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Normalization fails in type theory with an impredicative universe ofpropositions and a proof-irrelevant propositional equality. The counterexampleto normalization is adapted from Girard's counterexample against normalizationof System F equipped with a decider for type equality. It refutes Werner'snormalization conjecture [LMCS 2008].

Failure of Normalization in Impredicative Type Theory with Proof-Irrelevant Propositional Equality