diff --git a/pkg/planner/core/operator/logicalop/logical_aggregation.go b/pkg/planner/core/operator/logicalop/logical_aggregation.go
index 5f2e3f6fa650a..5cbfebfe6cbe6 100644
--- a/pkg/planner/core/operator/logicalop/logical_aggregation.go
+++ b/pkg/planner/core/operator/logicalop/logical_aggregation.go
@@ -447,7 +447,7 @@ func (la *LogicalAggregation) ExtractFD() *fd.FDSet {
 				determinants.Insert(int(one.UniqueID))
 				groupByColsOutputCols.Insert(int(one.UniqueID))
 			}
-			notnull := util.IsNullRejected(la.SCtx(), la.Schema(), x, true)
+			notnull := util.IsNullRejected(la.SCtx(), la.Schema(), x)
 			if notnull || determinants.SubsetOf(fds.NotNullCols) {
 				notnullColsUniqueIDs.Insert(scalarUniqueID)
 			}
diff --git a/pkg/planner/core/operator/logicalop/logical_join.go b/pkg/planner/core/operator/logicalop/logical_join.go
index abf074219eb36..872c32e1ffdf5 100644
--- a/pkg/planner/core/operator/logicalop/logical_join.go
+++ b/pkg/planner/core/operator/logicalop/logical_join.go
@@ -326,7 +326,7 @@ func simplifyOuterJoin(p *LogicalJoin, predicates []expression.Expression) {
 		if expression.ExprFromSchema(expr, outerTable.Schema()) {
 			continue
 		}
-		isOk := util.IsNullRejected(p.SCtx(), innerTable.Schema(), expr, true)
+		isOk := util.IsNullRejected(p.SCtx(), innerTable.Schema(), expr)
 		if isOk {
 			canBeSimplified = true
 			break
@@ -720,7 +720,7 @@ func (p *LogicalJoin) ConvertOuterToInnerJoin(predicates []expression.Expression
 	if p.JoinType == LeftOuterJoin || p.JoinType == RightOuterJoin {
 		canBeSimplified := false
 		for _, expr := range predicates {
-			isOk := util.IsNullRejected(p.SCtx(), innerTable.Schema(), expr, true)
+			isOk := util.IsNullRejected(p.SCtx(), innerTable.Schema(), expr)
 			if isOk {
 				canBeSimplified = true
 				break
@@ -1295,13 +1295,13 @@ func (p *LogicalJoin) ExtractOnCondition(
 				}
 				if leftCol != nil && rightCol != nil {
 					if deriveLeft {
-						if util.IsNullRejected(ctx, leftSchema, expr, true) && !mysql.HasNotNullFlag(leftCol.RetType.GetFlag()) {
+						if util.IsNullRejected(ctx, leftSchema, expr) && !mysql.HasNotNullFlag(leftCol.RetType.GetFlag()) {
 							notNullExpr := expression.BuildNotNullExpr(ctx.GetExprCtx(), leftCol)
 							leftCond = append(leftCond, notNullExpr)
 						}
 					}
 					if deriveRight {
-						if util.IsNullRejected(ctx, rightSchema, expr, true) && !mysql.HasNotNullFlag(rightCol.RetType.GetFlag()) {
+						if util.IsNullRejected(ctx, rightSchema, expr) && !mysql.HasNotNullFlag(rightCol.RetType.GetFlag()) {
 							notNullExpr := expression.BuildNotNullExpr(ctx.GetExprCtx(), rightCol)
 							rightCond = append(rightCond, notNullExpr)
 						}
@@ -1998,7 +1998,7 @@ func deriveNotNullExpr(ctx base.PlanContext, expr expression.Expression, schema
 	if childCol == nil {
 		childCol = schema.RetrieveColumn(arg1)
 	}
-	if util.IsNullRejected(ctx, schema, expr, true) && !mysql.HasNotNullFlag(childCol.RetType.GetFlag()) {
+	if util.IsNullRejected(ctx, schema, expr) && !mysql.HasNotNullFlag(childCol.RetType.GetFlag()) {
 		return expression.BuildNotNullExpr(ctx.GetExprCtx(), childCol)
 	}
 	return nil
diff --git a/pkg/planner/core/operator/logicalop/logical_projection.go b/pkg/planner/core/operator/logicalop/logical_projection.go
index f2f930f2df7fe..830f7e248b060 100644
--- a/pkg/planner/core/operator/logicalop/logical_projection.go
+++ b/pkg/planner/core/operator/logicalop/logical_projection.go
@@ -503,7 +503,7 @@ func (p *LogicalProjection) ExtractFD() *fd.FDSet {
 				// the dependent columns in scalar function should be also considered as output columns as well.
 				outputColsUniqueIDs.Insert(int(one.UniqueID))
 			}
-			notnull := util.IsNullRejected(p.SCtx(), p.Schema(), x, true)
+			notnull := util.IsNullRejected(p.SCtx(), p.Schema(), x)
 			if notnull || determinants.SubsetOf(fds.NotNullCols) {
 				notnullColsUniqueIDs.Insert(scalarUniqueID)
 			}
diff --git a/pkg/planner/util/funcdep_misc.go b/pkg/planner/util/funcdep_misc.go
index 6db8e65db7b0d..d98dec853ac4f 100644
--- a/pkg/planner/util/funcdep_misc.go
+++ b/pkg/planner/util/funcdep_misc.go
@@ -42,7 +42,7 @@ func ExtractNotNullFromConds(conditions []expression.Expression, p base.LogicalP
 		if len(cols) == 0 {
 			continue
 		}
-		if IsNullRejected(p.SCtx(), p.Schema(), condition, true) {
+		if IsNullRejected(p.SCtx(), p.Schema(), condition) {
 			for _, col := range cols {
 				notnullColsUniqueIDs.Insert(int(col.UniqueID))
 			}
diff --git a/pkg/planner/util/null_misc.go b/pkg/planner/util/null_misc.go
index ecb9d0bceb3b9..5028166c9c433 100644
--- a/pkg/planner/util/null_misc.go
+++ b/pkg/planner/util/null_misc.go
@@ -62,7 +62,9 @@ import (
 // classify that exact value. This recovers cases such as COALESCE/IF/IFNULL
 // that may hide NULL but still collapse after nullification. The bridge stays
 // conservative for plan-cache-sensitive expressions by refusing to treat
-// ParamMarker/DeferredExpr values as static fold results.
+// ParamMarker/DeferredExpr values as static fold results. DeferredExpr can
+// still be inspected symbolically, but its runtime value must not be folded or
+// classified as a compile-time constant.
 
