About Mass (4)

Here is our final conclusion:

The mass is treated consistently in the Newtonian system
In the Newtonian system, the constant mass and the rule of relative motion goes hand in hand with the first postulate.

The handling of mass is inconsistent under Special Relativity
As mass changes with reference frames, it cannot be cancelled from both sides of our equation. The fact that mass did not appear in the derivation of Special Relativity means it is wrong mathematically.

But we're talking about Special Relativity, why do we need the second law of motion?

Because the first postulate covers all physical laws. If the second law of motion does not work, then the first postulate is gone. Without the first postulate, where does Special Relativity come from?