Consider the following premises. forall x_11: ~Q_11(x_11). forall x_11: Q_11(x_11) -> P_11(x_11). exists x_11: P_11(x_11). forall x_11: P_11(x_11) <-> Q_11(x_11). Can we infer forall x_11: ~Q_1(x_11) from them?
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.