The total cross section of the reaction $ppto ppK^+K^-$ has been determined for proton--proton reactions with $p_{beam}=3.67 GeV/c$. This represents the first cross section measurement of the $pp to ppK^-K^+$ channel near threshold, and is equivalent to the inclusive $ppto ppK^-X$ cross section at this beam momentum. The cross section determined at this beam momentum is about a factor 20 lower than that for inclusive $ppto ppK^+X$ meson production at the same CM energy above the corresponding threshold. This large difference in the $K^+$ and $K^-$ meson inclusive production cross sections in proton-proton reactions is in strong contrast to cross sections measured in sub-threshold heavy ion collisions, which are similar in magnitude at the same energy per nucleon below the respective thresholds.
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