/usr/lib/petscdir/3.1/include/finclude/ftn-auto/ is in libpetsc3.1-dev 3.1.dfsg-11ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/makefile
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscao.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscda.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscdraw.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscis.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscksp.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscmat.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscmatfd.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscmatorderings.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscmesh.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscpc.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscpf.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscprofiling.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscsemilagrange.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscsnes.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscsys.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscts.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscvec.h90
/usr/lib/petscdir/3.1/include/finclude/ftn-auto/petscviewer.h90