The recently proposed, single-reference, coupled-cluster (CC) methods with singly, doubly, and triply excited clusters, in which triexcited clusters T-3 are restricted to internal and semi-internal components defined through active orbitals, designated as the CCSD{t(')} and CCSDt approaches [P. Piecuch, S. A. Kucharski, and R. J. Bartlett, J. Chem. Phys. 110, 6103 (1999)] have been used to obtain the potential energy function and the vibrational spectrum of the HF molecule, as described by the large, aug-cc-pvtz, basis set. A comparison has been made with the vibrational term values obtained at the very high, full CCSDT (CC singles, doubles, and triples), level and with the experimental (RKR) data. In spite of using the restricted Hartree-Fock reference, the calculated CCSD{t'} and CCSDt vibrational term values have been found to be in much better agreement with the full CCSDT and RKR data than the results of conventional CCSD (CC singles and doubles) calculations, which produce errors of an order of 2000 cm(-1) for high-lying states near dissociation. It has been demonstrated that the CCSDt approach is capable of providing the vibrational spectrum of the full CCSDT quality.