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- used to verify UNSAT results
- Idea is to derive empty clause
# RUP
- Reverse Unit Propagation
- Proofs only by [Unit propagation](SAT_in_general#Special Case Unit Resolution)
# RAT
- Reverse Asymmetric Tautology
- Idea: If all Resolutions end in Tautologies (or tautology by RUP) clause can be removed
- Supports more than just [UP](SAT_in_general#Special Case Unit Resolution)
- Way to represent [Blocked Clause removal](Preprocessing_Inprocessing#Blocked Clauses / Blocked literal)
- Replace need for tautology with RUP condition
# Redundancy
- A clause in a Formula is redundant
- Simplifying F by setting C to false implies any Formula simplified by another assignment
- $F_\alpha \models F_\omega$ , where $\omega$ satisfies $C$
- The idea of Propagation Redundancy (PR) is more general even than RAT