The collision of carbon nuclei with beryllium targets has been simulated in the framework of the Liège Intranuclear Cascade model at the carbon nuclei initial kinetic energies of 0.60, 0.95, 2.00 GeV / nucleon. Proton production invariant cross-sections at the nuclei collision angle of 3.5 degrees were obtained. It was shown that the dependence of experimental invariant cross-sections on the cumulative variable x in the range 0.9 < x < 2.4 could be interpret on the basis of taking into account the Fermi motion of nucleons in nuclei, multiple scattering processes, and the formation of delta resonance. The calculation results were compared with experimental data and findings of investigation where data was analyzed in the context of the quark cluster model.