Titlebook: Artificial Intelligence and Symbolic Computation; 7th International Co Bruno Buchberger,John Campbell Conference proceedings 2004 Springer-

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G. Beger,W. H. Uhl,M. W. Büchlerg ., and of opposite polarity. Note that for first order logic this restriction does not mean anything, since there are no higher order variables. However, when designing a proof search algorithm for first order logic only, one is naturally led into this fragment of higher order logic, where the algorithm works as well.