Consider the following premises. forall x_12: P_11(x_12) -> R_12(x_12). forall x_12: Q_12(x_12) -> R_12(x_12). forall x_12: P_2(x_12). forall x_12: P_12(x_12) -> Q_12(x_12). exists x_12: P_11(x_12) or P_12(x_12). Can we infer forall x_12: ~P_2(x_12) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.