Consider the following premises. forall z: T(z) or T_3(z). forall z: Q_1(z). exists z: T(z) -> S(z). forall z: T_3(z) -> S(z). Can we infer forall z: ~(Q_1(z) and S(z)) from them? If possible, name the inference rules being used at each step.
 From exists z: T(z) -> S(z), forall z: T_3(z) -> S(z), forall z: T(z) or T_3(z) we can infer exists z: S(z) via existential disjunction elimination. Finally, from forall z: Q_1(z), exists z: S(z) we can infer exists z: Q_1(z) and S(z) via existential conjunction, which contradicts forall z: ~(Q_1(z) and S(z)). Therefore, the answer is no.