diff --git a/src/ir/constraint.cpp b/src/ir/constraint.cpp
index 6e7c8ce81f2..d0ba04d88ab 100644
--- a/src/ir/constraint.cpp
+++ b/src/ir/constraint.cpp
@@ -314,6 +314,55 @@ std::optional<Constraint> fusedApproximateAndPair(const Constraint& a,
   return {};
 }
 
+bool isImmediateContradiction(const Constraint& c) {
+  using namespace Abstract;
+
+  auto* cc = std::get_if<Literal>(&c.term);
+  if (!cc) {
+    // Only operations on constants can be immediate contradictions.
+    return false;
+  }
+
+  auto minSigned = cc->type == Type::i32 ? std::numeric_limits<int32_t>::min()
+                                         : std::numeric_limits<int64_t>::min();
+  auto maxSigned = cc->type == Type::i32 ? std::numeric_limits<int32_t>::max()
+                                         : std::numeric_limits<int64_t>::max();
+  auto maxUnsigned = cc->type == Type::i32
+                       ? std::numeric_limits<uint32_t>::max()
+                       : std::numeric_limits<uint64_t>::max();
+
+  switch (c.op) {
+    case LtS:
+      if (cc->getInteger() == minSigned) {
+        // Less than the lowest possible number.
+        return true;
+      }
+      break;
+    case LtU:
+      if (cc->getInteger() == 0) {
+        // Less than the lowest possible number.
+        return true;
+      }
+      break;
+    case GtS:
+      if (cc->getInteger() == maxSigned) {
+        // Greater than the highest possible number.
+        return true;
+      }
+      break;
+    case GtU:
+      if (cc->getUnsigned() == maxUnsigned) {
+        // Greater than the highest possible number.
+        return true;
+      }
+      break;
+    default: {
+    }
+  }
+
+  return false;
+}
+
 } // anonymous namespace
 
 void AndedConstraintSet::approximateAnd(const Constraint& c) {
@@ -322,6 +371,12 @@ void AndedConstraintSet::approximateAnd(const Constraint& c) {
     return;
   }
 
+  // We don't store contradictions: identify them and mark us as such.
+  if (isImmediateContradiction(c)) {
+    setProvesEverything();
+    return;
+  }
+
   auto result = proves(c);
   if (result == True) {
     // We already prove c to be true, so it adds nothing.