diff --git a/src/lela/format/output.h b/src/lela/format/output.h
index 02a9c4f701563f11e6cdb33a6090b639f80b9149..27a2fde8a87c2d0f7641f7dce18abd769089ee1f 100644
--- a/src/lela/format/output.h
+++ b/src/lela/format/output.h
@@ -62,10 +62,7 @@ inline internal::Maybe<std::string> LookupSymbol(Symbol s) {
 }
 
 template<typename T1, typename T2>
-std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2> p) {
-  os << "(" << p.first << ", " << p.second << ")";
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2> p);
 
 template<typename Iter>
 std::ostream& print_sequence(std::ostream& os,
@@ -79,57 +76,28 @@ template<typename Range>
 std::ostream& print_range(std::ostream& os, const Range& r,
                           const char* pre = "[",
                           const char* post = "]",
-                          const char* sep = ", ") {
-  return print_sequence(os, r.begin(), r.end(), pre, post, sep);
-}
+                          const char* sep = ", ");
 
 template<typename T>
-std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
-  print_sequence(os, vec.begin(), vec.end(), "[", "]", ", ");
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec);
 
 template<typename T>
-std::ostream& operator<<(std::ostream& os, const std::list<T>& list) {
-  os << '[';
-  print_sequence(os, list.begin(), list.end(), "[", "]", ", ");
-  os << '[';
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::list<T>& list);
 
 template<typename T>
-std::ostream& operator<<(std::ostream& os, const std::set<T>& set) {
-  print_sequence(os, set.begin(), set.end(), "{", "}", ", ");
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::set<T>& set);
 
 template<typename T>
-std::ostream& operator<<(std::ostream& os, const std::multiset<T>& set) {
-  print_sequence(os, set.begin(), set.end(), "m{", "}m", ", ");
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::multiset<T>& set);
 
 template<typename K, typename T>
-std::ostream& operator<<(std::ostream& os, const std::map<K, T>& map) {
-  print_sequence(os, map.begin(), map.end(), "{", "}", ", ");
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::map<K, T>& map);
 
 template<typename K, typename T>
-std::ostream& operator<<(std::ostream& os, const std::multimap<K, T>& map) {
-  print_sequence(os, map.begin(), map.end(), "m{", "}m", ", ");
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const std::multimap<K, T>& map);
 
 template<typename T>
-std::ostream& operator<<(std::ostream& os, const internal::Maybe<T>& m) {
-  if (m) {
-    os << "Just(" << m.val << ")";
-  } else {
-    os << "Nothing";
-  }
-  return os;
-}
+std::ostream& operator<<(std::ostream& os, const internal::Maybe<T>& m);
 
 std::ostream& operator<<(std::ostream& os, const Symbol s) {
   internal::Maybe<std::string> sort_name = LookupSort(s.sort());
@@ -332,6 +300,68 @@ std::ostream& print_sequence(std::ostream& os,
   return os;
 }
 
+template<typename T1, typename T2>
+std::ostream& operator<<(std::ostream& os, const std::pair<T1, T2> p) {
+  os << "(" << p.first << ", " << p.second << ")";
+  return os;
+}
+
+template<typename Range>
+std::ostream& print_range(std::ostream& os, const Range& r,
+                          const char* pre,
+                          const char* post,
+                          const char* sep) {
+  return print_sequence(os, r.begin(), r.end(), pre, post, sep);
+}
+
+template<typename T>
+std::ostream& operator<<(std::ostream& os, const std::vector<T>& vec) {
+  print_sequence(os, vec.begin(), vec.end(), "[", "]", ", ");
+  return os;
+}
+
+template<typename T>
+std::ostream& operator<<(std::ostream& os, const std::list<T>& list) {
+  os << '[';
+  print_sequence(os, list.begin(), list.end(), "[", "]", ", ");
+  os << '[';
+  return os;
+}
+
+template<typename T>
+std::ostream& operator<<(std::ostream& os, const std::set<T>& set) {
+  print_sequence(os, set.begin(), set.end(), "{", "}", ", ");
+  return os;
+}
+
+template<typename T>
+std::ostream& operator<<(std::ostream& os, const std::multiset<T>& set) {
+  print_sequence(os, set.begin(), set.end(), "m{", "}m", ", ");
+  return os;
+}
+
+template<typename K, typename T>
+std::ostream& operator<<(std::ostream& os, const std::map<K, T>& map) {
+  print_sequence(os, map.begin(), map.end(), "{", "}", ", ");
+  return os;
+}
+
+template<typename K, typename T>
+std::ostream& operator<<(std::ostream& os, const std::multimap<K, T>& map) {
+  print_sequence(os, map.begin(), map.end(), "m{", "}m", ", ");
+  return os;
+}
+
+template<typename T>
+std::ostream& operator<<(std::ostream& os, const internal::Maybe<T>& m) {
+  if (m) {
+    os << "Just(" << m.val << ")";
+  } else {
+    os << "Nothing";
+  }
+  return os;
+}
+
 }  // namespace format
 }  // namespace lela
 
diff --git a/src/lela/formula.h b/src/lela/formula.h
index 9b3fa360b8f27d1eb060ac0a3cf790bd767e1a8a..fd9fde04c3ab8bebf0fee9715316d205b0b9bfbd 100644
--- a/src/lela/formula.h
+++ b/src/lela/formula.h
@@ -38,6 +38,14 @@ class Formula {
    public:
     enum Type { kClause, kNot, kOr, kExists };
 
+    // XXX The implicit operator= sometimes (in cli) takes a non-const reference. Why?!
+    Element& operator=(const Element& e) {
+      type_ = e.type_;
+      clause_ = e.clause_;
+      var_ = e.var_;
+      return *this;
+    }
+
     static Element Clause(const lela::Clause& c) { return Element(kClause, c); }
     static Element Not() { return Element(kNot); }
     static Element Or() { return Element(kOr); }
@@ -231,6 +239,10 @@ class Formula {
     Iter end_;
   };
 
+  Formula(Formula&&) = default;
+  Formula(const Formula&) = default;
+  Formula& operator=(const Formula&) = default;
+
   static Formula Clause(const lela::Clause& c) { return Atomic(Element::Clause(c)); }
   static Formula Not(const Formula& phi) { return Unary(Element::Not(), phi); }
   static Formula Or(const Formula& phi, const Formula& psi) { return Binary(Element::Or(), phi, psi); }
diff --git a/src/lela/solver.h b/src/lela/solver.h
index 1640f79f7c449b28c0d573a9a66cba736fa7c754..e698cf1e1814dcb71d7ec58943c266f97da2a69e 100644
--- a/src/lela/solver.h
+++ b/src/lela/solver.h
@@ -266,10 +266,10 @@ class Solver {
         }
       }
       case Formula::Element::kOr: {
-        Formula left = Formula::Not(phi.left().Build());
-        Formula right = Formula::Not(phi.right().Build());
-        return Reduce(s, names, left.reader()) ||
-               Reduce(s, names, right.reader());
+        Formula::Reader<T> left = phi.left();
+        Formula::Reader<T> right = phi.right();
+        return Reduce(s, names, left) ||
+               Reduce(s, names, right);
       }
       case Formula::Element::kExists: {
         const Term x = phi.head().var().val;