You can take any non-commutative group as a model. One examples is invertible (n x n)-matrices under multiplication (thus, + is interpreted as multiplication and 0 is interpreted as the identity matrix). Another example is the group of permutations , which is the group of bijections of {1, 2, 3} under composition. It is also a group of isometries (transformations that preserve distances, such as rotations, shifts and reflections) that map an equilateral triangle into itself.

It's not clear to me why there is an existential quantifier inIt does not seem more difficult to find a model of a similar sentence where all quantifiers are universal.for all x the exist y for all z (x+(y+z)=(x+y)+z)