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H is the theory extending &#946;-conversion by identifying all closedunsolvables. H&#969; is the closure of this theory under the &#969;-rule(and &#946;-conversion). A long-standing conjecture of H. Barendregt statesthat the provable equations of H&#969; form&#928;11-complete set. Here we prove that conjecture.Comment: 17 page

Solution of a Problem of Barendregt on Sensible lambda-Theories