The Unit Proof and the Input Proof in Theorem Proving
Journal of the ACM (JACM)
Unit Refutations and Horn Sets
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Experimentation with proof methods for non-Horn sets
SAC '92 Proceedings of the 1992 ACM/SIGAPP Symposium on Applied computing: technological challenges of the 1990's
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The concern here is with proof procedures which are generalizations of input or unit deduction. The author's generalizations of input deduction involve lemmas, whereas those of unit deduction involve longer clauses and are akin to Robinson's P1 deduction. Chang's theorem, which establishes the equivalence of input and unit refutation, is extended to these generalizations. Completeness results of Henschen, Wos, and Kuehner for input or unit deduction applied to Horn sets are generalized to apply also to non-Horn sets. A key result is that any unsatisfiable set can be refuted by a lock linear resolution procedure in which the only lemmas are positive clauses composed entirely of instances of a small set of literals which can be specified in advance. In an implementation such lemmas would be generated only infrequently, thus allowing one to periodically gather the lemmas, discard other generated clauses, and restart the proof procedure.