/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/ is in libpetsc3.1-dbg 3.1.dfsg-11ubuntu1.
This file is owned by root:root, with mode 0o755.
..
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petsc.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscao.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscaodef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscconf.h
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscconfiginfo.h
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscda.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscdadef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscfix.h
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscis.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscisdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscksp.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petsckspdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmachineinfo.h
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmat.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmatdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmesh.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmeshdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmg.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscmgdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscpc.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscpcdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscsnes.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscsnesdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscsys.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscsysdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscts.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petsctsdef.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscvec.mod
/usr/lib/petscdir/3.1/linux-gnu-c-debug/include/petscvecdef.mod