Consider the following premises. exists y: R(y). forall y: Q(y). forall y: T(y). Can we infer forall y: ~(Q(y) and R(y)) from them? If possible, name the inference rules being used at each step.
 From exists y: R(y), forall y: T(y) we can infer exists y: R(y) and T(y) via existential conjunction. From exists y: R(y) and T(y) we can infer exists y: R(y) via existential simplification. Finally, from forall y: Q(y), exists y: R(y) we can infer exists y: Q(y) and R(y) via existential conjunction, which contradicts forall y: ~(Q(y) and R(y)). Therefore, the answer is no.