diff --git a/tla-bmcmt/src/main/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/caches/UninterpretedLiteralCache.scala b/tla-bmcmt/src/main/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/caches/UninterpretedLiteralCache.scala
new file mode 100644
index 0000000000..2d1a7b9dac
--- /dev/null
+++ b/tla-bmcmt/src/main/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/caches/UninterpretedLiteralCache.scala
@@ -0,0 +1,80 @@
+package at.forsyte.apalache.tla.bmcmt.stratifiedRules.aux.caches
+
+import at.forsyte.apalache.tla.bmcmt.smt.SolverContext
+import at.forsyte.apalache.tla.bmcmt.types.{CellT, CellTFrom}
+import at.forsyte.apalache.tla.bmcmt.{ArenaCell, PureArena}
+import at.forsyte.apalache.tla.lir.{ConstT1, StrT1, TlaType1}
+import at.forsyte.apalache.tla.types.tla
+
+/**
+ * A cache for uninterpreted literals, that are translated to uninterpreted SMT constants, with a unique sort per
+ * uninterpreted type. Since two values are equal iff they are literally the same literal, we force inequality between
+ * all the respective SMT constants.
+ *
+ * Note that Strings are just a special kind of uninterpreted type.
+ *
+ * @author
+ *   Jure Kukovec
+ */
+class UninterpretedLiteralCache extends Cache[PureArena, (TlaType1, String), ArenaCell] {
+
+  /**
+   * Given a pair `(utype,idx)`, where `utype` represents an uninterpreted type name (possibly "Str") and `idx` some
+   * unique index within that type, returns an extension of `arena`, containing a cell, which represents "idx_OF_utype"
+   * (or "idx", if utype = "Str"), and said cell.
+   *
+   * Note that two values are equal (and get cached to the same cell) iff they have the same type and the same index, so
+   * e.g. "1_OF_A" and "1_OF_B" (passed here as ("A", "1") and ("B", "1")) get cached to different, incomparable cells,
+   * despite having the same index "1".
+   */
+  protected def create(
+      arena: PureArena,
+      typeAndIndex: (TlaType1, String)): (PureArena, ArenaCell) = {
+    val (utype, _) = typeAndIndex
+    require(utype == StrT1 || utype.isInstanceOf[ConstT1], "Type must be Str, or an uninterpreted type.")
+    // introduce a new cell
+    val newArena = arena.appendCell(CellT.fromType1(utype))
+    (newArena, newArena.topCell)
+  }
+
+  /**
+   * The UninterpretedLiteralCache maintains that a cell cache for a value `idx` of type `tp` is distinct from all other
+   * values of type `tp` (defined so far).
+   *
+   * Whenever possible, try to use [[addAllConstraints]] instead of this method, for performance reasons instead:
+   *
+   * If we consider a naive implementation of `distinct(a1,..., an)` as `a1 != a2 /\ a1 != a3 /\ ... /\ a{n-1} != an`, a
+   * `distinct` with `n` elements is equivalent to `dn = n(n-1)/2` disequalities. Suppose we end up with a collection of
+   * `N` cache values (of a given type). If we called `addConstaintsForElem` after each addition, we'd end up with `d1 +
+   * d2 + ... + dN` disequalities, i.e. {{{\sum_{n=1}^N n(n-1)/2 = N(N^2 -1)/6}}} In contrast, `addAllConstraints`
+   * produces `dN = N(N-1)/2` disequalities, which is `O(N^2)`, instead of `O(N^3)`.
+   */
+  override def addConstraintsForElem(ctx: SolverContext): (((TlaType1, String), ArenaCell)) => Unit = {
+    case ((utype, _), v) =>
+      require(utype == StrT1 || utype.isInstanceOf[ConstT1], "Type must be Str, or an uninterpreted type.")
+      val others = values().withFilter { c => c.cellType == CellTFrom(utype) && c != v }.map(_.toBuilder).toSeq
+      // The cell should differ from the previously created cells.
+      // We use the SMT constraint (distinct ...).
+      ctx.assertGroundExpr(tla.distinct(v.toBuilder +: others: _*))
+  }
+
+  /**
+   * A more efficient implementation, compared to the default one, as it introduces exactly one SMT `distinct` for each
+   * uninterpreted type instead of one `distinct` per cell.
