Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Resolution Games and Non-Liftable Resolution Orderings
CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
On Generating Small Clause Normal Forms
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
A Resolution-Based Decision Procedure for the Two-Variable Fragment with Equality
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Deciding the guarded fragments by resolution
Journal of Symbolic Computation
Combining superposition, sorts and splitting
Handbook of automated reasoning
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Translation of resolution proofs into short first-order proofs without choice axioms
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
The design and implementation of VAMPIRE
AI Communications - CASC
Deciding monodic fragments by temporal resolution
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Case Splitting in an Automatic Theorem Prover for Real-Valued Special Functions
Journal of Automated Reasoning
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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.