  A recent successful observation of a dense and deeply bound \bar{K} nuclear
system, K^-pp, in the p + p \rightarrow K^+ + K^-pp reaction in a DISTO
experiment indicates that the double-\bar{K} dibaryon, K^-K^-pp, which was
predicted to be a dense nuclear system, can also be formed in p+p collisions.
We find theoretically that the K^- -K^- repulsion plays no significant role in
reducing the density and binding energy of K^-K^-pp and that, when two
\Lambda(1405) resonances are produced simultaneously in a short-range p+p
collision, they act as doorways to copious formation of K^-K^-pp, if and only
if K^-K^-pp is a dense object, as predicted.
