Consider the following premises. forall x_12: P_10(x_12) -> R(x_12). forall x_12: P_12(x_12) or ~Q_12(x_12). exists x_12: P_10(x_12) <-> P_12(x_12). Can we infer forall x_12: ~(Q_12(x_12) -> R(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.