diff --git a/Comparator/Compare.lean b/Comparator/Compare.lean
index 1e0aff5..3718131 100644
--- a/Comparator/Compare.lean
+++ b/Comparator/Compare.lean
@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Henrik Böving
 -/
 import Comparator.ExportedEnv
+import Comparator.Utils
 
 namespace Comparator
 
@@ -54,24 +55,30 @@ partial def loop : CompareM Unit := do
 
 end Compare
 
-def compareAt (challenge solution : ExportedEnv) (targets : Array Lean.Name) :
+def compareAt (challenge solution : ExportedEnv) (targets axioms : Array Lean.Name) :
     Except String Unit := do
   let mut worklist := #[]
-  for target in targets do
+  for (target, isAxiom) in targets.map (·, false) ++ axioms.map (·, true) do
     let some challengeConst := challenge.constMap[target]?
       | throw s!"Const not found in challenge: '{target}'"
 
     let some solutionConst := solution.constMap[target]?
       | throw s!"Const not found in solution: '{target}'"
 
+    match challengeConst with
+    | .thmInfo _ | .axiomInfo _ => pure ()
+    | _ => throw s!"Challenge must be a theorem or axiom, not {Utils.constantKindName challengeConst}: '{target}'"
 
-    let (challengeConst, solutionConst) ←
-      match challengeConst, solutionConst with
-      | .thmInfo cc, .thmInfo sc
-      | .axiomInfo cc, .axiomInfo sc => pure (cc.toConstantVal, sc.toConstantVal)
-      | _, _ => throw s!"Challenge and solution constant kind don't match: '{target}'"
+    if isAxiom then
+      match solutionConst with
+      | .thmInfo _ | .axiomInfo _ => pure ()
+      | _ => throw s!"Permitted axiom in solution must be theorem or axiom, not {Utils.constantKindName solutionConst}: '{target}'"
+    else
+      match solutionConst with
+      | .axiomInfo _ => throw s!"Solution failed to prove axiom '{target}'"
+      | _ => pure ()
 
-    if challengeConst != solutionConst then
+    if challengeConst.toConstantVal != solutionConst.toConstantVal then
       throw s!"Challenge and solution theorem statement do not match: '{target}'"
 
     worklist := worklist ++ challengeConst.type.getUsedConstants
diff --git a/Comparator/Utils.lean b/Comparator/Utils.lean
new file mode 100644
index 0000000..6b2568c
--- /dev/null
+++ b/Comparator/Utils.lean
@@ -0,0 +1,21 @@
+import Lean.Environment
+
+namespace Comparator
+
+namespace Utils
+
+/-- Get a human-readable name for the kind of constant -/
+def constantKindName (info : Lean.ConstantInfo) : String :=
+  match info with
+  | .axiomInfo .. => "axiom"
+  | .defnInfo .. => "def"
+  | .thmInfo .. => "theorem"
+  | .opaqueInfo .. => "opaque"
+  | .quotInfo .. => "quot"
+  | .inductInfo .. => "inductive"
+  | .ctorInfo .. => "constructor"
+  | .recInfo .. => "recursor"
+
+end Utils
+
+end Comparator
diff --git a/Main.lean b/Main.lean
index 18b3088..91671e7 100644
--- a/Main.lean
+++ b/Main.lean
@@ -109,10 +109,8 @@ def runKernel (solution : Comparator.ExportedEnv) : M Unit := do
 def verifyMatch (challengeExport : String) (solutionExport : String) : M Unit := do
   let challenge ← IO.ofExcept <| Comparator.parse challengeExport
   let solution ← IO.ofExcept <| Comparator.parse solutionExport
-  let theoremNames ← getTheoremNames
-  let targets := (← getTheoremNames) ++ (← getLegalAxioms)
-  IO.ofExcept <| Comparator.compareAt challenge solution targets
-  IO.ofExcept <| Comparator.checkAxioms solution theoremNames (← getLegalAxioms)
+  IO.ofExcept <| Comparator.compareAt challenge solution (← getTheoremNames) (← getLegalAxioms)
+  IO.ofExcept <| Comparator.checkAxioms solution (← getTheoremNames) (← getLegalAxioms)
   runKernel solution
 
 def compareIt : M Unit := do