Proton energy loss spectroscopy (PELS) has been used to investigate the very high overtone states of the v(3) mode in CF4. With a new scattering apparatus, which is described here in detail, it has been possible to directly measure the energy levels of the dominantly excited v(3) mode up to its 14th overtone with an energy resolution of delta E = 10 - 15 meV, corresponding to 80-120 cm(-1). The data are interpreted using the Hecht vibrational Hamiltonian which predicts the tenser splitting of the v(3) mode energy levels into sublevel bands. By adjusting the values of the anharmonicity parameters X(33), G(33), and T-33, previously determined by IR spectroscopy and introducing a second-order anharmonicity parameter X(333), it was possible to fit the v(3) mode energy levels to the measured energy loss distributions. A model based on the earlier theoretical work of Levene and Perry [H. B. Levene and D. Perry, J. Chem. Phys. 84, 4385 (1986)] for the proton-CF4 scattering process is extended to allow the simulation of complete spectra including contributions from combinations with the v(1) and v(4) mode for comparison with the experimental energy loss spectra. The influence of all relevant parameters on the simulated data is analyzed in detail.