Consider the following premises. exists z: T(z) <-> P(z). forall z: W_3(z) or Q(z). forall z: ~W_3(z) or P(z). forall z: T(z) -> W(z). forall z: W(z) <-> Q(z). Can we infer forall z: ~W(z) from them? If possible, name the inference rules being used at each step.
 From forall z: W_3(z) or Q(z), forall z: ~W_3(z) or P(z) we can infer forall z: Q(z) or P(z) via universal resolution. From exists z: T(z) <-> P(z) we can infer exists z: P(z) -> T(z) via existential biconditional elimination. From forall z: W(z) <-> Q(z) we can infer forall z: Q(z) -> W(z) via universal biconditional elimination. From exists z: P(z) -> T(z), forall z: T(z) -> W(z) we can infer exists z: P(z) -> W(z) via existential transitivity. Finally, from forall z: Q(z) -> W(z), exists z: P(z) -> W(z), forall z: Q(z) or P(z) we can infer exists z: W(z) via existential disjunction elimination, which contradicts forall z: ~W(z). Therefore, the answer is no.