  We utilize existing inclusive data on K^+ meson momentum spectra of the
reaction pp -> K^+X at T_p = 2.3 - 2.85 GeV to deduce total cross sections for
pp -> K^+\Sigma^+n. The method used to extract those cross sections is
explained and discussed in detail. Our result for T_p = 2.85 GeV is consistent
with the data point from a direct measurement at the same beam energy. The
cross section obtained for T_p = 2.3 GeV is with 13.7\pm2.3 \mu b considerably
smaller than the value found in a recent experiment by the COSY-11
Collaboration at a somewhat lower beam energy, indicating that the pp ->
K^+\Sigma^+n reaction cross section could exhibit a rather unusual energy
dependence.
