Consider the following premises. forall x_10: P_10(x_10) -> Q_10(x_10). forall x_10: U(x_10) or S(x_10). exists x_10: ~Q_10(x_10). forall x_10: P_10(x_10) <-> U(x_10). Can we infer exists x_10: S(x_10) from them?
 From forall x_10: P_10(x_10) -> Q_10(x_10), exists x_10: ~Q_10(x_10) we can infer exists x_10: ~P_10(x_10). From forall x_10: P_10(x_10) <-> U(x_10), exists x_10: ~P_10(x_10) we can infer exists x_10: ~U(x_10). Finally, from forall x_10: U(x_10) or S(x_10), exists x_10: ~U(x_10) we can infer exists x_10: S(x_10). Therefore, the answer is yes.