The inclusive production of {Lambda} hyperons in proton-proton collisions at $sqrt{s}$ = 3.18 GeV was measured with HADES at the GSI Helmholtzzentrum fur Schwerionenforschung in Darmstadt. The experimental data are compared to a data-based model for individual exclusive {Lambda} production channels in the same reaction. The contributions of intermediate resonances such as {Sigma}(1385), {Delta}++ or N* are considered in detail. In particular, the result of a partial wave analysis is accounted for the abundant pK$^+${Lambda} final state. Model and data show a reasonable agreement at mid rapidities, while a difference is found for larger rapidities. A total {Lambda} production cross section in p+p collisions at $sqrt{s}$ = 3.18 GeV of {sigma}(pp $to$ {Lambda} + X) = 207.3 $pm$ 1.3 +6.0 -7.3 (stat.) $pm$ 8.4 (syst.) +0.4 -0.5 (model) {mu}b is found.
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