Problem when using CGAL Clip tool

[Giseribility]

When using the PMP Clip tools of CGAL to clip polyhedron with face (.obj format), the program runs successfully, but the clip result is not topologically correct, there is a single line in the result polyhedron. I wonder what causes the incorrect result, and how to avoid it?

the polyhedron and the face:

the clip result, 3 facets were deleted to show the single line:

the three model data (.obj format) is as follows:
https://gist.github.com/Giseribility/2d0d3a04ac73db77c74a410473eef03c

[sloriot]

I don't understand why you are saying that the output is not correct. face splits the volume defined by polyhedron in 2 sub-volumes. Only the volume on the negative side of face is kept.

[Giseribility]

but the volume on the negative side of face, its facets structure are not correct. Here is a facet degenerated into nearly a polyline (marked as red in the following figure).

Open the obj file as txt, we can see that the coordinate of some vertex is very close, how to avoid the slender triangle when using cilp tool?