Context. Detailed abundance studies have reported different trends between samples of stars with and without planets, possibly related to the planet formation process. Whether these differences are still present between samples of stars with and without debris disk is still unclear. Aims. We explore condensation temperature T c trends in the unique binary system ζ 1 Ret − ζ 2 Ret to determine whether there is a depletion of refractories that could be related to the planet formation process. The star ζ 2 Ret hosts a debris disk which was detected by an IR excess and confirmed by direct imaging and numerical simulations, while ζ 1 Ret does not present IR excess or planets. These characteristics convert ζ 2 Ret in a remarkable system where their binary nature together with the strong similarity of both components allow us, for the first time, to achieve the highest possible abundance precision in this system. Methods. We carried out a high-precision abundance determination in both components of the binary system via a line-by-line, strictly differential approach. First we used the Sun as a reference and then we used ζ 2 Ret. The stellar parameters T eff , log g, [Fe/H], and v turb were determined by imposing differential ionization and excitation equilibrium of Fe I and Fe II lines, with an updated version of the program FUNDPAR, together with plane-parallel local thermodynamic equilibrium ATLAS9 model atmospheres and the MOOG code. We then derived detailed abundances of 24 different species with equivalent widths and spectral synthesis with the MOOG program. The chemical patterns were compared with a recently calculated solar-twins T c trend, and then mutually between both stars of the binary system. The rocky mass of depleted refractory material was estimated according to recent data. Results. The star ζ 1 Ret is found to be slightly more metal rich than ζ 2 Ret by ∼0.02 dex. In the differential calculation of ζ 1 Ret using ζ 2 Ret as reference, the abundances of the refractory elements are higher than the volatile elements, and the trend of the refractory elements with T c shows a positive slope. These results together show a lack of refractory elements in ζ 2 Ret (a debris-disk host) relative to ζ 1 Ret. The T c trend would be in agreement with the proposed signature of planet formation rather than possible galactic chemical evolution or age effects, which are largely diminished here. Then, following the recent interpretation, we propose a scenario in which the refractory elements depleted in ζ 2 Ret are possibly locked up in the rocky material that orbits this star and produce the debris disk observed around this object. We estimated a lower limit of M rock ∼ 3 M ⊕ for the rocky mass of depleted material, which is compatible with rough estimations of 3−50 M ⊕ of a debris disk mass around a solar-type star.