Subproblem finder and instance checker, two cooperating modules for theorem provers

Abstract

Properties are proved about INSTANCE, a theorem prover module that recognizes that a formula is a special case and/or an alphabetic variant of another formula, and about INSURER, another theorem prover module that decomposes a problem, represented by a formula, into independent subproblems, using a conjunction. The main result of INSTANCE is soundness; the main result of INSURER is a maximum decomposition into subproblems (with some provisos). Experimental results show that a connection graph theorem prover extended with these modules is more effective than the resolution-based connection graph theorem prover alone.