  CPT symmetry, the combination of Charge Conjugation, Parity and Time
reversal, is a cornerstone of our model building strategy and therefore the
repercussions of its potential violation will severely threaten the most
extended tool we currently use to describe physics, i.e. local relativistic
quantum fields. However, limits on its conservation from the Kaon system look
indeed imposing. In this work we will show that neutrino oscillation
experiments can improve this limit by several orders of magnitude and therefore
are an ideal tool to explore the foundations of our approach to Nature.
  Strictly speaking testing CPT violation would require an explicit model for
how CPT is broken and its effects on physics. Instead, what is presented in
this paper is a test of one of the predictions of CPT conservation, i.e., the
same mass and mixing parameters in neutrinos and antineutrinos. In order to do
that we calculate the current CPT bound on all the neutrino mixing parameters
and study the sensitivity of the DUNE experiment to such an observable.
  After deriving the most updated bound on CPT from neutrino oscillation data,
we show that, if the recent T2K results turn out to be the true values of
neutrino and antineutrino oscillations, DUNE would measure the fallout of CPT
conservation at more than 3$\sigma$. Then, we study the sensitivity of the
experiment to measure CPT invariance in general, finding that DUNE will be able
to improve the current bounds on $\Delta(\Delta m^2_{31})$ by at least one
order of magnitude. We also study the sensitivity to the other oscillation
parameters. Finally we show that, if CPT is violated in nature, combining
neutrino with antineutrino data in oscillation analysis will produce imposter
solutions.
