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Massive ETGs are thought to form through a two-phase process. At early times,an intense and fast starburst forms blue and disk-dominated galaxies. Afterquenching, the remaining structures become red, compact and massive, i.e., 'rednuggets'. Then, a time-extended second phase which is dominated by mergers,causes structural evolution and size growth. Given the stochastic nature ofmergers, a small fraction of red nuggets survives, without any interaction,massive and compact until today: relic galaxies. Since this fraction depends onthe processes dominating the size growth, counting relics at low-z is avaluable way to disentangle between different galaxy evolution models. In thispaper, we introduce the INvestigating Stellar Population In RElics (INSPIRE)Project, that aims at spectroscopically confirming and fully characterizing alarge number of relics at 0.1<z<0.5. We focus here on the first results basedon a pilot program targeting three systems, representative of the whole sample.For these, we extract 1D optical spectra over an aperture comprising ~30 % ofthe galaxies light, and obtain line-of-sight integrated stellar velocity andvelocity dispersion. We also infer the stellar [$\alpha$/Fe] abundance fromline-index measurements and mass-weighted age and metallicity fromfull-spectral fitting with single stellar population models. Two galaxies havelarge integrated stellar velocity dispersion values, confirming their massivenature. They are populated by stars with super-solar metallicity and[$\alpha$/Fe]. Both objects have formed >80 % of their stellar mass within ashort (0.5 - 1.0 Gyrs) initial star formation episode occurred only ~1 Gyrafter the Big Bang. The third galaxy has a more extended star formation historyand a lower velocity dispersion. Thus we confirm two out of three candidates asrelics.

INSPIRE: INvestigating Stellar Population In RElics -- I. Survey presentation and pilot program