Consider the following premises. forall x_11: P_11(x_11) <-> Q_7(x_11). forall x_11: P_2(x_11) -> Q_9(x_11). forall x_11: P_11(x_11) -> ~Q_11(x_11). forall x_11: Q_9(x_11) -> P_2(x_11). forall x_11: Q_11(x_11). forall x_11: Q_7(x_11) <-> Q_9(x_11). Can we infer exists x_11: P_2(x_11) from them?
 From forall x_11: P_11(x_11) -> ~Q_11(x_11), forall x_11: Q_11(x_11) we can infer forall x_11: ~P_11(x_11). From forall x_11: P_2(x_11) -> Q_9(x_11), forall x_11: Q_9(x_11) -> P_2(x_11) we can infer forall x_11: P_2(x_11) <-> Q_9(x_11). From forall x_11: P_11(x_11) <-> Q_7(x_11), forall x_11: ~P_11(x_11) we can infer forall x_11: ~Q_7(x_11). From forall x_11: Q_7(x_11) <-> Q_9(x_11), forall x_11: ~Q_7(x_11) we can infer forall x_11: ~Q_9(x_11). Finally, from forall x_11: P_2(x_11) <-> Q_9(x_11), forall x_11: ~Q_9(x_11) we can infer forall x_11: ~P_2(x_11), which contradicts exists x_11: P_2(x_11). Therefore, the answer is no.