Frage

I am trying to obtain a quantifier-free formula using the following code:

S, E, I, R = Reals('S E I R')
b, n, s, g, m = Reals('b n s g m')
SS = Then('qe', 'smt').solver()
SS.add(Exists([S,E,I,R], And(m+g*R-m*S-b*I*S == 0,
   b*I*S-(m+s)*E==0, s*E-(n+m)*I==0, n*I-(m+g)*R==0,
   S > 0, I > 0, E > 0, R >0)))
SS.add(b > 0, n > 0, s >0 , g >0, m>0)
print SS
print SS.check()

but I am obtaining the output:

unknown

Please can you tell me what happens with my code? Many thanks.

War es hilfreich?

Lösung

Quantifier elimination works just for additive arithmetic. It does not eliminate quantifiers from formulas where variables are multiplied with other variables. This is why quantifier elimination does not produce a reduced formula for your problem.

Notice, however, that a formula Exists x . phi[x] is equi-satisfiable to a formula of the form phi[x], so it should not be required to put an existential quantifier on your formula. The nlsat strategy handles quantifier-free formulas over the reals with multiplication.

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