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Resolution Theorem Proving
TLDR
Lifting is one of the most important general techniques for accelerating dii-cult computations. Expand
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Rewrite-Based Equational Theorem Proving with Selection and Simplification
TLDR
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
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DPLL( T): Fast Decision Procedures
TLDR
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
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The two-variable guarded fragment with transitive relations
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
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Ordered chaining calculi for first-order theories of transitive relations
TLDR
We propose inference systems for binary relations that satisfy composition laws such as transitivity. Expand
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On Restrictions of Ordered Paramodulation with Simplification
TLDR
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
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Set constraints are the monadic class
TLDR
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
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New directions in instantiation-based theorem proving
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
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Basic Paramodulation
TLDR
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
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Smalltalk-80
TLDR
Smalltalk-80 ist das Ergebnis nahezu zehnjähriger Forschungsarbeiten im Xerox Palo Alto Research Center (PARC). Expand
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