Consider the following premises. forall x: R(x) -> W_2(x). forall x: U(x) -> R(x). forall x: U(x) or ~W_2(x). Can we infer exists x: ~(U(x) <-> W_2(x)) from them?
 From forall x: U(x) or ~W_2(x) we can infer forall x: W_2(x) -> U(x). From forall x: U(x) -> R(x), forall x: R(x) -> W_2(x) we can infer forall x: U(x) -> W_2(x). Finally, from forall x: U(x) -> W_2(x), forall x: W_2(x) -> U(x) we can infer forall x: U(x) <-> W_2(x), which contradicts exists x: ~(U(x) <-> W_2(x)). Therefore, the answer is no.