In English: “This sentence is not true”.
Liar_Paradox ≡ ∃X ~Provable(X, Liar_Paradox)
Minimal Type Theory (MTT) Knowledge Tree of the Liar Paradox:
Translated into a directed acyclic graph (DAG) by the MTT compiler
 Liar_Paradox (02)(04)
 THERE_EXISTS (03)
 NOT (05)
 Provable (03)(01) // cycle indicates infinite evaluation loop
The above formalism shows that the Liar Paradox gets stuck in an infinite evaluation loop and is thus not a Truth Bearer. Any expression that is impossibly true and impossibly false is not a truth bearer and therefore not a member of any Formal System even though it may otherwise be a syntactically WFF.
Copyright 2016 and 2017 Pete Olcott