In this paper we define a new clausal class, called $ \mathcal{B}\mathcal{U} $ \mathcal{B}\mathcal{U} , which can be decided by hyperresolution with splitting. We also consider the model generation problem for $ \mathcal{B}\mathcal{U} $ \mathcal{B}\mathcal{U} and show that hyperresolution plus splitting can also be used as a Herbrand model generation procedure for $ \mathcal{B}\mathcal{U} $ \mathcal{B}\mathcal{U} and, furthermore, that the addition of a local minimality test allows us to generate only minimal Herbrand models for clause sets in $ \mathcal{B}\mathcal{U} $ \mathcal{B}\mathcal{U} . In addition, we investigate the relationship of $ \mathcal{B}\mathcal{U} $ \mathcal{B}\mathcal{U} to other solvable classes.