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Tests of the T, CP and CPT symmetries in the neutral kaon system are performed by the direct comparison of the probabilities of a kaon transition process to its symmetry-conjugate. The exchange of in and out states required for a genuine test involving an anti-unitary transformation implied by time-reversal is implemented exploiting the entanglement of $K^0\bar{K}{}^0$ pairs produced at a $ϕ$-factory. A data sample collected by the KLOE experiment at DA$Φ$NE corresponding to an integrated luminosity of about 1.7 fb$^{-1}$ is analysed to study the $Δ$t distributions of the $ϕ\to K_{S}K_{L}\to π^+π^- \: π^{\pm}e^{\mp}ν$ and $ϕ\to K_{S}K_{L}\to π^{\pm}e^{\mp}ν\: 3π^0$ processes, with $Δ$t the difference of the kaon decay times. A comparison of the measured $Δ$t distributions in the asymptotic region $Δt \gg τ_{S}$ allows to test for the first time T and CPT symmetries in kaon transitions with a precision of few percent, and to observe CP violation with this novel method.