/***********************************************************************************[SimpSolver.cc]
 The MIT License (MIT)

 Copyright (c) 2014, 	 Sam Bayless
 Copyright (c) 2006,      Niklas Een, Niklas Sorensson
 Copyright (c) 2007-2010, Niklas Sorensson

 Permission is hereby granted, free of charge, to any person obtaining a copy of this software and
 associated documentation files (the "Software"), to deal in the Software without restriction,
 including without limitation the rights to use, copy, modify, merge, publish, distribute,
 sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is
 furnished to do so, subject to the following conditions:

 The above copyright notice and this permission notice shall be included in all copies or
 substantial portions of the Software.

 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT
 NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
 NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM,
 DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT
 OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 **************************************************************************************************/

#include "monosat/simp/SimpSolver.h"

using namespace Monosat;

//=================================================================================================
// Options:

static const char* _cat = "SIMP";

static BoolOption opt_use_asymm(_cat, "asymm", "Shrink clauses by asymmetric branching.", false);
static BoolOption opt_use_rcheck(_cat, "rcheck", "Check if a clause is already implied. (costly)", false);
static BoolOption opt_use_elim(_cat, "elim", "Perform variable elimination.", true);
static IntOption opt_grow(_cat, "grow", "Allow a variable elimination step to grow by a number of clauses.", 0);
static IntOption opt_clause_lim(_cat, "cl-lim",
                                "Variables are not eliminated if it produces a resolvent with a length above this limit. -1 means no limit",
                                20,
                                IntRange(-1, INT32_MAX));
static IntOption opt_subsumption_lim(_cat, "sub-lim",
                                     "Do not check if subsumption against a clause larger than this. -1 means no limit.",
                                     1000,
                                     IntRange(-1, INT32_MAX));
static DoubleOption opt_simp_garbage_frac(_cat, "monosat/simp-gc-frac",
                                          "The fraction of wasted memory allowed before a garbage collection is triggered during simplification.",
                                          0.5,
                                          DoubleRange(0, false, HUGE_VAL, false));

//=================================================================================================
// Constructor/Destructor:

SimpSolver::SimpSolver() :
        grow(opt_grow), clause_lim(opt_clause_lim), subsumption_lim(opt_subsumption_lim), simp_garbage_frac(
        opt_simp_garbage_frac), use_asymm(opt_use_asymm), use_rcheck(opt_use_rcheck), use_elim(opt_use_elim), merges(
        0), asymm_lits(0), eliminated_vars(0), elimorder(1), use_simplification(true), occurs(
        ClauseDeleted(ca)), elim_heap(ElimLt(n_occ)), bwdsub_assigns(0), n_touched(0){
    vec<Lit> dummy(1, lit_Undef);
    ca.extra_clause_field = true; // NOTE: must happen before allocating the dummy clause below.
    bwdsub_tmpunit = ca.alloc(dummy);
    remove_satisfied = false;
}

SimpSolver::~SimpSolver(){
}

Var SimpSolver::newVar(bool sign, bool dvar){
    Var v = Solver::newVar(sign, dvar);

    frozen.growTo(v + 1, (char) false);
    frozen[v] = (char) false;

    eliminated.growTo(v + 1, (char) false);
    eliminated[v] = (char) false;

    if(use_simplification){
        Lit l = mkLit(v);
        n_occ.growTo(toInt(l) + 2, 0);
        n_occ[toInt(l)] = 0;
        n_occ[toInt(~l)] = 0;
        occurs.init(v);
        touched.growTo(v + 1, 0);
        touched[v] = 0;
        elim_heap.insert(v);
    }
    return v;
}

void SimpSolver::releaseVar(Lit l){
    assert(!isFrozen(var(l)));
    assert(!isEliminated(var(l)));
    if(!use_simplification && var(l) >= max_simp_var && !hasTheory(l))
        // Note: Guarantees that no references to this variable is
        // left in model extension datastructure. Could be improved!
        Solver::releaseVar(l);
    else
        // Otherwise, don't allow variable to be reused.
        Solver::addClause(l);
}

bool SimpSolver::propagateAssignment(const vec<Lit>& assumps){
    only_propagate_assumptions = true;
    budgetOff();
    assumps.copyTo(assumptions);
    lbool val = solve_(false, false);
    only_propagate_assumptions = false;
    return val == l_True;
}

lbool SimpSolver::solve_(bool do_simp, bool turn_off_simp){
    vec<Var> extra_frozen;
    lbool result = l_True;
    clearInterrupt();
    cancelUntil(0);
    do_simp &= ok && use_simplification;
    if(do_simp){
        if(pbsolver){
            pbsolver->convert();
        }
        // Assumptions must be temporarily frozen to run variable elimination:
        for(int i = 0; i < assumptions.size(); i++){
            Var v = var(assumptions[i]);

