Consider the following premises. forall x_11: ~P_5(x_11). forall x_11: P(x_11) <-> Q_11(x_11). exists x_11: P_5(x_11) <-> Q_11(x_11). Can we infer forall x_11: P(x_11) from them?
 From forall x_11: P(x_11) <-> Q_11(x_11) we can infer forall x_11: P(x_11) -> Q_11(x_11). From exists x_11: P_5(x_11) <-> Q_11(x_11), forall x_11: ~P_5(x_11) we can infer exists x_11: ~Q_11(x_11). Finally, from forall x_11: P(x_11) -> Q_11(x_11), exists x_11: ~Q_11(x_11) we can infer exists x_11: ~P(x_11), which contradicts forall x_11: P(x_11). Therefore, the answer is no.