Consider the following premises. forall z: ~W_1(z). forall z: W_1(z) or W_3(z). exists z: R(z). Can we infer forall z: ~(R(z) and W_3(z)) from them? If possible, name the inference rules being used at each step.
 From forall z: W_1(z) or W_3(z), forall z: ~W_1(z) we can infer forall z: W_3(z) via universal disjunctive syllogism. Finally, from exists z: R(z), forall z: W_3(z) we can infer exists z: R(z) and W_3(z) via existential conjunction, which contradicts forall z: ~(R(z) and W_3(z)). Therefore, the answer is no.