Consider the following premises. exists x_11: Q_11(x_11) -> S(x_11). forall x_11: ~S(x_11). forall x_11: P_11(x_11) or Q_11(x_11). forall x_11: P_11(x_11) -> S(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.