Before the question, let me explain better what E-KRHyper is:

E-KRHyper is a system for generating models and proof of theorems for first-order logic with equality. It is an implementation of the E-hyper tableau calculation, which integrates an equality management based on the superposition in the hyper-tableau calculation (source: System description: E-KRHyper).

I am interested in the complexity of the E-KRHyper system because it is used in the Log-Answer question and answer system (LogAnswer: a question based on deduction

Answering system (system description))

I found a partial answer:

our calculation is a non-trivial decision procedure for this

fragment (with equality), which captures the complexity classNEXT(Source: Hyper Tableaux with Equality).

I don't understand much about complexity theory, so my question is:

What is the complexity of a theorem to be tested in terms of the number of axioms in the database and in terms of some parameter of the question to answer?