            // If an assumption has been eliminated, remember it.
            assert(!isEliminated(v));

            if(!frozen[v]){
                // Freeze and store.
                setFrozen(v, true);
                extra_frozen.push(v);
            }
        }

        result = lbool(eliminate(turn_off_simp));
    }

    if(result == l_True)
        result = Solver::solve_();
    else if(verbosity >= 1)
        printf("===============================================================================\n");

    if(result == l_True)
        extendModel();

    if(do_simp)
        // Unfreeze the assumptions that were frozen:
        for(int i = 0; i < extra_frozen.size(); i++)
            setFrozen(extra_frozen[i], false);

    return result;
}

bool SimpSolver::addClause_(vec<Lit>& ps, bool is_derived_clause){
#ifdef DEBUG_CORE
    for(int i = 0; i < ps.size(); i++)
        assert(!isEliminated(var(ps[i])));
#endif

    int nclauses = clauses.size();

    if(use_rcheck && implied(ps))
        return true;

    if(!Solver::addClause_(ps, is_derived_clause))
        return false;

    if(use_simplification && clauses.size() == nclauses + 1){
        CRef cr = clauses.last();
        const Clause& c = ca[cr];

        // NOTE: the clause is added to the queue immediately and then
        // again during 'gatherTouchedClauses()'. If nothing happens
        // in between, it will only be checked once. Otherwise, it may
        // be checked twice unnecessarily. This is an unfortunate
        // consequence of how backward subsumption is used to mimic
        // forward subsumption.
        subsumption_queue.insert(cr);
        for(int i = 0; i < c.size(); i++){
            occurs[var(c[i])].push(cr);
            n_occ[toInt(c[i])]++;
            touched[var(c[i])] = 1;
            n_touched++;
            if(elim_heap.inHeap(var(c[i])))
                elim_heap.increase(var(c[i]));
        }
    }

    return true;
}

void SimpSolver::removeClause(CRef cr){
    const Clause& c = ca[cr];
    if(use_simplification)
        for(int i = 0; i < c.size(); i++){
            n_occ[toInt(c[i])]--;
            updateElimHeap(var(c[i]));
            occurs.smudge(var(c[i]));
        }

    Solver::removeClause(cr);
}

bool SimpSolver::strengthenClause(CRef cr, Lit l){
    //assert(qhead==trail.size());
    Clause& c = ca[cr];
    assert(decisionLevel() == 0);
    assert(use_simplification);

    // FIX: this is too inefficient but would be nice to have (properly implemented)
    // if (!find(subsumption_queue, &c))
    subsumption_queue.insert(cr);

    if(c.size() == 2){
        removeClause(cr);
        c.strengthen(l);
    }else{
        detachClause(cr, true);
        int size = c.size();
        //remove any false lits from this clause
        for(int i = 0; i < c.size(); i++){
            Lit lit = c[i];
            if(lit != l){
                if(value(lit) == l_False){
                    size--;
                    i--;
                    c.strengthen(lit);    //can do this more efficiently, obviously...
                }else if(value(lit) == l_True){
                    size = -1;
                    removeClause(cr);
                    break;
                }
            }
        }
        if(size == -1){
            return true;
        }else if(size == 0){
            ok = false;
            return false;
        }else if(size == 1){
            ok = false;
            c.strengthen(l);
            return false;
        }else if(size == 2){
            removeClause(cr);
            c.strengthen(l);
        }else{
            c.strengthen(l);
            attachClause(cr);
            remove(occurs[var(l)], cr);
            n_occ[toInt(l)]--;
            updateElimHeap(var(l));
        }
    }

    return c.size() == 1 ?
           enqueue(c[0]) &&
           propagate(!disable_theories && opt_propagate_theories_during_simplification) == CRef_Undef && ok : true;
}

