  A MINOS result seemed to hint a different anti-neutrino mass splitting and
mixing angle with respect to the neutrino ones, offering a hint for a CPT
violation in lepton sector. However more recent MINOS data reduced the
neutrino-antineutrino differences leading to a narrow discrepancy almost
compatible with no CPT violation, hard to be disentangled. Moreover last a few
years of OPERA activity on tau appearance is still un-probed (one unique
event). Both flavor muon-tau mixing, tau appearance and eventual CPT violation
disentanglement need more tools to be enhanced. Atmospheric muon neutrino
spectra and anisotropy in Deep Core at ten-tens GeV (yet unpublished) may test
the muon-tau conversion but they can hardly reveal such last tiny MINOS CPT
asymmetry. We show how the longest baseline neutrino oscillation available,
crossing most of the Earth diameter, within an OPERA-like experiment from CERN
(or FERMILAB) to ICECUBE-Deep Core neutrino detector at 21 GeV energy, may at
best disentangle even last tiny CPT violation (within 6 sigma a year) while
testing at highest rate tau-antitau appearance. We propose the muon neutrino
disappearance or (for any CPT violation) the partial anti-muon appearance at
the longest distances. Such a tuned detection experiment may lead to a clear
and strong signature of tau or anti-tau generation (even within its neutral
current noise background events): nearly one antitau or two tau a day. The tau
appearance signal is above (or within) 10 sigma a year, even for 1% OPERA-like
experiment. Peculiar configurations for theta_13 angle test and hierarchy
neutrino mass test may also be addressed by a Deep Core-PINGU array detector
observing electron neutrino shower at 6 GeV neutrino energy windows.