+   */
+  override def addAllConstraints(ctx: SolverContext): Unit = {
+    val utypes = cache.keySet.map { _._1 }
+
+    val initMap = utypes.map { _ -> Set.empty[ArenaCell] }.toMap
+
+    val cellsByUtype = cache.foldLeft(initMap) { case (map, ((utype, _), (cell, _))) =>
+      map + (utype -> (map(utype) + cell))
+    }
+
+    // For each utype, all cells of that type are distinct
+    cellsByUtype.foreach { case (_, cells) =>
+      ctx.assertGroundExpr(tla.distinct(cells.toSeq.map { _.toBuilder }: _*))
+    }
+
+  }
+}
diff --git a/tla-bmcmt/src/test/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/UninterpretedLiteralCacheTest.scala b/tla-bmcmt/src/test/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/UninterpretedLiteralCacheTest.scala
new file mode 100644
index 0000000000..868cfa9e87
--- /dev/null
+++ b/tla-bmcmt/src/test/scala/at/forsyte/apalache/tla/bmcmt/stratifiedRules/aux/UninterpretedLiteralCacheTest.scala
@@ -0,0 +1,147 @@
+package at.forsyte.apalache.tla.bmcmt.stratifiedRules.aux
+
+import at.forsyte.apalache.tla.bmcmt.PureArena
+import at.forsyte.apalache.tla.bmcmt.stratifiedRules.aux.caches.UninterpretedLiteralCache
+import at.forsyte.apalache.tla.lir.{StrT1, TlaType1}
+import at.forsyte.apalache.tla.types.{tla, ModelValueHandler}
+import org.junit.runner.RunWith
+import org.scalatest.BeforeAndAfterEach
+import org.scalatest.funsuite.AnyFunSuite
+import org.scalatestplus.junit.JUnitRunner
+
+@RunWith(classOf[JUnitRunner])
+class UninterpretedLiteralCacheTest extends AnyFunSuite with BeforeAndAfterEach {
+
+  var cache: UninterpretedLiteralCache = new UninterpretedLiteralCache
+
+  def tpAndIdx(s: String): (TlaType1, String) = {
+    val (utype, idx) = ModelValueHandler.typeAndIndex(s).getOrElse((StrT1, s))
+    (utype, idx)
+  }
+
+  override def beforeEach(): Unit = {
+    cache = new UninterpretedLiteralCache
+  }
+
+  test("Cache returns stored values after the first call to getOrCreate") {
+    val str: String = "idx"
+
+    val utypeAndIdx = tpAndIdx(str)
+
+    val arena = PureArena.empty
+
+    // No cached value for the pair
+    assert(cache.get(utypeAndIdx).isEmpty)
+
+    val (newArena, iCell) = cache.getOrCreate(arena, utypeAndIdx)
+
+    // pair now cached, arena has changed
+    assert(cache.get(utypeAndIdx).nonEmpty && newArena != arena)
+
+    val (newArena2, iCell2) = cache.getOrCreate(newArena, utypeAndIdx)
+
+    // 2nd call returns the _same_ arena and the previously computed cell
+    assert(newArena == newArena2 && iCell == iCell2)
+  }
+
+  test("Same index of different types is cached separately") {
+    val str1: String = "idx"
+    val str2: String = "idx_OF_A"
+    val str3: String = "idx_OF_B"
+
+    val pa1 = tpAndIdx(str1)
+    val pa2 = tpAndIdx(str2)
+    val pa3 = tpAndIdx(str3)
+
+    val arena = PureArena.empty
+
+    val (newArena1, cell1) = cache.getOrCreate(arena, pa1)
+
+    assert(arena != newArena1)
+
+    val (newArena2, cell2) = cache.getOrCreate(newArena1, pa2)
+
+    assert(newArena2 != newArena1 && cell2 != cell1)
+
+    val (newArena3, cell3) = cache.getOrCreate(newArena2, pa3)
+
+    assert(newArena3 != newArena2 && cell3 != cell2)
+  }
+
+  test("Constraints are only added when addAllConstraints is explicitly called, and only once per value") {
+    val mockCtx: MockZ3SolverContext = new MockZ3SolverContext
+
+    val str1: String = "1_OF_A"
+    val str2: String = "2_OF_A"
+    val str3: String = "3_OF_A"
+
+    val pa1 = tpAndIdx(str1)
+    val pa2 = tpAndIdx(str2)
+    val pa3 = tpAndIdx(str3)
+
+    val a0 = PureArena.empty
+    val (a1, c1) = cache.getOrCreate(a0, pa1)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a0, pa1)
+    cache.getOrCreate(a0, pa1)
+    val (a2, c2) = cache.getOrCreate(a1, pa2)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a1, pa2)
+    cache.getOrCreate(a1, pa2)
+    val (_, c3) = cache.getOrCreate(a2, pa3)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a2, pa3)
+    cache.getOrCreate(a2, pa3)
+
+    assert(mockCtx.constraints.isEmpty)
+
+    cache.addAllConstraints(mockCtx)
+
+    // Due to the optimized `addAllConstraints` override, we only have 1 "distinct"
+    assert(mockCtx.constraints == Seq(
+        tla.distinct(c3.toBuilder, c2.toBuilder, c1.toBuilder).build
+    ))
+  }
+
+  test("Constraints are only added when addConstraintsForElem is explicitly called, and only once per value") {
+    val mockCtx: MockZ3SolverContext = new MockZ3SolverContext
+
+    val str1: String = "1_OF_A"
+    val str2: String = "2_OF_A"
+    val str3: String = "3_OF_A"
+
+    val pa1 = tpAndIdx(str1)
+    val pa2 = tpAndIdx(str2)
+    val pa3 = tpAndIdx(str3)
+
+    val a0 = PureArena.empty
+    val (a1, c1) = cache.getOrCreate(a0, pa1)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a0, pa1)
+    cache.getOrCreate(a0, pa1)
+
+    cache.addConstraintsForElem(mockCtx)(pa1, c1)
+
+    val (a2, c2) = cache.getOrCreate(a1, pa2)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a1, pa2)
+    cache.getOrCreate(a1, pa2)
+
+    cache.addConstraintsForElem(mockCtx)(pa2, c2)
+
+    val (_, c3) = cache.getOrCreate(a2, pa3)
+    // Some extra calls, which shouldn't affect constraint generation
+    cache.getOrCreate(a2, pa3)
+    cache.getOrCreate(a2, pa3)
+
+    cache.addConstraintsForElem(mockCtx)(pa3, c3)
+
+    // -ForElem creates 3 "distinct" constraints
+    assert(mockCtx.constraints == Seq(
+        tla.distinct(c1.toBuilder).build,
+        tla.distinct(c2.toBuilder, c1.toBuilder).build,
+        tla.distinct(c3.toBuilder, c1.toBuilder, c2.toBuilder).build,
+    ))
+  }
+
+}