How can I write a long smt-lib expression with an existential quantifier?

Question

I have the following expression

(declare-fun x00 () Real)
(declare-fun x01 () Real)
(declare-fun x10 () Real)
(declare-fun x11 () Real)
(declare-fun t0init () Real)
(declare-fun z0init0 () Real)
(declare-fun z0init1 () Real)
(assert (>= t0init 0))
(assert (= (+ x00 z0init0) x10))
(assert (= (+ x01 z0init1) x11))
(assert (< (+ (* 1 x00)(* 0 x01)) 0.0))
(assert (= (+ (* 0 x00)(* 1 x01)) 0.0))
(assert (< (+ (* 1 x10)(* 0 x11)) 0.0))
(assert (= (+ (* 0 x10)(* 1 x11)) 0.0))
...
(assert (< (+ (* 1 x40)(* 0 x41)) 0.0))
(assert (= (+ (* 0 x40)(* 1 x41)) 0.0))
(assert (= (+ (* 1 z4end0)(* 0 z4end1)) (* t4end 1)))
(assert (= (+ (* 0 z4end0)(* 1 z4end1)) (* t4end -2)))

and I would like to express as a simple formula in order to express the following:

(assert exists (x00 x01) ("the above expression"))

and then perform a quantifier elimination.

Is there anyone who knows how to proceed? I know how to do it with z3py but I need some faster solution.

Thank you very much for any hint.

Answer 1

One possible solution is as follows

(declare-fun x00 () Real)
(declare-fun x01 () Real)
(declare-fun x10 () Real)
(declare-fun x11 () Real)
(declare-fun t0init () Real)
(declare-fun z0init0 () Real)
(declare-fun z0init1 () Real)
(define-fun conjecture () Bool
   (and (>= t0init 0) (= (+ x00 z0init0) x10) (= (+ x01 z0init1) x11)))
(assert (exists ((x00 Real) (x01 Real)) conjecture))
(check-sat)

and the corresponding output is

sat

I am not sure if the quantifier elimination that you need will work with Z3. Maybe for your problem "Redlog" of "Reduce" is the better option. All the best.