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diff --git a/src/expr/proof_step_buffer.cpp b/src/expr/proof_step_buffer.cpp
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+/*********************                                                        */
+/*! \file proof_step_buffer.cpp
+ ** \verbatim
+ ** Top contributors (to current version):
+ **   Andrew Reynolds
+ ** This file is part of the CVC4 project.
+ ** Copyright (c) 2009-2020 by the authors listed in the file AUTHORS
+ ** in the top-level source directory) and their institutional affiliations.
+ ** All rights reserved.  See the file COPYING in the top-level source
+ ** directory for licensing information.\endverbatim
+ **
+ ** \brief Implementation of proof step and proof step buffer utilities.
+ **/
+
+#include "expr/proof_step_buffer.h"
+
+using namespace CVC4::kind;
+
+namespace CVC4 {
+
+ProofStep::ProofStep() : d_rule(PfRule::UNKNOWN) {}
+ProofStep::ProofStep(PfRule r,
+                     const std::vector<Node>& children,
+                     const std::vector<Node>& args)
+    : d_rule(r), d_children(children), d_args(args)
+{
+}
+std::ostream& operator<<(std::ostream& out, ProofStep step)
+{
+  out << "(step " << step.d_rule;
+  for (const Node& c : step.d_children)
+  {
+    out << " " << c;
+  }
+  if (!step.d_args.empty())
+  {
+    out << " :args";
+    for (const Node& a : step.d_args)
+    {
+      out << " " << a;
+    }
+  }
+  out << ")";
+  return out;
+}
+
+ProofStepBuffer::ProofStepBuffer(ProofChecker* pc) : d_checker(pc) {}
+
+Node ProofStepBuffer::tryStep(PfRule id,
+                              const std::vector<Node>& children,
+                              const std::vector<Node>& args,
+                              Node expected)
+{
+  if (d_checker == nullptr)
+  {
+    Assert(false) << "ProofStepBuffer::ProofStepBuffer: no proof checker.";
+    return Node::null();
+  }
+  Node res =
+      d_checker->checkDebug(id, children, args, expected, "pf-step-buffer");
+  if (!res.isNull())
+  {
+    // add proof step
+    d_steps.push_back(
+        std::pair<Node, ProofStep>(res, ProofStep(id, children, args)));
+  }
+  return res;
+}
+
+void ProofStepBuffer::addStep(PfRule id,
+                              const std::vector<Node>& children,
+                              const std::vector<Node>& args,
+                              Node expected)
+{
+  d_steps.push_back(
+      std::pair<Node, ProofStep>(expected, ProofStep(id, children, args)));
+}
+
+void ProofStepBuffer::addSteps(ProofStepBuffer& psb)
+{
+  const std::vector<std::pair<Node, ProofStep>>& steps = psb.getSteps();
+  for (const std::pair<Node, ProofStep>& step : steps)
+  {
+    addStep(step.second.d_rule,
+            step.second.d_children,
+            step.second.d_args,
+            step.first);
+  }
+}
+
+void ProofStepBuffer::popStep()
+{
+  Assert(!d_steps.empty());
+  if (!d_steps.empty())
+  {
+    d_steps.pop_back();
+  }
+}
+
+size_t ProofStepBuffer::getNumSteps() const { return d_steps.size(); }
+
+const std::vector<std::pair<Node, ProofStep>>& ProofStepBuffer::getSteps() const
+{
+  return d_steps;
+}
+
+void ProofStepBuffer::clear() { d_steps.clear(); }
+
+}  // namespace CVC4