  Measurements of $K_S^0$ meson production via its $\pi^{+} \pi^{-}$ decay mode
in inelastic $\textit{p+p}$ interactions at incident projectile momenta of 31,
40 and 80 GeV/$c$ ($\sqrt{s_{NN}}=7.7, 8.8$ and $12.3$ GeV, respectively) are
presented. The data were recorded by the NA61/SHINE spectrometer at the CERN
Super Proton Synchrotron. Double-differential distributions were obtained in
transverse momentum and rapidity. The mean multiplicities of $K_S^0$ mesons
were determined to be $(5.95 \pm 0.19 (stat) \pm 0.22 (sys)) \times 10^{-2}$ at
31 GeV/$c$, $(7.61 \pm 0.13 (stat) \pm 0.31 (sys)) \times 10^{-2}$ at 40
GeV/$c$ and $(11.58 \pm 0.12 (stat) \pm 0.37 (sys)) \times 10^{-2}$ at 80
GeV/$c$. The results on $K^{0}_{S}$ production are compared with model
calculations (Epos1.99, SMASH 2.0 and PHSD) as well as with published data from
other experiments.
