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

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Production of light-flavor hadrons in pp collisions at  $$\sqrt{s}~=~7\text { and }\sqrt{s} = 13 \, \text { TeV} $$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mspace width="3.33333pt"></mspace> <mo>=</mo> <mspace width="3.33333pt"></mspace> <mn>7</mn> <mspace width="0.333333em"></mspace> <mtext>and</mtext> <mspace width="0.333333em"></mspace> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>13</mn> <mspace width="0.166667em"></mspace> <mspace width="0.333333em"></mspace> <mtext>TeV</mtext> </mrow> </math>