Consider the following premises. forall x_11: P_11(x_11) <-> P(x_11). forall x_11: P_11(x_11) -> Q_7(x_11). forall x_11: ~P_6(x_11) or Q_7(x_11). forall x_11: Q_7(x_11) -> P_11(x_11). forall x_11: P_6(x_11) or P(x_11). Can we infer forall x_11: P_11(x_11) from them?
 From forall x_11: P_11(x_11) <-> P(x_11) we can infer forall x_11: P(x_11) -> P_11(x_11). From forall x_11: P_11(x_11) -> Q_7(x_11), forall x_11: Q_7(x_11) -> P_11(x_11) we can infer forall x_11: P_11(x_11) <-> Q_7(x_11). From forall x_11: P_6(x_11) or P(x_11), forall x_11: ~P_6(x_11) or Q_7(x_11) we can infer forall x_11: P(x_11) or Q_7(x_11). From forall x_11: P_11(x_11) <-> Q_7(x_11) we can infer forall x_11: Q_7(x_11) -> P_11(x_11). Finally, from forall x_11: P(x_11) -> P_11(x_11), forall x_11: Q_7(x_11) -> P_11(x_11), forall x_11: P(x_11) or Q_7(x_11) we can infer forall x_11: P_11(x_11). Therefore, the answer is yes.