Vanishing conjecture for reverse-oriented complex-hyperbolic 4-manifolds

Let $M^{4}=\overline{{\mathbb C}{\mathcal H}_{2}/\Gamma}$ be a reverse-oriented compact complex-hyperbolic $4$-manifold. Reverse-oriented complex-hyperbolic vanishing conjecture. All the Seiberg–Witten invariants of $M$ vanish for the fixed orientation; in particular, there is no symplectic structure on $M$ compatible with the non-complex orientation. Complex-hyperbolic $4$-manifolds are Kähler, and hence symplectic, in their standard complex orientation; the conjecture concerns the opposite orientation and is presented as open.