// Returns FALSE if clause is always satisfied ('out_clause' should not be used).
bool SimpSolver::merge(const Clause& _ps, const Clause& _qs, Var v, vec<Lit>& out_clause){
    merges++;
    out_clause.clear();

    bool ps_smallest = _ps.size() < _qs.size();
    const Clause& ps = ps_smallest ? _qs : _ps;
    const Clause& qs = ps_smallest ? _ps : _qs;

    for(int i = 0; i < qs.size(); i++){
        if(var(qs[i]) != v){
            for(int j = 0; j < ps.size(); j++)
                if(var(ps[j]) == var(qs[i])){
                    if(ps[j] == ~qs[i])
                        return false;
                    else
                        goto next;
                }
            out_clause.push(qs[i]);
        }
        next:;
    }

    for(int i = 0; i < ps.size(); i++)
        if(var(ps[i]) != v)
            out_clause.push(ps[i]);

    return true;
}

// Returns FALSE if clause is always satisfied.
bool SimpSolver::merge(const Clause& _ps, const Clause& _qs, Var v, int& size){
    merges++;

    bool ps_smallest = _ps.size() < _qs.size();
    const Clause& ps = ps_smallest ? _qs : _ps;
    const Clause& qs = ps_smallest ? _ps : _qs;
    const Lit* __ps = (const Lit*) ps;
    const Lit* __qs = (const Lit*) qs;

    size = ps.size() - 1;

    for(int i = 0; i < qs.size(); i++){
        if(var(__qs[i]) != v){
            for(int j = 0; j < ps.size(); j++)
                if(var(__ps[j]) == var(__qs[i])){
                    if(__ps[j] == ~__qs[i])
                        return false;
                    else
                        goto next;
                }
            size++;
        }
        next:;
    }

    return true;
}

void SimpSolver::gatherTouchedClauses(){
    if(n_touched == 0)
        return;

    int i, j;
    for(i = j = 0; i < subsumption_queue.size(); i++)
        if(ca[subsumption_queue[i]].mark() == 0)
            ca[subsumption_queue[i]].mark(2);

    for(i = 0; i < touched.size(); i++)
        if(touched[i]){
            const vec<CRef>& cs = occurs.lookup(i);
            for(j = 0; j < cs.size(); j++)
                if(ca[cs[j]].mark() == 0){
                    subsumption_queue.insert(cs[j]);
                    ca[cs[j]].mark(2);
                }
            touched[i] = 0;
        }

    for(i = 0; i < subsumption_queue.size(); i++)
        if(ca[subsumption_queue[i]].mark() == 2)
            ca[subsumption_queue[i]].mark(0);

    n_touched = 0;
}

bool SimpSolver::implied(const vec<Lit>& c){
    assert(decisionLevel() == 0);

    trail_lim.push(trail.size());
    for(int i = 0; i < c.size(); i++)
        if(value(c[i]) == l_True){
            cancelUntil(0);
            return false;
        }else if(value(c[i]) != l_False){
            assert(value(c[i]) == l_Undef);
            uncheckedEnqueue(~c[i]);
        }

    bool result = propagate(!disable_theories && opt_propagate_theories_during_simplification) != CRef_Undef;
    cancelUntil(0);
    return result;
}

// Backward subsumption + backward subsumption resolution
bool SimpSolver::backwardSubsumptionCheck(bool verbose){
    int cnt = 0;
    int subsumed = 0;
    int deleted_literals = 0;
    assert(decisionLevel() == 0);

    while(subsumption_queue.size() > 0 || bwdsub_assigns < trail.size()){

        // Empty subsumption queue and return immediately on user-interrupt:
        if(asynch_interrupt){
            subsumption_queue.clear();
            bwdsub_assigns = trail.size();
            break;
        }

        // Check top-level assignments by creating a dummy clause and placing it in the queue:
        if(subsumption_queue.size() == 0 && bwdsub_assigns < trail.size()){
            Lit l = trail[bwdsub_assigns++];
            ca[bwdsub_tmpunit][0] = l;
            ca[bwdsub_tmpunit].calcAbstraction();
            subsumption_queue.insert(bwdsub_tmpunit);
        }

