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  1. The propositional skeleton $\skel$ of a formula $\varphi$ is obtained by replacing each occurance of a $\Theory$-literal with a propositional variable.
  2. An example for a formula $\varphi$ in $\LIA$:
  3. $$ \varphi \coloneqq (x > y) \lor (x > z),$$
  4. and the corresponding skeleton $\skel$:
  5. $$ e_1 \lor e_2, $$
  6. where $e_1 \equiv x > y$ and $e_2 \equiv x > z$.