0) print a warning about the contradiction. and that it's going to
evaluate both (the user might decide to stop if he or she understand
this better)
1) "split" the assumption in two:
a) first, assume the left hand is correct and proceed
b) when completed, assume the right hand is correct and proceed
2) print both results as possible, and that's going to investigate why
(the user might decide to stop if he or she understand this better)
3) backtrace to the source of the contradiction and print the results.
BTW, I haven't used MatLab, Mathematica or Maple recently, but if I
remember right, they just stop (by the way, if you are thinking just
to the symbolic inference part, not the numerical/imperative one,
there are engine out there that are open source and you may try).
Have a nice weekend,
Davide