using Microsoft.Z3; Z3_context context = new Z3_context(); Expr x = context.MkIntConst("x"); Expr y = context.MkIntConst("y"); // Define the equation Expr eq = context.MkAdd(x, y) == context.MkInt(10); // Solve the equation Solver s = context.MkSolver(); s.Assert(eq); if (s.Check() == Status.SATISFIABLE) { Console.WriteLine("Solution found: x = " + s.Model.Eval(x) + ", y = " + s.Model.Eval(y)); } else { Console.WriteLine("No solution found."); }
using Microsoft.Z3; Z3_context context = new Z3_context(); FuncDecl isPrime = context.MkFuncDecl("isPrime", context.IntSort(), context.BoolSort()); IntExpr n = context.MkIntConst("n"); IntExpr i = context.MkIntConst("i"); // Define the predicate for prime numbers Expr primePredicate = context.MkForall(new Expr[] { n }, context.MkImplies(context.MkAnd(context.MkLe(context.MkInt(2), n), context.MkLt(n, context.MkInt(100))), context.MkEq(isPrime.Apply(n), context.MkNot(context.MkExists(new Expr[] { i }, context.MkAnd(context.MkLe(context.MkInt(2), i), context.MkLt(i, n), context.MkEq(context.MkRem(n, i), context.MkInt(0))))))), 1, null, null, null, null); Solver s = context.MkSolver(); s.Assert(primePredicate); // Check if there are any prime numbers between 50 and 100 for (int j = 50; j <= 100; j++) { Expr expr = isPrime.Apply(context.MkInt(j)); if (s.Check(expr) == Status.SATISFIABLE && s.Model.Eval(expr).BoolValue) { Console.WriteLine(j + " is prime."); } else { Console.WriteLine(j + " is not prime."); } }This code creates a Z3_context instance and defines a predicate for prime numbers. The predicate is then passed to a Solver instance and the solver checks if there are any prime numbers between 50 and 100. If a number is prime, it is displayed in the console. Z3_context is a part of the Z3 library package and can be found in the Microsoft.Z3 namespace.