  CPT theorem has been known to imply the equality of mass and lifetime between
particle and antiparticle even if C(charge conjugation) symmetry is violated.
However, its mathematical verification is insufficient and limited as it
considers only one type of C violation. Here C, not CPT, symmetry will be shown
to imply the equality of mass and coupling constants and the lifetime could be
the same regardless of C and CPT violation. And we conclude that the equality
of mass and lifetime is prerequisite for the CPT theorem to be valid and it is
not implied by CPT symmetry.
