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