We present various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses under application of non-redundant inferences.Expand

We propose a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver Solver T for a given theory T, and our solver for EUF, which includes incremental and backtrackable congruence closure algorithms.Expand

Proceedings. 14th Symposium on Logic in Computerâ€¦

2 July 1999

TLDR

We consider the restriction of the guarded fragment to the two-variable case where, in addition, binary relations may be specified as transitive.Expand

We consider a restricted version of ordered paramodulation, called strict superposition, which is refutationally complete for Horn clauses, but not for general first-order clauses.Expand

The authors investigate the relationship between set constraints and the monadic class of first-order formulas and show that the satisfiability problem for set constraints is complete for NEXPTIME, for some c>0.Expand

18th Annual IEEE Symposium of Logic in Computerâ€¦

22 June 2003

TLDR

We consider instantiation-based theorem proving whereby instances of clauses are generated by certain inferences, and where inconsistency is detected by proposition tests.Expand

We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing) and prove refutational completeness in the context of deletion rules, such as simplification by rewriting (demodulation) and subsumption) and techniques for eliminating redundant inferences.Expand