Consider the following premises. forall x_10: W_1(x_10) -> W(x_10). forall x_10: ~Q_10(x_10). exists x_10: W(x_10) -> W_1(x_10). forall x_10: S(x_10) <-> W_1(x_10). forall x_10: S(x_10) <-> Q_10(x_10). Can we infer exists x_10: ~W(x_10) from them?
 From forall x_10: S(x_10) <-> Q_10(x_10), forall x_10: ~Q_10(x_10) we can infer forall x_10: ~S(x_10). From exists x_10: W(x_10) -> W_1(x_10), forall x_10: W_1(x_10) -> W(x_10) we can infer exists x_10: W(x_10) <-> W_1(x_10). From forall x_10: S(x_10) <-> W_1(x_10), forall x_10: ~S(x_10) we can infer forall x_10: ~W_1(x_10). Finally, from exists x_10: W(x_10) <-> W_1(x_10), forall x_10: ~W_1(x_10) we can infer exists x_10: ~W(x_10). Therefore, the answer is yes.