Consider the following premises. forall y: W_1(y) <-> U_1(y). forall y: W_1(y) -> W(y). exists y: W(y) -> U_1(y). Can we infer forall y: ~(W_1(y) -> U_1(y)) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.