An abstract proof system is a polynomial time function $f$ whose  range is equal to the set of tautologies. If $\tau$ is a tautology, then an $f$-proof of $\tau$ is any value $\pi$ such that $f(\pi) = \tau$.Is there an example of a propositional  proof system which doesn't satisfy this definition?
Are there any propositional proof systems which are not Cook-Reckhow proof systems?
cc.complexity theory;lo.logic;computability;proof complexity