  We consider an electron model of superconductivity on a three-dimensional
lattice where there are on-site attractive Hubbard interaction and long-range
repulsive Coulomb interaction. It is claimed that fully gapped $s$-wave
superconductivity within this model, if present, exhibits spontaneous
translation symmetry breaking possibly related to a charge order. Our
discussions are based on an application of the Lieb-Schultz-Mattis theorem
under some physical assumptions. The inconsistency between the proposed
supersolid and experiments can impose some constraints on a reasonable choice
of a theoretical model.
