Electrical resistivity $rho(T)$ and specific heat $C(T)$ measurements have been made on the diluted 4$f^2$ system Y(Pr)Ir$_2$Zn$_{20}$. Both data of $rho$ and magnetic specific heat $C_{rm m}$ per Pr ion are well scaled as a function of $T/T_{rm 0}$, where $T_{rm 0}$ is a characteristic temperature of non-Fermi liquid (NFL) behaviors. Furthermore, the temperature dependences of $rho$ and $C_{mathrm{m}}/T$ agree with the NFL behaviors predicted by the two-channel Kondo model for the strong coupling limit. Therefore, we infer that the observed NFL behaviors result from the single-site quadrupole Kondo effect due to the hybridization of the 4$f^2$ states with multi-channel conduction electrons.
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