Linear or nonlinear? CPLEX solver

[Ana Celeste Batista German]

Dear Robert,

I am working on a model which has the following constraint. I assume is nonlinear due to the product expression, (1-prod{(i,j) in LINKS: i<>j}(1-beta[i]*A[i,j]*pi[j,t])):

subject to SP1 {s in SK, i in STAFF_SK[s], t in TIME:t!=6}:    
 pi[i, t+1] = (1-tau[s])*pi[i,t] + (1- pi[i,t] - pq[i, t])*(1-prod{(i,j) in LINKS: i<>j}(1-beta[i]*A[i,j]*pi[j,t]));

Among other constraints the aforementioned is related to the following one:

subject to ALL1   :
    1/T*sum{i in STAFF, s in SK,t in TIME} pi[i,t]*X[i,s,t]  <= br + UPI;    

I am solving the model with CPLEX in AMPL and it works pretty well; It reports an optimal integer solution. The CPLEX log reports all the constraints as linear:

**CPLEX log**
Presolve eliminates 1500 constraints and 2900 variables.
Adjusted problem:
3101 variables:
    2800 binary variables
    301 linear variables
1009 constraints, all linear; 9201 nonzeros
    1009 inequality constraints
1 linear objective; 1001 nonzeros.

I wonder whether I am missing something in the formulation or if the solver wrongly considers the constraint as linear.

Thank you!