Fix "Package system is broken" error without synaptic

Question

The package system is broken

If you are using third party repositories then disable them, since they are a common source of problems.
Now run the following command in a terminal: apt-get install -f

The following packages have unmet dependencies.
 libegl1-mesa : Depends: libgl1-mesa-dri (= 10.5~git1411191810.9460cd~gd~t) but 10.4~git1411171930.920f87~gd~t is installed
 libgbm1 : Depends: libgl1-mesa-dri (= 10.5~git1411191810.9460cd~gd~t) but 10.4~git1411171930.920f87~gd~t is installed
 libgl1-mesa-dri : Breaks: libgl1-mesa-dri:i386 (!= 10.4~git1411171930.920f87~gd~t) but 10.5~git1411191810.9460cd~gd~t is installed
 libgl1-mesa-dri:i386 : Breaks: libgl1-mesa-dri (!= 10.5~git1411191810.9460cd~gd~t) but 10.4~git1411171930.920f87~gd~t is installed
 libgl1-mesa-glx : Depends: libgl1-mesa-dri (= 10.5~git1411191810.9460cd~gd~t) but 10.4~git1411171930.920f87~gd~t is installed
E: Error, pkgProblemResolver::Resolve generated breaks, this may be caused by held packages.
E: Unable to correct dependencies

I'm on Ubuntu 14.04. I was using the update drivers from Updated and Optimized Open Graphics Drivers , so the first thing I did was remove that PPA, but this doesn't seem to have helped.

EDIT: I've followed these instructions, but to no avail:

How do I resolve unmet dependencies after adding a PPA?
How to Fix the "Package System is Broken" Error on Ubuntu 11.04 / 10.10 / 10.04
Package system is broken. How to fix it?

Running these commands achieves nothing:

sudo apt-get clean
sudo apt-get -f install
sudo apt-get update

I don't have synaptic installed and when I try to install it, or remove packages using sudo apt-get remove --dry-run I just get more errors about unmet dependencies. I've been using Ubuntu for years and have always been able to resolve problems like this in the past, but something is eluding me here.

Solution

I eventually traced the problem to a broken package from the oibaf PPA, as described here.

Following advice from one of the posters there, I eventually fixed my problem by manually downloading the offending mesa packages and all their cross-dependencies from the official Ubuntu repositories (http://packages.ubuntu.com/) and installing them using dpkg -i.

I then ran apt-get install -f, which revealed some more broken dependencies, so I found and installed these as with the previous packages.

After a few rounds of this, I eventually managed to run apt-get install -f without errors, then ran `apt-get dist-upgrade' to update with the latest (unbroken) versions (having already removed the oibaf PPA).

Painful, but effective.

Comments

[Vladislava Frantskevich]

Thanks for the suggestions, but the the proposed duplicate doesn't resolve my issue. I've updated the description to explain in more detail.