We prove that the homotopy spheres \(\Sigma_{n} = -W\smile_{f^{n}}W\), formed by doubling the infinite order loose-cork \((W,f)\), by the iterates of the cork automorphism \(f: \partial W \to \partial W\), is \(S^4\). To do this we first show that \(\Sigma_{n} \) are obtained by Gluck twistings of \(S^4\). Then, from this we show how to cancel \(3\)-handles of \(\Sigma_{n}\) and identify it by \(S^{4}\).