  This paper reports the track multiplicity and kinematics of muons, charged
pions, and protons from charged-current inclusive $\bar{\nu}_{\mu}$ and
$\nu_{\mu}$ interactions on a water target, measured using a nuclear emulsion
detector in the NINJA experiment. A 3-kg water target was exposed to the T2K
antineutrino-enhanced beam with a mean energy of 1.3 GeV. Owing to the
high-granularity of the nuclear emulsion, protons with momenta down to 200
MeV/$c$ from the neutrino-water interactions were detected. We find good
agreement between the observed data and model predictions for all kinematic
distributions other than the number of charged pions. These results demonstrate
the capability of measurements with nuclear emulsion to improve neutrino
interaction models.