        CRef cr = subsumption_queue.peek();
        subsumption_queue.pop();
        Clause& c = ca[cr];

        if(c.mark())
            continue;

        if(verbose && verbosity >= 2 && cnt++ % 1000 == 0)
            printf("subsumption left: %10d (%10d subsumed, %10d deleted literals)\r", subsumption_queue.size(),
                   subsumed, deleted_literals);

        assert(c.size() > 1 || value(c[0]) == l_True);    // Unit-clauses should have been propagated before this point.

        // Find best variable to scan:
        Var best = var(c[0]);
        for(int i = 1; i < c.size(); i++)
            if(occurs[var(c[i])].size() < occurs[best].size())
                best = var(c[i]);

        // Search all candidates:
        vec<CRef>& _cs = occurs.lookup(best);
        CRef* cs = (CRef*) _cs;

        for(int j = 0; j < _cs.size(); j++)
            if(c.mark())
                break;
            else if(!ca[cs[j]].mark() && cs[j] != cr
                    && (subsumption_lim == -1 || ca[cs[j]].size() < subsumption_lim)){
                Lit l = c.subsumes(ca[cs[j]]);

                if(l == lit_Undef)
                    subsumed++, removeClause(cs[j]);
                else if(l != lit_Error){
                    deleted_literals++;

                    if(!strengthenClause(cs[j], ~l))
                        return false;

                    // Did current candidate get deleted from cs? Then check candidate at index j again:
                    if(var(l) == best)
                        j--;
                }
            }
    }

    return true;
}

bool SimpSolver::asymm(Var v, CRef cr){
    Clause& c = ca[cr];
    assert(decisionLevel() == 0);

    if(c.mark() || satisfied(c))
        return true;

    trail_lim.push(trail.size());
    Lit l = lit_Undef;
    for(int i = 0; i < c.size(); i++)
        if(var(c[i]) != v && value(c[i]) != l_False)
            uncheckedEnqueue(~c[i]);
        else
            l = c[i];

    if(propagate(!disable_theories && opt_propagate_theories_during_simplification) != CRef_Undef){
        cancelUntil(0);
        asymm_lits++;
        if(!strengthenClause(cr, l))
            return false;
    }else
        cancelUntil(0);

    return true;
}

bool SimpSolver::asymmVar(Var v){
    assert(use_simplification);

    const vec<CRef>& cls = occurs.lookup(v);

    if(value(v) != l_Undef || cls.size() == 0)
        return true;

    for(int i = 0; i < cls.size(); i++)
        if(!asymm(v, cls[i]))
            return false;

    return backwardSubsumptionCheck();
}

static void mkElimClause(vec<uint32_t>& elimclauses, Lit x){
    elimclauses.push(toInt(x));
    elimclauses.push(1);
}

static void mkElimClause(vec<uint32_t>& elimclauses, Var v, Clause& c){
    int first = elimclauses.size();
    int v_pos = -1;

    // Copy clause to elimclauses-vector. Remember position where the
    // variable 'v' occurs:
    for(int i = 0; i < c.size(); i++){
        elimclauses.push(toInt(c[i]));
        if(var(c[i]) == v)
            v_pos = i + first;
    }
    assert(v_pos != -1);

    // Swap the first literal with the 'v' literal, so that the literal
    // containing 'v' will occur first in the clause:
    uint32_t tmp = elimclauses[v_pos];
    elimclauses[v_pos] = elimclauses[first];
    elimclauses[first] = tmp;

    // Store the length of the clause last:
    elimclauses.push(c.size());
}

bool SimpSolver::eliminateVar(Var v){
    assert(!frozen[v]);
    assert(!isEliminated(v));
    assert(value(v) == l_Undef);
    // Split the occurrences into positive and negative:
    //
    const vec<CRef>& cls = occurs.lookup(v);
    vec<CRef> pos, neg;
    for(int i = 0; i < cls.size(); i++)
        (find(ca[cls[i]], mkLit(v)) ? pos : neg).push(cls[i]);

