Consider the following premises. forall y: T_3(y) -> S(y). exists y: T_3(y) or ~U(y). Can we infer exists y: U(y) -> S(y) from them? If possible, name the inference rules being used at each step.
 From exists y: T_3(y) or ~U(y) we can infer exists y: U(y) -> T_3(y) via existential rewriting. Finally, from exists y: U(y) -> T_3(y), forall y: T_3(y) -> S(y) we can infer exists y: U(y) -> S(y) via existential transitivity. Therefore, the answer is yes.