  On the basis of the L\"uscher's finite volume formula, a simple test
(consistency check or sanity check) is introduced and applied to inspect the
recent claims of the existence of the nucleon-nucleon ($NN$) bound state(s) for
heavy quark masses in lattice QCD. We show that the consistency between the
scattering phase shifts at $k^2 > 0$ and/or $k^2 < 0$ obtained from the lattice
data and the behavior of phase shifts from the effective range expansion (ERE)
around $k^2=0$ exposes the validity of the original lattice data, otherwise
such information is hidden in the energy shift $\Delta E$ of the two nucleons
on the lattice. We carry out this sanity check for all the lattice results in
the literature claiming the existence of the $NN$ bound state(s) for heavy
quark masses, and find that (i) some of the $NN$ data show clear inconsistency
between the behavior of ERE at $k^2 > 0$ and that at $k^2 < 0$, (ii) some of
the $NN$ data exhibit singular behavior of the low energy parameter (such as
the divergent effective range) at $k^2<0$, (iii) some of the $NN$ data have the
unphysical residue for the bound state pole in S-matrix, and (iv) the rest of
the $NN$ data are inconsistent among themselves. Furthermore, we raise a
caution of using the ERE in the case of the multiple bound states. Our finding,
together with the fake plateau problem previously pointed out by the present
authors, brings a serious doubt on the existence of the $NN$ bound states for
pion masses heavier than 300 MeV in the previous studies.

High Energy Physics - Lattice;High Energy Physics - Phenomenology;Nuclear Theory