The Krillitanes took over Deffry Vale High School to crack the paradigm. The Krillitane, Lassar, posing as headmaster Mr Finch, believed that if he could crack the paradigm he would be able to redo all of reality and improve it.
Unfortunately for him, the Skasis Paradigm did not just require computational power to crack it. It also needed imagination. That was why the Krillitanes were using the Krillitane oil to enhance the children of the school, since they had the imagination needed to crack the Paradigm. However, their integration of other species' biology from conquering their planets made the oil lethal to the Krillitanes. The Tenth Doctor, Rose Tyler, Mickey Smith, Sarah Jane Smith, and K9 Mark III all fought against the Krillitanes to keep them from cracking the Skasis Paradigm. Though Lassar tempted the Doctor with a way to reverse the horrors of the Last Great Time War and undo ageing and death by use of the Paradigm, Sarah Jane reminded the Doctor that these experiences are necessary to make life meaningful. After brief hesitation, the Doctor hurtled a classroom chair into the supercomputer decoding the Skasis Paradigm and destroyed it. The Krillitanes responded by preying on every human life at the school. K9 Mark III would give up his life to slay the entire horde with the same oil they had grown vulnerable to. (TV: School Reunion)