Consider the following premises. exists x_11: ~Q_11(x_11). forall x_11: P_11(x_11) -> Q_11(x_11). forall x_11: P_11(x_11) or S_2(x_11). Can we infer forall x_11: ~(S_2(x_11) or S(x_11)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.