diff --git a/ortools/sat/cp_model.proto b/ortools/sat/cp_model.proto
index fd24988813..9746b958ce 100644
--- a/ortools/sat/cp_model.proto
+++ b/ortools/sat/cp_model.proto
@@ -740,6 +740,10 @@ message CpSolverResponse {
   // changing your model to minimize the number of assumptions at false, but
   // this is likely an harder problem to solve.
   //
+  // Important: Currently, this is minimized only in single-thread and if the
+  // problem is not an optimization problem, otherwise, it will always include
+  // all the assumptions.
+  //
   // TODO(user): Allows for returning multiple core at once.
   repeated int32 sufficient_assumptions_for_infeasibility = 23;
 
diff --git a/ortools/sat/cp_model_presolve.cc b/ortools/sat/cp_model_presolve.cc
index 132571cc02..89a7abba30 100644
--- a/ortools/sat/cp_model_presolve.cc
+++ b/ortools/sat/cp_model_presolve.cc
@@ -6425,6 +6425,7 @@ CpModelPresolver::CpModelPresolver(PresolveContext* context,
       context_->params().keep_all_feasible_solutions_in_presolve() ||
       context_->params().enumerate_all_solutions() ||
       context_->params().fill_tightened_domains_in_response() ||
+      !context_->working_model->assumptions().empty() ||
       !context_->params().cp_model_presolve();
 
   // We copy the search strategy to the mapping_model.