 // nullRejectProof holds the two proof results for a sub-expression.
 // See the file-level comment above for the full model.
@@ -71,7 +73,8 @@ type nullRejectProof struct {
 	mustNull bool
 }
 
-// allConstants checks whether the expression tree consists entirely of constants.
+// allConstants checks whether the expression tree can be attempted as a static
+// constant tree without lazy constants.
 func allConstants(ctx expression.BuildContext, expr expression.Expression) bool {
 	if expression.MaybeOverOptimized4PlanCache(ctx, []expression.Expression{expr}) {
 		return false // expression contains non-deterministic parameter
@@ -92,9 +95,7 @@ func allConstants(ctx expression.BuildContext, expr expression.Expression) bool
 
 // IsNullRejected proves whether `predicate` can be TRUE after every column in
 // `innerSchema` is replaced with SQL NULL.
-func IsNullRejected(ctx base.PlanContext, innerSchema *expression.Schema, predicate expression.Expression,
-	skipPlanCacheCheck bool) bool {
-	_ = skipPlanCacheCheck // kept for API compatibility; the new proof does not use EvaluateExprWithNull
+func IsNullRejected(ctx base.PlanContext, innerSchema *expression.Schema, predicate expression.Expression) bool {
 	predicate = expression.PushDownNot(ctx.GetNullRejectCheckExprCtx(), predicate)
 	return proveNullRejected(ctx, innerSchema, predicate, true).nonTrue
 }
diff --git a/pkg/planner/util/null_misc_test.go b/pkg/planner/util/null_misc_test.go
index 1e8da35666fde..fe4d051605456 100644
--- a/pkg/planner/util/null_misc_test.go
+++ b/pkg/planner/util/null_misc_test.go
@@ -451,7 +451,7 @@ func TestIsNullRejectedProofModes(t *testing.T) {
 
 	for _, tt := range cases {
 		t.Run(tt.name, func(t *testing.T) {
-			require.Equal(t, tt.expected, IsNullRejected(sctx, innerSchema, tt.expr, true))
+			require.Equal(t, tt.expected, IsNullRejected(sctx, innerSchema, tt.expr))
 		})
 	}
 }