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We define a superposition calculus with explicit splitting and an explicit, new backtracking rule on the basis of labelled clauses. For the first time we show a superposition calculus with explicit backtracking rule sound and complete. The new backtracking rule advances backtracking with branch condensing known from SPASS. An experimental evaluation of an(More)
LEO-II is a standalone, resolution-based higher-order theorem prover designed for effective cooperation with specialist provers for natural fragments of higher-order logic. At present LEO-II can cooperate with the first-order automated theorem provers E, SPASS, and Vampire. The improved performance of LEO-II, especially in comparison to its predecessor LEO,(More)
The success of superposition-based theorem proving in first-order logic relies in particular on the fact that the superposition calculus is able to decide well-known classical decidable fragments of first-order logic and has been successful in identifying new decidable classes. In this paper, we extend this story to the hierarchic combination of linear(More)
The hierarchic combination of linear arithmetic and first-order logic with free function symbols, FOL(LA), results in a strictly more expressive logic than its two parts. The SUP(LA) calculus can be turned into a decision procedure for interesting fragments of FOL(LA). For example, reachability problems for timed automata can be decided by SUP(LA) using an(More)
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