Consider the following premises. exists x_10: T_4(x_10) <-> P(x_10). forall x_10: Q_5(x_10) -> T_4(x_10). forall x_10: T_4(x_10) -> Q_5(x_10). Can we infer forall x_10: ~(P(x_10) -> Q_5(x_10)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.