Consider the following premises. forall x_4: W_4(x_4) or ~W_2(x_4). forall x_4: W_4(x_4) -> W_2(x_4). forall x_4: W_2(x_4) -> W_4(x_4). Can we infer exists x_4: ~(W_2(x_4) <-> W_4(x_4)) from them?
 From forall x_4: W_2(x_4) -> W_4(x_4), forall x_4: W_4(x_4) -> W_2(x_4) we can infer forall x_4: W_2(x_4) <-> W_4(x_4). From forall x_4: W_4(x_4) or ~W_2(x_4) we can infer forall x_4: W_2(x_4) -> W_4(x_4). From forall x_4: W_2(x_4) <-> W_4(x_4) we can infer forall x_4: W_4(x_4) -> W_2(x_4). Finally, from forall x_4: W_2(x_4) -> W_4(x_4), forall x_4: W_4(x_4) -> W_2(x_4) we can infer forall x_4: W_2(x_4) <-> W_4(x_4), which contradicts exists x_4: ~(W_2(x_4) <-> W_4(x_4)). Therefore, the answer is no.