Consider the following premises. forall y: P_2(y) -> U(y). forall y: S(y). exists y: P_2(y). Can we infer forall y: ~(U(y) and S(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: P_2(y) -> U(y), exists y: P_2(y) we can infer exists y: U(y) via existential modus ponens. Finally, from exists y: U(y), forall y: S(y) we can infer exists y: U(y) and S(y) via existential conjunction, which contradicts forall y: ~(U(y) and S(y)). Therefore, the answer is no.