prove of the simple problem of Fig. 1

[foldl]

I have tried the simple problem of Fig. 1, and it can be proved.

Is there anything wrong?

test
a b c = eq2_triangle a b c ? eqangle b c b a c a c b

where eq2_triangle is defined as:

eq2_triangle a b c
c : a b
 =
a : ; b : ; c : cong a b a c
eq2_triangle

def sketch_eq2_triangle(args: tuple[gm.Point, ...]) -> tuple[Point, ...]:
  b = Point(0.0, 0.0)
  c = Point(np.random.uniform(0.5, 1.0), 0)
  a = Point((b.x + c.x) / 2, np.random.uniform(0.5, 10.0))
  return a, b, c

[Jerry-Master]

If you add the eq2_triangle definition to defs.txt without adding an extra breakline (\n) at the end you get this:

Traceback (most recent call last):
  File "/home/user/anaconda3/envs/alphageo/lib/python3.10/runpy.py", line 196, in _run_module_as_main
    return _run_code(code, main_globals, None,
  File "/home/user/anaconda3/envs/alphageo/lib/python3.10/runpy.py", line 86, in _run_code
    exec(code, run_globals)
  File "/mnt/array50tb/projects/alphageometry/alphageometry.py", line 645, in <module>
    app.run(main)
  File "/home/user/anaconda3/envs/alphageo/lib/python3.10/site-packages/absl/app.py", line 308, in run
    _run_main(main, args)
  File "/home/user/anaconda3/envs/alphageo/lib/python3.10/site-packages/absl/app.py", line 254, in _run_main
    sys.exit(main(argv))
  File "/mnt/array50tb/projects/alphageometry/alphageometry.py", line 603, in main
    DEFINITIONS = pr.Definition.from_txt_file(_DEFS_FILE.value, to_dict=True)
  File "/mnt/array50tb/projects/alphageometry/problem.py", line 304, in from_txt_file
    return cls.from_string(lines, to_dict)
  File "/mnt/array50tb/projects/alphageometry/problem.py", line 309, in from_string
    data = [cls.from_txt('\n'.join(group)) for group in reshape(lines, 6)]
  File "/mnt/array50tb/projects/alphageometry/problem.py", line 34, in reshape
    assert len(l) % n == 0
AssertionError

When solving that and adding the sketch_eq2_triangle function to numericals.py I get the following output which is valid:

==========================
 * From theorem premises:
A B C : Points
AB = AC [00]

 * Auxiliary Constructions:
: Points


 * Proof steps:
001. AB = AC [00] ⇒  ∠ABC = ∠BCA
==========================

[foldl]

My point is that, with the above codes, it can be proved successfully. But, in Fig 1, it is stated that it can't be proved without the auxiliary construction provided by LLM.

There must be something wrong, either my code, or Fig 1.