The simple type conjecture for mod 2 Seiberg–Witten invariants

We prove that, under a simple condition on the cohomology ring, every closed 4-manifold has mod 2 Seiberg–Witten type. This result shows that there exists large class of topological 4-manifolds such all smooth structures have type, and yet some non-vanishing (mod 2) invariants. As corollaries, we obtain adjunction inequalities show mild condition, geometrically simply connected vanishing invariant for at least one orientation.