  We derive and apply a general scheme for mapping a setup consisting of a
half-filled single level quantum dot coupled to one normal metallic and two
superconducting phase-biased leads onto an ordinary half-filled single impurity
Anderson model with single modified tunneling density of states. The theory
allows for the otherwise unfeasible application of the standard numerical
renormalization group and enables to obtain phase-dependent local spectral
properties as well as phase-dependent induced pairing and Josephson current.
The resulting transport properties match well with the numerically exact
continuous-time hybridization-expansion quantum Monte Carlo. For weakly coupled
normal electrode, the spectral properties can be interpreted in terms of
normal-electrode-broadened Andreev bound states with phase-dependent position
analogous to the superconducting Anderson model, which coexist in the
$\pi$-like phase with a Kondo peak whose phase-dependent Kondo temperature
follows the form conjectured previously in Doma\'nski et al., Phys.~Rev.~B {\bf
95}, 045104 (2017)
