  The grand partition functions of ABJ theory can be factorized into even and
odd parts under the reflection of fermion coordinate in the Fermi gas approach.
In some cases, the even/odd part of ABJ grand partition function is equal to
that of $\mathcal{N}=5$ $O(n)\times USp(n')$ theory, hence it is natural to
think of the even/odd projection of grand partition function as an
orientifolding of ABJ Fermi gas system. By a systematic WKB analysis, we
determine the coefficients in the perturbative part of grand potential of such
orientifold ABJ theory. We also find the exact form of the first few
"half-instanton" corrections coming from the twisted sector of the reflection
of fermion coordinate. For the Chern-Simons level $k=2,4,8$ we find closed form
expressions of the grand partition functions of orientifold ABJ theory, and for
$k=2,4$ we prove the functional relations among the grand partition functions
conjectured in arXiv:1410.7658.
