Consider the following premises. forall y_2: T_3(y_2) or ~S(y_2). forall y_2: ~T_3(y_2). exists y_2: T_4(y_2) <-> S(y_2). Can we infer exists y_2: ~T_4(y_2) from them? If possible, name the inference rules being used at each step.
 From forall y_2: T_3(y_2) or ~S(y_2) we can infer forall y_2: S(y_2) -> T_3(y_2) via universal rewriting. From forall y_2: S(y_2) -> T_3(y_2), forall y_2: ~T_3(y_2) we can infer forall y_2: ~S(y_2) via universal modus tollens. Finally, from exists y_2: T_4(y_2) <-> S(y_2), forall y_2: ~S(y_2) we can infer exists y_2: ~T_4(y_2) via existential biconditional elimination. Therefore, the answer is yes.