Consider the following premises. forall x_5: P_5(x_5) -> W_2(x_5). forall x_5: W_2(x_5) -> P_5(x_5). exists x_5: W_2(x_5) -> P_5(x_5). Can we infer forall x_5: ~(W_2(x_5) <-> P_5(x_5)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.