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