Consider the following premises. exists x_7: Q_7(x_7) <-> U(x_7). forall x_7: P_7(x_7) or ~Q_7(x_7). Can we infer forall x_7: ~(U(x_7) -> P_7(x_7)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.