    // Check wether the increase in number of clauses stays within the allowed ('grow'). Moreover, no
    // clause must exceed the limit on the maximal clause size (if it is set):
    //
    int cnt = 0;
    int clause_size = 0;

    for(int i = 0; i < pos.size(); i++)
        for(int j = 0; j < neg.size(); j++)
            if(merge(ca[pos[i]], ca[neg[j]], v, clause_size)
               && (++cnt > cls.size() + grow || (clause_lim != -1 && clause_size > clause_lim)))
                return true;

    // Delete and store old clauses:
    eliminated[v] = true;
    setDecisionVar(v, false);
    eliminated_vars++;

    if(pos.size() > neg.size()){
        for(int i = 0; i < neg.size(); i++)
            mkElimClause(elimclauses, v, ca[neg[i]]);
        mkElimClause(elimclauses, mkLit(v));
    }else{
        for(int i = 0; i < pos.size(); i++)
            mkElimClause(elimclauses, v, ca[pos[i]]);
        mkElimClause(elimclauses, ~mkLit(v));
    }
    bool all_derived = true;
    for(int i = 0; i < cls.size(); i++){
        all_derived &= ca[cls[i]].derivedClause();
        removeClause(cls[i]);
    }
    // Produce clauses in cross product:
    vec<Lit>& resolvent = add_tmp;
    for(int i = 0; i < pos.size(); i++)
        for(int j = 0; j < neg.size(); j++)
            if(merge(ca[pos[i]], ca[neg[j]], v, resolvent) &&
               !addClause_(resolvent, all_derived))//should this clause always be treated as derived?
                return false;

    // Free occurs list for this variable:
    occurs[v].clear(true);

    // Free watchers lists for this variable, if possible:
    if(watches[mkLit(v)].size() == 0)
        watches[mkLit(v)].clear(true);
    if(watches[~mkLit(v)].size() == 0)
        watches[~mkLit(v)].clear(true);

    return backwardSubsumptionCheck();
}

bool SimpSolver::substitute(Var v, Lit x){
    assert(!frozen[v]);
    assert(!isEliminated(v));
    assert(value(v) == l_Undef);

    if(!ok)
        return false;

    eliminated[v] = true;
    setDecisionVar(v, false);
    const vec<CRef>& cls = occurs.lookup(v);

    vec<Lit>& subst_clause = add_tmp;
    for(int i = 0; i < cls.size(); i++){
        Clause& c = ca[cls[i]];

        subst_clause.clear();
        for(int j = 0; j < c.size(); j++){
            Lit p = c[j];
            subst_clause.push(var(p) == v ? x ^ sign(p) : p);
        }

        removeClause(cls[i]);

        if(!addClause_(subst_clause))//should this clause be treated as derived?
            return (ok = false);
    }

    return true;
}

void SimpSolver::extendModel(){
    int i, j;
    Lit x;

    for(i = elimclauses.size() - 1; i > 0; i -= j){
        for(j = elimclauses[i--]; j > 1; j--, i--)
            if(modelValue(toLit(elimclauses[i])) != l_False)
                goto next;

        x = toLit(elimclauses[i]);
        model[var(x)] = lbool(!sign(x));
        next:;
    }
}

void SimpSolver::disablePreprocessing(){
    if(use_simplification){
        touched.clear(true);
        occurs.clear(true);
        n_occ.clear(true);
        elim_heap.clear(true);
        subsumption_queue.clear(true);

        use_simplification = false;
        max_simp_var = nVars();
        remove_satisfied = true;
        ca.extra_clause_field = false;

        // Force full cleanup (this is safe and desirable since it only happens once):
        rebuildOrderHeap();
        garbageCollect();
    }
}

bool SimpSolver::eliminate(bool turn_off_elim){
    for(int i = 0; i < qhead; i++){
        Lit p = trail[i];
        if(hasTheory(p)){
            for(int n = 0; n < getNTheories(var(p)); n++){
                int theoryID = getTheoryID(p, n);
                Lit l = getTheoryLit(p, n);
                theories[theoryID]->enqueueTheory(l);
            }
        }
    }

    if(!simplify()){
        if(turn_off_elim){
            disablePreprocessing();
        }
        return false;
    }else if(!use_simplification)
        return true;



