Consider the following premises. exists y: W(y) and U(y). forall y: S_2(y). Can we infer forall y: ~W(y) from them? If possible, name the inference rules being used at each step.
 From exists y: W(y) and U(y) we can infer exists y: W(y) via existential simplification. From forall y: S_2(y), exists y: W(y) we can infer exists y: S_2(y) and W(y) via existential conjunction. Finally, from exists y: S_2(y) and W(y) we can infer exists y: S_2(y) via existential simplification, which contradicts forall y: ~W(y). Therefore, the answer is no.