Consider the following premises. exists x_10: W(x_10) -> S_1(x_10). forall x_10: S_1(x_10) -> W(x_10). forall x_10: S_1(x_10) and Q_10(x_10). Can we infer exists x_10: W(x_10) from them?
 From forall x_10: S_1(x_10) and Q_10(x_10) we can infer forall x_10: S_1(x_10). From exists x_10: W(x_10) -> S_1(x_10), forall x_10: S_1(x_10) -> W(x_10) we can infer exists x_10: W(x_10) <-> S_1(x_10). From exists x_10: W(x_10) <-> S_1(x_10) we can infer exists x_10: S_1(x_10) -> W(x_10). Finally, from exists x_10: S_1(x_10) -> W(x_10), forall x_10: S_1(x_10) we can infer exists x_10: W(x_10). Therefore, the answer is yes.