- 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