Consider the following premises. exists x_12: P_12(x_12) <-> W_1(x_12). forall x_12: Q(x_12) -> W_1(x_12). forall x_12: P_12(x_12) -> Q(x_12). Can we infer forall x_12: ~(Q(x_12) -> W_1(x_12)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.