Consider the following premises. forall y_2: S(y_2) -> W(y_2). forall y_2: R(y_2). forall y_2: U(y_2) or S(y_2). exists y_2: U(y_2) -> W(y_2). Can we infer forall y_2: ~(R(y_2) and W(y_2)) from them? If possible, name the inference rules being used at each step.
 From exists y_2: U(y_2) -> W(y_2), forall y_2: S(y_2) -> W(y_2), forall y_2: U(y_2) or S(y_2) we can infer exists y_2: W(y_2) via existential disjunction elimination. Finally, from forall y_2: R(y_2), exists y_2: W(y_2) we can infer exists y_2: R(y_2) and W(y_2) via existential conjunction, which contradicts forall y_2: ~(R(y_2) and W(y_2)). Therefore, the answer is no.