calculus for first-order logic without equality modulo a background theory. In

a nutshell, the SCL(T) calculus describes a new way to guide hierarchic

resolution inferences by a partial model assumption instead of an a priori

fixed order as done for instance in hierarchic superposition. The model

representation consists of ground background theory literals and ground

foreground first-order literals. One major advantage of the model guided

approach is that clauses generated by SCL(T) enjoy a non-redundancy property

that makes expensive testing for tautologies and forward subsumption completely

obsolete. SCL(T) is a semi-decision procedure for pure clause sets that are

clause sets without first-order function symbols ranging into the background

theory sorts. Moreover, SCL(T) can be turned into a decision procedure if the

considered combination of a first-order logic modulo a background theory enjoys

an abstract finite model property.

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