  It is a natural consequence of fundamental properties of the Casson invariant
that the Rokhlin invariant of an amphichiral integral homology 3-sphere M
vanishes. In this paper, we give a new direct proof of this vanishing property.
For such an M, we construct a manifold pair (Y,Q) of dimensions 6 and 3
equipped with some additional structure (6-dimensional spin e-manifold), such
that Q = M \cup M \cup (-M) and (Y,Q) \cong (-Y,-Q). We prove that (Y,Q) bounds
a 7-dimensional spin e-manifold (Z,X) by studying the cobordism group of
6-dimensional spin e-manifolds and the Z/2-actions on the two--point
configuration space of M minus one point. For any such (Z,X), the signature of
X vanishes, and this implies the vanishing of the Rokhlin invariant. The idea
of the construction of (Y,Q) comes from the definition of the
Kontsevich-Kuperberg-Thurston invariant for rational homology 3-spheres.
