  Superstrong cardinals are never Laver indestructible. Similarly, almost huge
cardinals, huge cardinals, superhuge cardinals, rank-into-rank cardinals,
extendible cardinals, 1-extendible cardinals, 0-extendible cardinals, weakly
superstrong cardinals, uplifting cardinals, pseudo-uplifting cardinals,
superstrongly unfoldable cardinals, \Sigma_n-reflecting cardinals,
\Sigma_n-correct cardinals and \Sigma_n-extendible cardinals (all for n>2) are
never Laver indestructible. In fact, all these large cardinal properties are
superdestructible: if \kappa\ exhibits any of them, with corresponding target
\theta, then in any forcing extension arising from nontrivial strategically
<\kappa-closed forcing Q in V_\theta, the cardinal \kappa\ will exhibit none of
the large cardinal properties with target \theta\ or larger.
