Naïve external sort in C#

DirtyMergeSort.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.IO;

namespace DirtyMergeSort
{
    public static class Program
    {
        public static void Main(string[] args)
        {
            File.WriteAllLines(@"d:\sorted.txt",
                File.ReadLines(@"d:\data.txt")
                    .Select(Progress("read"))
                    .Sorted(1000000)
                    .Select(Progress("write")));
        }

        private static Func<string, int, string> Progress(string type)
        {
            return (x, i) =>
            {
                if (i % 100000 == 0) Console.WriteLine("{0}: {1}", type, i);
                return x;
            };
        }

        public static IEnumerable<string> Sorted(this IEnumerable<string> lines, int size)
        {
            var files = lines.Partition(size)
                .Select(x=>new {File = x, Lines = File.ReadLines(x).GetEnumerator()})
                .Where(x=>x.Lines.MoveNext())
                .ToList();

            while (files.Any())
            {
                var current = files.Min(x => x.Lines.Current);
                yield return current;

                files = files.Where(x =>
                {
                    while (x.Lines.Current == current)
                    {
                        if (!x.Lines.MoveNext())
                        {
                            File.Delete(x.File);
                            Console.WriteLine("Deleted file {0}", x.File);
                            return false;
                        }
                    }
                    return true;
                }).ToList();
            }

        }

        public static IEnumerable<string> Partition(this IEnumerable<string> lines, int size)
        {
            return lines.Batch(size)
                .AsParallel()
                .WithMergeOptions(ParallelMergeOptions.NotBuffered)
                .Select(batch =>
                {
                    var temp = Path.GetTempFileName();
                    File.WriteAllLines(temp, batch.OrderBy(x=>x));
                    Console.WriteLine("Wrote file {0}", temp);
                    return temp;
                });
        }

        public static IEnumerable<List<T>> Batch<T>(this IEnumerable<T> collection, int size)
        {
            var batch = new List<T>(size);
            foreach (T item in collection)
            {
                batch.Add(item);
                if (batch.Count == size)
                {
                    yield return batch;
                    batch = new List<T>(size);
                }
            }
            if (batch.Any())
                yield return batch;
        }
    }
}