 However, the theories of Curry and Church were almost immediately shown inconsistent in 1934, by Kleene and Rosser, who (essentially) proved a version of the Richard paradox (both systems can provably enumerate their own provably total definable number theoretic functions). The result was triggered by Church himself in 1934, when he used the Richard paradox to prove a kind of incompleteness theorem (with respect to statements asserting the totality of number theoretic functions).