We have performed several simulations on non-rotational core-collapses of a star with 4OM⊙ by a general relativistic ν-radiation-hydrodynamics code and computed quantitatively the dynamics up to the black hole formation as well as the neutrino luminosities and spectra. Employing different hadronic equations of state (EOS), we have demonstrated that the duration of neutrino emissions from this event is sensitive to the stiffness of EOS at supra-nuclear densities and, therefore, that the observation of neutrinos from such an event will provide us with valuable information on the properties of dense and hot hadronic matter as well as on the maximum mass of proto-neutron stars. However, this approach can not distinguish EOS's with a similar stiffness: a soft nucleonic EOS and a hyperonic EOS, for example. In this study, we attempt to break this degeneracy by analyzing more in detail the time variation of neutrino numbers observed at a terrestrial detector. Performing the Kolmogolov- Smirnovtest, which is free from the ambiguity of the distance to the progenitor, we show that the break-up of the degeneracy of hadronic EOS's is indeed feasible for Galactic events.