Consider the following premises. forall y_3: T_4(y_3) <-> W_1(y_3). forall y_3: ~S(y_3). forall y_3: T_4(y_3) <-> S(y_3). Can we infer exists y_3: W_1(y_3) from them? If possible, name the inference rules being used at each step.
 From forall y_3: T_4(y_3) <-> W_1(y_3) we can infer forall y_3: W_1(y_3) -> T_4(y_3) via universal biconditional elimination. From forall y_3: T_4(y_3) <-> S(y_3), forall y_3: ~S(y_3) we can infer forall y_3: ~T_4(y_3) via universal biconditional elimination. Finally, from forall y_3: W_1(y_3) -> T_4(y_3), forall y_3: ~T_4(y_3) we can infer forall y_3: ~W_1(y_3) via universal modus tollens, which contradicts exists y_3: W_1(y_3). Therefore, the answer is no.