The term 'Does Not Exist' can be expressed in two different ways using crossword solutions. The first solution is 'ARENT' which is a contraction of the phrase 'Are Not'. This phrase is used to express the idea that something does not exist. The second solution is 'ISNT' which is a contraction of the phrase 'Is Not'. This phrase is also used to express the idea that something does not exist. Both of these solutions are commonly used to express the concept of something not existing.