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A search for $CP$ violation in charmless four-body decays of $\Lambda_b$ and$\Xi_b^0$ baryons with a proton and three charged mesons in the final state isperformed. To cancel out production and detection charge-asymmetry effects, thesearch is carried out by measuring the difference between the $CP$ asymmetriesin a charmless decay and in a decay with an intermediate charmed baryon withthe same particles in the final state. The data sample used was recorded in2011 and 2012 with the LHCb detector and corresponds to an integratedluminosity of $3 {\rm fb}^{-1}$. A total of 18 $CP$ asymmetries are considered,either accounting for the full phase space of the decays or exploring specificregions of the decay kinematics. No significant $CP$-violation effect isobserved in any of the measurements.

Measurements of $CP$ asymmetries in charmless four-body $\Lambda_b$ and $\Xi_b^0$ decays