Consider the following premises. exists y_4: ~U(y_4). forall y_4: U(y_4) or T(y_4). Can we infer exists y_4: T(y_4) or S_4(y_4) from them? If possible, name the inference rules being used at each step.
 From forall y_4: U(y_4) or T(y_4), exists y_4: ~U(y_4) we can infer exists y_4: T(y_4) via existential disjunctive syllogism. Finally, from exists y_4: T(y_4) we can infer exists y_4: T(y_4) or S_4(y_4) via existential addition. Therefore, the answer is yes.