Consider the following premises. exists y: T(y) and U_2(y). forall y: S_3(y). Can we infer forall y: ~(T(y) and S_3(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: T(y) and U_2(y) we can infer exists y: T(y) via existential simplification. Finally, from exists y: T(y), forall y: S_3(y) we can infer exists y: T(y) and S_3(y) via existential conjunction, which contradicts forall y: ~(T(y) and S_3(y)). Therefore, the answer is no.