Consider the following premises. exists x_10: U(x_10) -> ~Q_10(x_10). forall x_10: Q_10(x_10). forall x_10: U(x_10). forall x_10: Q_7(x_10). Can we infer exists x_10: P(x_10) from them?
 From exists x_10: U(x_10) -> ~Q_10(x_10), forall x_10: Q_10(x_10) we can infer exists x_10: ~U(x_10). From forall x_10: U(x_10), forall x_10: Q_7(x_10) we can infer forall x_10: U(x_10) and Q_7(x_10). From forall x_10: U(x_10) and Q_7(x_10) we can infer forall x_10: U(x_10). From forall x_10: U(x_10) we can infer forall x_10: U(x_10) or P(x_10). Finally, from forall x_10: U(x_10) or P(x_10), exists x_10: ~U(x_10) we can infer exists x_10: P(x_10). Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.