Abstract
Some new approaches to mechanical theorem proving in the first-order predicate calculus are presented. These are based on a natural deduction system which can be used to show that a set of clauses is inconsistent. This natural deduction system distinguishes positive from negative literals and treats clauses having 0, 1, and 2 or more positive literals in three separate ways. Several such systems are presented. The systems are complete and relatively simple and allow a goal to be decomposed into subgoals, and solutions to the subgoals can then be searched for in the same way. Also, the systems permit a natural use of semantic information to delete unachievable subgoals. The goal-subgoal structure of these systems should allow much of the current artificial intelligence methodology to be applied to mechanical theorem proving.
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