Consider the following premises. forall x: U(x) -> R(x). forall x: R(x) -> Q_4(x). forall x: Q_1(x) -> U(x). exists x: T(x) -> Q_1(x). Can we infer forall x: ~(T(x) -> Q_4(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.