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Comprehension and Description in Tableaux
, 1997
"... Various approaches have been invented for enabling an automated theorem proving program to find proofs in set theory. The present approach is completely automatic and quite successful on many problems which are showcased as challenge problems for provers in set theory. In fact, this procedure fi ..."
Abstract

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Various approaches have been invented for enabling an automated theorem proving program to find proofs in set theory. The present approach is completely automatic and quite successful on many problems which are showcased as challenge problems for provers in set theory. In fact, this procedure finds proofs of several of these examples without search. We implement the comprehension schema by means of tableau reduction and expansion rules. We also discuss the implementation of the definite descriptor in tableaux and special rules for handling equality effectively and in a tractable way in set theory. 1 Introduction An inference rule that "builds in" set theory at the inference level is the objective of Research Problem 8. More precisely, just as the employment of paramodulation permits one to avoid using any equality axioms other than reflexivity, the soughtafter inference rule for set theory would permit one to avoid using a number of the axioms in Godel's approach. L...