  We determined perturbatively the low-energy universal thermodynamics of
dilute one-dimensional bosons with the three-body repulsive forces. The final
results are presented for the limit of vanishing potential range in terms of
three-particle scattering length. An analogue of Tan`s energy theorem for
considered system is derived in generic case without assuming weakness of the
interparticle interaction. We also obtained an exact identity relating the
three-body contact to the energy density.
