Consider the following premises. forall y: S(y) or ~W_2(y). exists y: U(y). forall y: W_2(y). Can we infer forall y: ~(S(y) and U(y)) from them? If possible, name the inference rules being used at each step.
 From forall y: S(y) or ~W_2(y) we can infer forall y: W_2(y) -> S(y) via universal rewriting. From forall y: W_2(y) -> S(y), forall y: W_2(y) we can infer forall y: S(y) via universal modus ponens. Finally, from forall y: S(y), exists y: U(y) we can infer exists y: S(y) and U(y) via existential conjunction, which contradicts forall y: ~(S(y) and U(y)). Therefore, the answer is no.