Consider the following premises. exists z: ~T(z). forall z: U_1(z) -> U_4(z). forall z: U_4(z) <-> T(z). forall z: U_4(z) -> U_1(z). Can we infer forall z: U_4(z) -> U_1(z) from them? If possible, name the inference rules being used at each step.
That is one of the premises. Therefore, the answer is yes.