    // Main simplification loop:
    //
    while(n_touched > 0 || bwdsub_assigns < trail.size() || elim_heap.size() > 0){

        gatherTouchedClauses();
        // printf("  ## (time = %6.2f s) BWD-SUB: queue = %d, trail = %d\n", cpuTime(), subsumption_queue.size(), trail.size() - bwdsub_assigns);
        if((subsumption_queue.size() > 0 || bwdsub_assigns < trail.size()) && !backwardSubsumptionCheck(true)){
            ok = false;
            goto cleanup;
        }

        // Empty elim_heap and return immediately on user-interrupt:
        if(asynch_interrupt){
            assert(bwdsub_assigns == trail.size());
            assert(subsumption_queue.size() == 0);
            assert(n_touched == 0);
            elim_heap.clear();
            goto cleanup;
        }

        // printf("  ## (time = %6.2f s) ELIM: vars = %d\n", cpuTime(), elim_heap.size());
        for(int cnt = 0; !elim_heap.empty(); cnt++){
            Var elim = elim_heap.removeMin();

            if(asynch_interrupt)
                break;

            if(isEliminated(elim) || value(elim) != l_Undef)
                continue;

            if(verbosity >= 2 && cnt % 100 == 0)
                printf("elimination left: %10d\r", elim_heap.size());

            if(use_asymm){
                // Temporarily freeze variable. Otherwise, it would immediately end up on the queue again:
                bool was_frozen = frozen[elim];
                frozen[elim] = true;
                if(!asymmVar(elim)){
                    ok = false;
                    goto cleanup;
                }
                frozen[elim] = was_frozen;
            }

            // At this point, the variable may have been set by assymetric branching, so check it
            // again. Also, don't eliminate frozen variables:
            if(use_elim && value(elim) == l_Undef && !frozen[elim] && !eliminateVar(elim)){
                ok = false;
                goto cleanup;
            }

            checkGarbage(simp_garbage_frac);
        }

        assert(subsumption_queue.size() == 0);
    }
    cleanup:

    // If no more simplification is needed, free all simplification-related data structures:
    if(turn_off_elim){
        disablePreprocessing();
    }else{
        // Cheaper cleanup:
        cleanUpClauses(); // TODO: can we make 'cleanUpClauses()' not be linear in the problem size somehow?
        checkGarbage();
    }

    if(verbosity >= 1 && elimclauses.size() > 0)
        printf("|  Eliminated clauses:     %10.2f Mb                                      |\n",
               double(elimclauses.size() * sizeof(uint32_t)) / (1024 * 1024));

    return ok;
}

void SimpSolver::cleanUpClauses(){
    occurs.cleanAll();
    int i, j;
    for(i = j = 0; i < clauses.size(); i++)
        if(ca[clauses[i]].mark() == 0)
            clauses[j++] = clauses[i];
    clauses.shrink(i - j);
}

//=================================================================================================
// Garbage Collection methods:

void SimpSolver::relocAll(ClauseAllocator& to){
    if(!use_simplification)
        return;

    // All occurs lists:
    //
    for(int i = 0; i < nVars(); i++){
        vec<CRef>& cs = occurs[i];
        for(int j = 0; j < cs.size(); j++)
            ca.reloc(cs[j], to);
    }

    // Subsumption queue:
    //
    for(int i = 0; i < subsumption_queue.size(); i++)
        ca.reloc(subsumption_queue[i], to);

    // Temporary clause:
    //
    ca.reloc(bwdsub_tmpunit, to);
}

void SimpSolver::garbageCollect(){
    // Initialize the next region to a size corresponding to the estimated utilization degree. This
    // is not precise but should avoid some unnecessary reallocations for the new region:
    ClauseAllocator to(ca.size() - ca.wasted());

    cleanUpClauses();
    to.extra_clause_field = ca.extra_clause_field; // NOTE: this is important to keep (or lose) the extra fields.
    relocAll(to);
    Solver::relocAll(to);
    if(verbosity >= 2)
        printf("|  Garbage collection:   %12d bytes => %12d bytes             |\n",
               ca.size() * ClauseAllocator::Unit_Size, to.size() * ClauseAllocator::Unit_Size);
    to.moveTo(ca);
}
