Abstract: We calculate the cooling curves of superfluid neutron stars with the Brueckner-Hartree-Fock (BHF) equation of state (EOS) by employing the AV18 two body force with a microscopic three body force. The gap energy is calculated within the BCS theory, including in the pairing interaction not only two body force but also three body force. The calculated cooling curves show that the nucleon superfluidity strongly reduces the difference between standard and enhanced cooling. This enables one to explain the majority of observational data by the enhanced cooling of the stars with superfluid cores. The possibility of strong direct Urca processes still cannot be excluded from the cooling analysis.