diff --git a/R/CnfFormula_simplify1.R b/R/CnfFormula_simplify1.R
index 7aae90e96..4cee6a104 100644
--- a/R/CnfFormula_simplify1.R
+++ b/R/CnfFormula_simplify1.R
@@ -619,19 +619,24 @@ simplify_cnf = function(entries, universe) {
 
   second_order_enabled = TRUE
   second_order_enabled_matrix = not_subset_count > 2L  # allow cascading of indirect SSE, except for the combinations where we trigger it manually (otherwise we'd be running them twice)
+  # we need to make sure we don't trigger for eliminated / unit clauses, so we set them to TRUE here.
+  # This means all remaining entries of the second_order_enabled_matrix are exactly the ones for which we trigger on_updated_subset_relations() manually.
+  meta_disabled = eliminated[available] | is_unit[available]
+  second_order_enabled_matrix[meta_disabled, ] = TRUE
+  second_order_enabled_matrix[, meta_disabled] = TRUE
   # alternatively, we could also enable none of the cascading in the beginning and have a nested loop in the following, where we 'repeat' until there are no more rowsum <= 2L
   # That would probably give uns less cascading, but we'd have to run 'which()' on a N^2 matrix potentially many times.
-  sse_to_trigger = which(not_subset_count <= 2L, arr.ind = TRUE)
+
+  sse_to_trigger = which(!second_order_enabled_matrix, arr.ind = TRUE)
   for (sse_idx in seq_len(nrow(sse_to_trigger))) {
     meta_idx = sse_to_trigger[sse_idx, 1L]
     meta_idx_other = sse_to_trigger[sse_idx, 2L]
+    if (eliminated[[available[[meta_idx]]]] || is_unit[[available[[meta_idx]]]] || eliminated[[available[[meta_idx_other]]]] || is_unit[[available[[meta_idx_other]]]]) next
     second_order_enabled_matrix[meta_idx, meta_idx_other] = TRUE
-    on_updated_subset_relations(meta_idx, meta_idx_other, TRUE)
+    if (identical(on_updated_subset_relations(meta_idx, meta_idx_other, TRUE), TRUE)) return(return_entries(FALSE))
   }
 
 
-
-
   # Now for the big one: Asymmetric Hidden Literal Addition (Marijn et al.)
 
   # First, we do non-units, then we do units separately.
diff --git a/attic/experiments.R b/attic/experiments.R
index c72ac7e3d..1aa5a3e35 100644
--- a/attic/experiments.R
+++ b/attic/experiments.R
@@ -1245,6 +1245,8 @@ meta_idx_inner
 c
 lapply(seq_along(eliminated), function(x) if (eliminated[[x]]) FALSE else structure(entries[[x]], class = "CnfClause"))
 
+
+
 entries[!eliminated] |> lapply(structure, class = "CnfClause")
 which(eliminated)
 
@@ -1307,6 +1309,34 @@ C = CnfSymbol(u, "C", c("c1", "c2", "c3"))
 
 
 
+quote(
+  (W %among% "p" | Y %among% "x") |
+   Y %among% "x" & W %among% "p"
+) |> eval() |> formula_to_expression() |> evaluate_expression(assignment)
+
+
+(W %among% "p" | Y %among% "x")
+
+ Y %among% "x" & W %among% "p"
+
+
+e1 <- (W %among% "p" | Y %among% "x")
+e2 <- Y %among% "x" & W %among% "p"
+
+e1
+e2
+
+e1 | e2
+
+
+
+ assignment
+
+
+  (W %among% "p" | Y %among% "x" |
+   Y %among% "x" & W %among% "p")
+
+
 
 
 
diff --git a/tests/testthat/test_CnfFormula_simplify.R b/tests/testthat/test_CnfFormula_simplify.R
index fae8fe3f9..d59fcf739 100644
--- a/tests/testthat/test_CnfFormula_simplify.R
+++ b/tests/testthat/test_CnfFormula_simplify.R
@@ -68,7 +68,6 @@ test_that("CnfFormula Regression Tests", {
         paste(capture.output(print(assignment)), collapse = "\n"),
         deparse1(simplified)
     ))
-
   }
 
   dti <- as.data.table(stats)