Consider the following premises. forall x_11: Q_11(x_11) -> Q_1(x_11). forall x_11: P_8(x_11) -> Q_11(x_11). forall x_11: P_8(x_11) or P_11(x_11). exists x_11: P(x_11). forall x_11: P_11(x_11) <-> Q_11(x_11). Can we infer exists x_11: P(x_11) and Q_1(x_11) from them?
 From forall x_11: P_11(x_11) <-> Q_11(x_11) we can infer forall x_11: P_11(x_11) -> Q_11(x_11). From forall x_11: P_8(x_11) -> Q_11(x_11), forall x_11: P_11(x_11) -> Q_11(x_11), forall x_11: P_8(x_11) or P_11(x_11) we can infer forall x_11: Q_11(x_11). From forall x_11: Q_11(x_11) -> Q_1(x_11), forall x_11: Q_11(x_11) we can infer forall x_11: Q_1(x_11). Finally, from exists x_11: P(x_11), forall x_11: Q_1(x_11) we can infer exists x_11: P(x_11) and Q_1(x_11). Therefore, the answer is yes.