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Thanks for going with the intended meaning.
My thinking is that for any system A, in any inertial reference
frame, there is a system B having a three-momentum that is the
negative of that of system A. So, for system C, consisting of both A
and B, in that inertial reference frame, the total energy of system C
is the mass of system C and it is the internal energy of system A +
the internal energy of system B + the kinetic energy associated with
the motion of the center of mass of system A + the kinetic energy
associated with the motion of the center of mass of system B + the
potential energy associated with any interactions that might be
taking place between systems A and B. In other words all the energy
of system A contributes to the mass of system C,
hence, all the energy of system A is mass.