Internal Consistency and Truth

It is possible for a system to be internally consistent and yet false. For instance a system might assert five truths, call them A, B, C, D and E.

Suppose that someone who holds this ABCDE system is asked to prove the A. Suppose then that person says, B proves A. Suppose the proof is asked for B. Suppose the person says C proves B. Suppose that this goes on like:

A is proved b B,
B is proved by C,
C is proved by D,
D is proved by E,
E is proved by A.

What is the problem With ABCDE?

ABCDE is a tautology. The argument is circular. But the argument is not proven since it remains circular. External facts are not required since the system is internally coherent. External facts may be introduced but in essence they reduce to restatements of A, B, C, D or E.