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Abstract The production of $$\pi ^{\pm }$$ π ± , $$\mathrm{K}^{\pm }$$ K ± , $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\mathrm{K}^{*}(892)^{0}$$ K ∗ ( 892 ) 0 , $$\mathrm{p}$$ p , $$\phi (1020)$$ ϕ ( 1020 ) , $$\Lambda $$ Λ , $$\Xi ^{-}$$ Ξ - , $$\Omega ^{-}$$ Ω - , and their antiparticles was measured in inelastic proton–proton (pp) collisions at a center-of-mass energy of $$\sqrt{s}$$ s = 13 TeV at midrapidity ( $$|y|<0.5$$ | y | < 0.5 ) as a function of transverse momentum ( $$p_{\mathrm{T}}$$ p T ) using the ALICE detector at the CERN LHC. Furthermore, the single-particle $$p_{\mathrm{T}}$$ p T distributions of $$\mathrm{K}^{0}_{S}$$ K S 0 , $$\Lambda $$ Λ , and $$\overline{\Lambda }$$ Λ ¯ in inelastic pp collisions at $$\sqrt{s} = 7$$ s = 7  TeV are reported here for the first time. The $$p_{\mathrm{T}}$$ p T distributions are studied at midrapidity within the transverse momentum range $$0\le p_{\mathrm{T}}\le 20$$ 0 ≤ p T ≤ 20 GeV/ c , depending on the particle species. The $$p_{\mathrm{T}}$$ p T spectra, integrated yields, and particle yield ratios are discussed as a function of collision energy and compared with measurements at lower $$\sqrt{s}$$ s and with results from various general-purpose QCD-inspired Monte Carlo models. A hardening of the spectra at high $$p_{\mathrm{T}}$$ p T with increasing collision energy is observed, which is similar for all particle species under study. The transverse mass and $$x_{\mathrm{T}}\equiv 2p_{\mathrm{T}}/\sqrt{s}$$ x T ≡ 2 p T / s scaling properties of hadron production are also studied. As the collision energy increases from $$\sqrt{s}$$ s = 7–13 TeV, the yields of non- and single-strange hadrons normalized to the pion yields remain approximately constant as a function of $$\sqrt{s}$$ s , while ratios for multi-strange hadrons indicate enhancements. The $$p_\mathrm{{T}}$$ p T -differential cross sections of $$\pi ^{\pm }$$ π ± , $$\mathrm {K}^{\pm }$$ K ± and $$\mathrm {p}$$ p ( $$\overline{\mathrm{p}}$$ p ¯ ) are compared with next-to-leading order perturbative QCD calculations, which are found to overestimate the cross sections for $$\pi ^{\pm }$$ π ± and $$\mathrm{p}$$ p ( $$\overline{\mathrm{p}}$$ p ¯ ) at high $$p_\mathrm{{T}}$$ p T .