  The equilibrium properties of the lattice fluid with the repulsion between
the nearest neighbors on the two-level planar triangular lattice are
investigated. The numerical results obtained from the analytical expressions
are compared with the Monte Carlo simulation data. It is shown that the
previously proposed diagrammatic approximation makes it possible to determine
the equilibrium characteristics of the lattice fluid with the repulsion between
the nearest neighbors on a two-level lattice with an accuracy comparable to the
accuracy of modelling the system using the Monte Carlo method in the entire
range of thermodynamic parameters. It was found that, in contrast to a similar
one-level system, a lattice fluid with the repulsion between the nearest
neighbors undergoes a first-order phase transition.
