  The inclusive production of four isolated charged leptons in $pp$ collisions
is analysed for the presence of hard double-parton scattering, using 20.2
fb$^{-1}$ of data recorded in the ATLAS detector at the LHC at centre-of-mass
energy $\sqrt{s}$ = 8 TeV. In the four-lepton invariant-mass range of
$80<m_{4\ell}<1000$ GeV, an artificial neural network is used to enhance the
separation between single- and double-parton scattering based on the kinematics
of the four leptons in the final state. An upper limit on the fraction of
events originating from double-parton scattering is determined at 95%
confidence level to be $f_{\mathrm{DPS}} = 0.042$, which results in an
estimated lower limit on the effective cross section at 95% confidence level of
$1.0$ mb.
