  We use atmospheric neutrino phenomenology to obtain the expected background
to proton decay in large underground neutrino detectors, like DUNE. We
introduced, for the first time in this kind of analysis, the experimentally
confirmed neutrino oscillations of the atmospheric neutrino observations which
reduce by a factor of 40\% the corresponding background for nucleon decay
channel $p\rightarrow \mu^{+}+\pi^{0}$. Furthermore, we infer the impact of
four systematics on such background: the overall efficiency, the muon
reconstruction energy resolution, the resonant neutral pion cross-section and
the neutral pion angular resolution. Considering a 40 kton detector with
efficiency 45\%, our analysis leads to an error band in the lower limit for the
proton lifetime, from $7.9 \times 10^{33}$~years to {\bf $1.1 \times
10^{34}$}~years at $90\%$~C.L.. These numbers can be compared with the current
mode dependent experimental limits $\tau > 10^{31}-10^{33}$~years at
$90\%$~C.L.. Finally we investigate how this limit can be further improved with
the enhancement of the efficiency of the experiment which can be obtained, for
instance, with the implementation of the ARAPUCA device in DUNE.
