Consider the following premises. forall y_4: U(y_4). exists y_4: ~Q_4(y_4). forall y_4: T(y_4). forall y_4: Q_4(y_4) or S(y_4). Can we infer forall y_4: ~(S(y_4) and T(y_4)) from them? If possible, name the inference rules being used at each step.
 From forall y_4: Q_4(y_4) or S(y_4), exists y_4: ~Q_4(y_4) we can infer exists y_4: S(y_4) via existential disjunctive syllogism. From exists y_4: S(y_4), forall y_4: U(y_4) we can infer exists y_4: S(y_4) and U(y_4) via existential conjunction. From exists y_4: S(y_4) and U(y_4) we can infer exists y_4: S(y_4) via existential simplification. Finally, from exists y_4: S(y_4), forall y_4: T(y_4) we can infer exists y_4: S(y_4) and T(y_4) via existential conjunction, which contradicts forall y_4: ~(S(y_4) and T(y_4)). Therefore, the answer is no.