If I have a theory with the following axioms:
$\forall x.(x=x)$
$\forall x\forall y.\left(x=y\rightarrow\left(\varphi\left(x,x\right)\rightarrow\varphi\left(x,y\right)\right)\right)$, where $\varphi$ is any atomic formula.
And any model of these axioms is an equivalence relation, how do I prove that this theory isn't complete?