Consider the following premises. forall x: T(x) -> R_3(x). exists x: U(x) -> S(x). forall x: U_4(x) -> U(x). forall x: S(x) -> T(x). Can we infer forall x: ~(U_4(x) -> R_3(x)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.