  Emission of AGNs and neutral pion decay - are the two most natural
mechanisms, that could make a galaxy cluster be a source of gamma-rays in the
GeV regime. We revisited this problem by using 52.5-month FERMI-LAT data above
10 GeV and stacking 55 clusters from the HIFLUGS sample of the X-ray brightest
clusters. The choice of >10 GeV photons is optimal from the point of view of
angular resolution, while the sample selection optimizes the chances of
detecting signatures of the neutral pion decay, arising from hadronic
interactions of relativistic protons with an intra-cluster medium, which scale
with the X-ray flux. In the stacked data we detected a signal for the central
0.25 deg circle at the level of 4.3 sigma. An evidence for a spatial extent of
the signal is marginal. A subsample of cool-core clusters has higher count rate
1.9+/-0.3 per cluster compared to the subsample of non-cool core clusters
1.3+/-0.2. Several independent arguments suggest that the contribution of AGNs
to the observed signal is substantial if not dominant. No strong support for
the large contribution of pion decay was found. In terms of a limit on the
relativistic protons energy density, we got an upper limit of ~1.5% relative to
the gas thermal energy density, provided that the spectrum of relativistic
protons is hard (s=4.1 in dN/dp=p^-s). This estimate assumes that relativistic
and thermal components are mixed. For softer spectra the limits are weaker.
