Consider the following premises. exists x_14: Q_14(x_14) or ~P(x_14). forall x_14: Q_1(x_14) -> P(x_14). forall x_14: Q_1(x_14) or ~Q_14(x_14). Can we infer forall x_14: ~(P(x_14) -> Q_1(x_14)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.