  We have recently proposed a simple SU(5) theory with an adjoint fermionic
multiplet on top of the usual minimal spectrum. This leads to the hybrid
scenario of both type I and type III seesaw and it predicts the existence of
the fermionic SU(2) triplet between 100 GeV and 1 TeV for a conventional GUT
scale of about 10^{16} GeV, with main decays into W (Z) and leptons, correlated
through Dirac Yukawa couplings, and lifetimes shorter than about 10^{-12} sec.
These decays are lepton number violating and they offer an exciting signature
of Delta L=2 dilepton events together with 4 jets at future pp (p\bar p)
colliders. Increasing the triplet mass endangers the proton stability and so
the seesaw mechanism could be directly testable at LHC.
