Consider the following premises. forall y: ~S_3(y). forall y: T(y) <-> S_3(y). Can we infer exists y: T(y) from them? If possible, name the inference rules being used at each step.
 From forall y: T(y) <-> S_3(y) we can infer forall y: T(y) -> S_3(y) via universal biconditional elimination. Finally, from forall y: T(y) -> S_3(y), forall y: ~S_3(y) we can infer forall y: ~T(y) via universal modus tollens, which contradicts exists y: T(y). Therefore, the answer is no.