The sentence "If two plus two equals four, then the premise of this sentence contains numbers" is true, while its literal contrapositive "If the premise of this sentence does not contain numbers, then two plus two does not equal four" is false. Can anyone find a more elegant example of a true self-referential sentence of the form "If ..., then ..." whose literal contrapositive is false? One might limit oneself to sentences that do not explicitly refer to their own structure as English sentences, but only refer to their own logical structure. Then the search for a true sentence with a false contrapositive could be set up as a "logical programming" problem on the space of all sentences of the form "If P then Q" where P and Q are arbitrary 6-variable Boolean functions of "this sentence", "the premise of this sentence", "the conclusion of this sentence", "the inverse of this sentence", "the converse of this sentence", and "the contrapositive of this sentence"; but since there are (2^(2^6))^2 = 2^128 or about 10^40 possibilities, a brute-force search of the space won't be feasible. I raised a version of this question in some forum (sci.math.research?) a number (20?) of years ago, and I think someone gave an answer that ruled out candidate solutions of a particular form (perhaps "If A implies B then C implies D"), but I can't remember any details. (Can anyone else?). I also sent the question to Raymond Smullyan and I think to Douglas Hofstadter as well, but I don't recall either of them replying. Can anyone come up with such a sentence or show that none exists? Jim Propp