I'm afraid that your x_ne_y axiom is already too "powerful" and "extending" 
the example is not gonna help (if you mean "adding" statements)

You might replace x_ne_y with something like 

  0_ne_1 $a true 0 != 1 $.
  1_ne_0 $a true 1 != 0 $.

but, of course, this does not scale at all

Glauco

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