Consider the following premises. exists x_3: Q(x_3) -> W_2(x_3). forall x_3: Q(x_3) -> W_2(x_3). forall x_3: W_2(x_3) -> Q(x_3). Can we infer forall x_3: ~(W_2(x_3) -> Q(x_3)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.