Question

I want to know if Z3 can show equivalent formulas after Quantifier Elimination.

Example (exists k) (i x k) = 1 and k > 5
is equivalent to

i > 0 and 5 i – 1 < 0.

Here, quantifier k has been eliminated.

Is this possible?

Thanks,
Kaustubh.

Answer 1

Yes, Z3 can check whether two formulas are equivalent. To check whether p and q are equivalent. We must check whether (not (iff p q)) is unsatisfiable.

Your example uses nonlinear arithmetic i*k. The quantifier elimination module in Z3 has limited support for nonlinear real arithmetic. It is based on virtual term substitution, which is not complete. However, it is sufficient for your example.
We must enable the quantifier elimination module in Z3, and the nonlinear extensions (i.e., virtual term substitution).

Here is how we can encode your example in Z3: http://rise4fun.com/Z3/rXfi