how to get LP to prove things like ~(1 <= 0) and (0 <= 2)?

I'm trying to use LP, so I can teach my students about it.
So please forgive this question (which should probably be a FAQ).

I'm using a few traits that make use of the LSL trait Integer,
and I always seem to run into proofs that require me to show
facts like  ~(1 <= 0) and (0 <= 2).  But I can't figure out
what to say to LP about this.  (I guess it's something with
critical-pairs, but I'm not sure what?)

Here's the trait if you want to try it yourself...

DecimalProblem: trait
  includes Integer
      ~(1 <= 0);
      0 <= 2;

Any help would be appreciated.

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