Consider the following premises. exists x_10: ~Q_10(x_10). forall x_10: W(x_10) <-> Q_10(x_10). forall x_10: W(x_10). Can we infer exists x_10: Q_1(x_10) from them?
 From forall x_10: W(x_10) <-> Q_10(x_10), exists x_10: ~Q_10(x_10) we can infer exists x_10: ~W(x_10). From forall x_10: W(x_10) we can infer forall x_10: W(x_10) or Q_1(x_10). Finally, from forall x_10: W(x_10) or Q_1(x_10), exists x_10: ~W(x_10) we can infer exists x_10: Q_1(x_10). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.