Three-body and decays are studied using a data sample corresponding to an integrated luminosity of 3.0 collected by the LHCb experiment in proton-proton collisions at center-of-mass energies of and TeV. Evidence of CP violation in the decay is found in regions of the phase space, representing the first measurement of this kind for a final state containing baryons. Measurements of the forward-backward asymmetry of the light meson in the rest frame yield $A_{}(p \overline p K^+,~m_{p\overline p}<2.85\mathrm{,Ge\kern -0.1em V!/}c^2)=0.495\pm0.012~()\pm0.007~()A_{}(p\overline p \pi^+,~m_{p\overline p}<2.85\mathrm{,Ge\kern -0.1em V!/}c^2)=-0.409\pm0.033~()\pm0.006~()$. In addition, the branching fraction of the decay $B^+\to\kern 0.1em\overline{\kern -0.1em\Lambda}(1520)p(B^+ \to \kern 0.1em\overline{\kern -0.1em\Lambda}(1520)p)=(3.15\pm0.48~()\pm0.07~()\pm0.26~())\times 10^{-7}$, where BF denotes the uncertainty on secondary branching fractions.

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