The SS-HORSE-NCSM method is generalized to the case of democratic decay into an odd number of fragments. This method is applied to the search for resonances in three-neutron system (trineutron) using ab initio no-core shell model calculations with realistic nucleon-nucleon (NN) potentials. The 3/2- and 1/2- strongly overlapping resonances are predicted when softened NN interactions are used and are preferred over the case where bare NN interactions of the chiral effective field theory are used with no resonance obtained.