Consider the following premises. forall x_2: W_3(x_2) <-> T_4(x_2). forall x_2: T_4(x_2) <-> W_3(x_2). forall x_2: ~T_4(x_2). Can we infer exists x_2: W_3(x_2) from them? If possible, name the inference rules being used at each step.
 From forall x_2: T_4(x_2) <-> W_3(x_2) we can infer forall x_2: W_3(x_2) -> T_4(x_2) via universal biconditional elimination. From forall x_2: W_3(x_2) <-> T_4(x_2) we can infer forall x_2: T_4(x_2) -> W_3(x_2) via universal biconditional elimination. From forall x_2: T_4(x_2) -> W_3(x_2), forall x_2: W_3(x_2) -> T_4(x_2) we can infer forall x_2: T_4(x_2) <-> W_3(x_2) via universal biconditional introduction. Finally, from forall x_2: T_4(x_2) <-> W_3(x_2), forall x_2: ~T_4(x_2) we can infer forall x_2: ~W_3(x_2) via universal biconditional elimination, which contradicts exists x_2: W_3(x_2). Therefore, the answer is no.