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