Consider the following premises. forall x_8: Q_8(x_8) -> W(x_8). exists x_8: W(x_8) <-> P(x_8). forall x_8: P(x_8) -> Q_8(x_8). Can we infer forall x_8: ~(W(x_8) -> P(x_8)) from them?
That contradicts the premises. Therefore the answer is no.