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Solving Logic Problems

A few years ago I asked this question. I have another question along the same lines. Sorry about the <-> notation, I don't know how else to indicate bijection:

children = { Abe, Dan, Mary, Sue }
ages = { 3, 5, 6, 9 }
children <-> ages  #bijection - one child per one age

Abe > Dan          #Abe is older than Dan
Sue < Mary         #Sue is younger than Mary
Sue = Dan + 3      #Sue's age is Dan's age plus 3 years
Mary > Abe         #Mary is older than Abe

Can sagemath determine that:

Abe = 5
Dan = 3
Mary = 9
Sue = 6