  Within CPT-symmetric quantum mechanics the most elementary differential form
of the charge operator C is assumed. A closed-form integrability of the related
coupled differential self-consistency conditions and a natural embedding of the
Hamiltonians in a supersymmetric scheme is achieved. For a particular choice of
the interactions the rigorous mathematical consistency of the construction is
scrutinized suggesting that quantum systems with non-self-adjoint Hamiltonians
may admit probabilistic interpretation even in presence of a manifest breakdown
of both T symmetry (i.e., Hermiticity) and PT symmetry.
