The authors show that if \(X\) is a closed spin 4-manifold which has the same rational cohomology ring as \(K3\# K3\), then the stable-homotopy Seiberg-Witten invariant is non-trivial for every spin structure on \(X\). As an application, they obtain the following adjunction inequality: If \(\Sigma\) is an embedded oriented closed surface of genus \(g(\Sigma)\) in an oriented closed spin 4-manifold \(X\) which has the same rational cohomology ring as \(K3\# K3\), then \(\max\{2g(\Sigma)-2,0\}\geq [\Sigma][\Sigma]\).