The constraint resulting from this proof
Formulae that are introduced into the antecedent by this rule application (one set for each subproof).
Formulae that are introduced into the antecedent by this rule application (one set for each subproof). This will implicitly simplify formulae (all simplifications that are built into the datastructures are carried out).
Formulae that the proof assumes to be present on this branch (i.e., premisses of rules applied in the proof).
Formulae that the proof assumes to be present on this branch (i.e., premisses of rules applied in the proof). We assume that all formulae live in the antecedent.
Set of constants occurring in this certificate.
Set of constants occurring in this certificate. By default this will contain the set of all constants in sub-certificates, as well as constants in assumed formulas.
Constants bound by the root operator of the certificate.
Datastructures used to express and extract whole, detailed proofs, which can independently be checked and be used for further processing (e.g., to compute interpolants). Certificates are trees/proof terms, with the following class as the abstract superclass of all tree nodes. Proofs are more or less tableau proofs, with rule applications assuming certain formulae on a branch and producing new formulae.