diff --git a/package/version b/package/version
index 09bc4f7cc..c037e80c7 100644
--- a/package/version
+++ b/package/version
@@ -1 +1 @@
-0.1.558
+0.1.559
diff --git a/pyproject.toml b/pyproject.toml
index 1f4c7061c..0f8ec8b46 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -4,7 +4,7 @@ build-backend = "poetry.core.masonry.api"
 
 [tool.poetry]
 name = "pyk"
-version = "0.1.558"
+version = "0.1.559"
 description = ""
 authors = [
     "Runtime Verification, Inc. <contact@runtimeverification.com>",
diff --git a/src/pyk/proof/reachability.py b/src/pyk/proof/reachability.py
index 7d260a7ea..13a2e4f09 100644
--- a/src/pyk/proof/reachability.py
+++ b/src/pyk/proof/reachability.py
@@ -1280,7 +1280,7 @@ def steps(self, proof: APRProof) -> Iterable[APRProofStep]:
                     target_is_terminal=(proof.target not in proof._terminal),
                     main_module_name=self.prover.main_module_name,
                     dependencies_as_claims=[d.as_claim(self.kprint) for d in apr_subproofs],
-                    self_proof_as_claim=proof.as_claim(self.kprint),
+                    self_proof_as_claim=(proof.as_claim(self.kprint) if proof.circularity else None),
                     circularity=proof.circularity,
                     depth_is_nonzero=self.prover.nonzero_depth(pending_node),
                 )
@@ -1405,7 +1405,7 @@ class APRProofStep(parallel.ProofStep[APRProofResult, APRProofProcessData]):
     trace_rewrites: bool
 
     dependencies_as_claims: list[KClaim]
-    self_proof_as_claim: KClaim
+    self_proof_as_claim: KClaim | None
     circularity: bool
     depth_is_nonzero: bool
 
@@ -1470,7 +1470,12 @@ def exec(self, data: APRProofProcessData) -> APRProofResult:
                 kcfg_explore.add_dependencies_module(
                     self.main_module_name,
                     self.circularities_module_name,
-                    self.dependencies_as_claims + ([self.self_proof_as_claim] if self.circularity else []),
+                    self.dependencies_as_claims
+                    + (
+                        [self.self_proof_as_claim]
+                        if (self.circularity and (self.self_proof_as_claim is not None))
+                        else []
+                    ),
                     priority=1,
                 )