We investigate the connection between optimal propositional

proof systems and complete languages for promise classes.

We prove that an optimal propositional proof system exists

if and only if there exists a propositional proof system

in which every promise class with the test set in co-NP

is representable. Additionally, we prove that there exists

a complete language for UP if and only if there exists

a propositional proof system such that UP is representable

in it. UP is the standard promise class with the test set

in co-NP.