We have analyzed data of the DISTO experiment on the exclusive $pp\ensuremath{\rightarrow}p\ensuremath{\Lambda}{K}^{+}$ reaction at 2.85 GeV to search for a strongly bound compact ${K}^{\ensuremath{-}}pp(\ensuremath{\equiv}X)$ state to be formed in the $pp\ensuremath{\rightarrow}{K}^{+}+X$ reaction. The observed spectra of the ${K}^{+}$ missing mass and the $p\ensuremath{\Lambda}$ invariant-mass with high transverse momenta of $p$ and ${K}^{+}$ revealed a broad distinct peak of $26\mathrm{\text{\ensuremath{-}}}\ensuremath{\sigma}$ confidence with a mass ${M}_{X}=2267\ifmmode\pm\else\textpm\fi{}3(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}5(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}/{c}^{2}$ and a width ${\ensuremath{\Gamma}}_{X}=118\ifmmode\pm\else\textpm\fi{}8(\mathrm{stat})\ifmmode\pm\else\textpm\fi{}10(\mathrm{syst})\text{ }\text{ }\mathrm{MeV}$. The enormously large cross section indicates formation of a compact ${K}^{\ensuremath{-}}pp$ with a large binding energy of ${B}_{K}=103\text{ }\text{ }\mathrm{MeV}$, which can be a possible gateway toward cold and dense kaonic nuclear matter.