  Resolution and superposition are common techniques which have seen widespread
use with propositional and first-order logic in modern theorem provers. In
these cases, resolution proof production is a key feature of such tools;
however, the proofs that they produce are not necessarily as concise as
possible. For propositional resolution proofs, there are a wide variety of
proof compression techniques. There are fewer techniques for compressing
first-order resolution proofs generated by automated theorem provers. This
paper describes an approach to compressing first-order logic proofs based on
lifting proof compression ideas used in propositional logic to first-order
logic. One method for propositional proof compression is partial
regularization, which removes an inference $\eta$ when it is redundant in the
sense that its pivot literal already occurs as the pivot of another inference
in every path from $\eta$ to the root of the proof. This paper describes the
generalization of the partial-regularization algorithm
RecyclePivotsWithIntersection [10] from propositional logic to first-order
logic. The generalized algorithm performs partial regularization of resolution
proofs containing resolution and factoring inferences with unification. An
empirical evaluation of the generalized algorithm and its combinations with the
previously lifted GreedyLinearFirstOrderLowerUnits algorithm [12] is also
presented

Logic in Computer Science