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The Art of Computer Programming: Satisfiability, Volume 4, Fascicle 6 by Donald E. Knuth

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Tseytin pointed out that there’s a simple way to get around the lower bounds he had proved for his graph-oriented problems, by allowing new kinds of proof steps: Given any set of axioms F, we can introduce a new variable z that doesn’t appear anywhere in F, and add three new clauses Image; here x and y are arbitrary literals of F. It’s clear that F is satisfiable if and only if FG is satisfiable, because G essentially says that z = NAND(x, y). Adding new variables in this way is somewhat analogous to using lemmas when proving a theorem, or to introducing a memo cache in a computer program.

His method, which is called extended resolution, can be much ...

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