diff --git a/src/Lean/Meta/Tactic/Grind/Order/Assert.lean b/src/Lean/Meta/Tactic/Grind/Order/Assert.lean
index bdaeb5777e..c2618593d0 100644
--- a/src/Lean/Meta/Tactic/Grind/Order/Assert.lean
+++ b/src/Lean/Meta/Tactic/Grind/Order/Assert.lean
@@ -156,6 +156,7 @@ associated with `(u, v)` IF
 
 /-- Equality propagation. -/
 def checkEq (u v : NodeId) (k : Weight) : OrderM Unit := do
+  if (← isPartialOrder) then
   if !k.isZero then return ()
   let some k' ← getDist? v u | return ()
   if !k'.isZero then return ()
diff --git a/tests/lean/run/grind_order_3.lean b/tests/lean/run/grind_order_3.lean
index caf950db08..81b229e0e2 100644
--- a/tests/lean/run/grind_order_3.lean
+++ b/tests/lean/run/grind_order_3.lean
@@ -18,3 +18,25 @@ example [LE α] [LT α] [Std.LawfulOrderLT α] [Std.IsLinearPreorder α] [CommRi
 
 example (p : Prop) (a b c : Int) : (p ↔ b ≤ a) → (p ↔ c ≤ b) → ¬ p → c ≤ a + 1 → False := by
   grind -linarith -cutsat (splits := 0)
+
+/--
+error: `grind` failed
+case grind
+α : Type u_1
+inst : LE α
+inst_1 : Std.IsPreorder α
+a b c : α
+h : a ≤ b
+h_1 : b ≤ c
+h_2 : c ≤ a
+h_3 : ¬a = c
+⊢ False
+-/
+#guard_msgs in
+example [LE α] [Std.IsPreorder α]
+    (a b c : α) : a ≤ b → b ≤ c → c ≤ a → a = c := by
+  grind -linarith -verbose
+
+example [LE α] [Std.IsPartialOrder α]
+    (a b c : α) : a ≤ b → b ≤ c → c ≤ a → a = c := by
+  grind -linarith -verbose