Consider the following premises. forall x_4: W(x_4) -> U(x_4). exists x_4: U(x_4) <-> W(x_4). forall x_4: ~U(x_4). Can we infer forall x_4: W(x_4) from them? If possible, name the inference rules being used at each step.
 From exists x_4: U(x_4) <-> W(x_4) we can infer exists x_4: U(x_4) -> W(x_4) via existential biconditional elimination. From forall x_4: W(x_4) -> U(x_4), exists x_4: U(x_4) -> W(x_4) we can infer exists x_4: W(x_4) <-> U(x_4) via existential biconditional introduction. Finally, from exists x_4: W(x_4) <-> U(x_4), forall x_4: ~U(x_4) we can infer exists x_4: ~W(x_4) via existential biconditional elimination, which contradicts forall x_4: W(x_4). Therefore, the answer is no.