This paper presents the first two steps of a benchmark on in-vessel corium thermochemistry, which is part of the IAEA Coordinated Research Project on In-Vessel Melt Retention. The benchmark focuses on the stratification of corium in the lower plenum of a reactor vessel during a severe accident. The experimental data from the MASCA test facilities are used to validate/calibrate the models of the different codes used by the participants. The paper gives an overview of the different models, including their underlying assumptions. The results show that the models are generally in good agreement with the experimental data, but further experimental data is needed for model validation. Besides the need for further work, this paper highlights the fact that integral models (published in the open literature for most of them) are available to account for the first-order phenomena associated with in-vessel corium. Accordingly, this paper may be useful for code developers that would like to upgrade their models in order to take into account transient stratification kinetics, a prerequisite for a state-of-the-art analysis of in-vessel melt retention.