), forall x_3: Q_3(x_3) -> S_2(x_3) we can infer exists x_3: W(x_3) -> S_2(x_3). From forall x_3: S_2(x_3) -> W(x_3), exists x_3: W(x_3) -> S_2(x_3) we can infer exists x_3: S_2(x_3) <-> W(x_3). Finally, from exists x_3: S_2(x_3) <-> W(x_3), forall x_3: ~W(x_3) we can infer exists x_3: ~S_2(x_3). Therefore, the answer is yes.