  The Leggett-Garg inequality (LGI), derived under the assumption of realism,
acts as the temporal Bell's inequality. It is studied in electromagnetic and
strong interaction like photonics, superconducting qu-bits and nuclear spin.
Until the weak interaction two-state oscillations of neutrinos affirmed the
violation of Leggett-Garg-type inequalities (LGtI). We make an empirical test
for the deviation of experimental results with the classical limits by
analyzing the survival probability data of reactor neutrinos at a distinct
range of baseline dividing energies, as an analog to a single neutrino detected
at different time. A study of the updated data of Daya-Bay experiment
unambiguously depicts an obvious cluster of data over the classical bound of
LGtI and shows a $6.1\sigma$ significance of the violation of them.
