  The expected opacity of the intergalactic space limits the mean free path of
TeV gamma rays to dozens of Megaparsecs. However, TeV photons from numerous
more distant sources have been detected. This might be interpreted, in each
particular case, in terms of hardening of the emitted spectrum caused by
presently unknown mechanisms at work in the sources. Here we show that this
interpretation is not supported by the analysis of the ensemble of all observed
sources. In the frameworks of an infrared-background model with the lowest
opacity, we reconstruct the emitted spectra of distant blazars and find that
upward spectral breaks appear precisely at those energies where absorption
effects are essential. Since these energies are very different for similar
sources located at various distances, we conclude that the breaks are artefacts
of the incorrect account of absorption and, therefore, the opacity of the
Universe for gamma rays is overestimated even in the most conservative model.
This implies that some novel physical or astrophysical phenomena should affect
long-distance propagation of gamma rays. A scenario in which a part of
energetic photons is converted to an inert new particle in the vicinity of the
source and reconverts back close to the observer does not contradict to our
results. [abridged]
