Splitting Through New Proposition Symbols

The splitting rule is a tableau-like rule, that is used in the resolution context. In case the search state contains a clause C1 V C2, which has no shared variables between C1 and C2, the prover splits the search state, and tries to refute C1 and C2 separately. Instead of splitting the state of the theorem prover, one can create a new proposition symbol α, and replace C1 V C2 by C1 V α and ¬α V C2. In the first clause a is the least preferred literal. In the second clause α is selected. In this way, nothing can be done with C2 as long as C1 has not been refuted. This way of splitting simulates search state splitting only partially, because a clause that inherits from C1 V α cannot subsume or simplify a clause that does not inherit from C1. With search state splitting, a clause that inherits from C1 can in principle subsume or simplify clauses that do not derive from C1. As a consequence, splitting through new symbols is less powerfull than search state splitting. In this paper, we present a solution for this problem.