  A proposal for an experiment to measure the cross section of antiproton
production in a proton-nuclear collision in a kinematically forbidden region
for nucleon-nucleon interaction on a fixed LHC target is considered. It is
shown that this process can be separated from the kinematically allowed
production process using the existing detectors of the ALICE facility at a
proton energy of 7 TeV with a fixed nuclear target. Assuming the scale
dependence of the cross section, the data obtained can be used to estimate the
subthreshold cross section for the production of superheavy particles with a
mass of several tens of TeV in the LHC lead nucleus beam.
