Consider the following premises. forall x_3: T(x_3) -> W(x_3). forall x_3: W(x_3) -> T(x_3). forall x_3: W(x_3) or ~T(x_3). Can we infer exists x_3: ~(W(x_3) <-> T(x_3)) from them? If possible, name the inference rules being used at each step.
 From forall x_3: W(x_3) -> T(x_3), forall x_3: T(x_3) -> W(x_3) we can infer forall x_3: W(x_3) <-> T(x_3) via universal biconditional introduction. From forall x_3: W(x_3) or ~T(x_3) we can infer forall x_3: T(x_3) -> W(x_3) via universal rewriting. From forall x_3: W(x_3) <-> T(x_3) we can infer forall x_3: W(x_3) -> T(x_3) via universal biconditional elimination. Finally, from forall x_3: W(x_3) -> T(x_3), forall x_3: T(x_3) -> W(x_3) we can infer forall x_3: W(x_3) <-> T(x_3) via universal biconditional introduction, which contradicts exists x_3: ~(W(x_3) <-> T(x_3)). Therefore, the answer is no.