Z3 .NET API for existence quantifier

Question

I am trying to use Z3 .net API to get an existence quantifier expr. Following are my code:

RealExpr c = ctx.MkRealConst("c");
BoolExpr Eqzero = ctx.MkGt(c,ctx.MkReal(0));    
BoolExpr Gezero = ctx.MkGe(c,ctx.MkReal(0));
BoolExpr Lttwo = ctx.MkLt(c,ctx.MkReal(2));
BoolExpr Gtthree = ctx.MkGt(c,ctx.MkReal(3)); 

BoolExpr b1 = ctx.MkBoolConst("b1");
BoolExpr b2 = ctx.MkBoolConst("b2");
BoolExpr b3 = ctx.MkBoolConst("b3");
BoolExpr b0 = ctx.MkBoolConst("b0");   

RealExpr[] lamb=new RealExpr[1];

lamb[0]=ctx.MkRealConst("lamb");

BoolExpr temp=ctx.MkAnd(
     ctx.MkGt(lamb[0],ctx.MkReal(0)),
     ctx.MkEq(b0,ctx.MkTrue()),
     ctx.MkEq(b1,ctx.MkTrue()),
     ctx.MkGe(ctx.MkAdd(c,lamb[0]),ctx.MkReal(0)),
     ctx.MkLe(ctx.MkAdd(c,lamb[0]),ctx.MkReal(3)),
     ctx.MkGe(c,ctx.MkReal(0)),
     ctx.MkLe(c,ctx.MkReal(3))
                    );   


BoolExpr exist = ctx.MkExists(lamb, temp, 1, null, null, ctx.MkSymbol("Q2"),            ctx.MkSymbol("skid2"));

Console.WriteLine(exist.ToString());
Solver s1 = ctx.MkSolver();
s1.Assert(exist);
if (s1.Check() == Status.SATISFIABLE)
{
  Console.WriteLine("get pre");
  Console.Write(s1);
}
else
{
   Console.WriteLine("Not reach");
}
Console.ReadKey();

'

For the program, I got the following result:

(exists ((lamb Real))
 (! (and (> lamb 0.0)
      (= b0 true)
      (= b1 true)
      (>= (+ c lamb) 0.0)
      (<= (+ c lamb) 3.0)
      (>= c 0.0)
      (<= c 3.0))
 :skid skid2
 :qid Q2))
 Not reach

My questions are 1. What is the meaning of the ! in the result/ 2. What is the reason that I cannot get sat result? 3. Could someone offer some martial corresponding to the Z3 .NET　API　besides the API　menu on the Z3 website.

Thanks very much!

Answer 1

The meaning of the (! ...) function is an annotation that binds patterns and quantifier and Skolem IDs to the expression. When this line

BoolExpr exist = ctx.MkExists(lamb, temp, 1, null, null, ctx.MkSymbol("Q2"), ctx.MkSymbol("skid2"));

is changed to

BoolExpr exist = ctx.MkExists(lamb, temp, 1);

then there is no (! ...) in the output.

I can't replicate the UNSAT result: When I run this example using Z3 4.0, I get SAT and the following model:

(define-fun lamb!0 () Real  1.0)
(define-fun c () Real  1.0)
(define-fun b1 () Bool true)
(define-fun b0 () Bool true)