Investigation of Monotonous Properties for Frege Systems - Hambardzumyan, Arsen A. (Mathematical Problems of Computer Science, 2020)
In this paper, we investigate the relations between the Frege proof lines of minimal tautologies and the results of substitutions in them. We show that there is a sequence of tautologies ψn, each of which has a unique minimal tautology ϕn, such that for every n the Frege proof lines of ϕn are an order more than the Frege proof lines for ψn.