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I'm using a Cartesian Kernel. I have been trying to test with
Exact_predicates_exact_constructions_kernel in this code, but it gives me some
errors that I haven't could solucionate yet.

That's my code:

//The head:
typedef CGAL::Cartesian<CGAL::Gmpq> Kernel;
typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
typedef CGAL::Nef_polyhedron_3<Kernel> Nef_polyhedron;

//The functions:
bool SaveOFF( char* filename, Polyhedron &aux )
{
        const char*  name = "cout";
        ostream*  p_out = &cout;
        ofstream  out;

        out.open( filename );
        p_out = &out;
        name = filename;
        if ( !*p_out ) return false;
        CGAL::set_ascii_mode( *p_out );
        (*p_out ) << aux;
        if ( !*p_out ) return false;
        return true;
}

bool ReadOFF( char* filename, Polyhedron &P )
{
        const char*  name = "cin";
        istream*     p_in = &cin;
        ifstream     in;

        in.open( filename);
        p_in = &in;
        name = filename;
        if ( !*p_in ) return false;
        (*p_in ) >> P;
        if ( !*p_in ) return false;
        return true;
}
//typedef Nef2Mesh<Kernel,Nef_polyhedron> MyNef2Mesh;

//****************************************************************************************

void TEST3()
{

        FILE *fich1,*fich2;
        Polyhedron P1,P2,SOL1;


        ReadOFF( "c:\\temp\\diff1.off", P1 );
        Nef_polyhedron N1( P1 );

        ReadOFF( "c:\\temp\\diff2.off", P2 );
        Nef_polyhedron N2( P2 );

        Nef_polyhedron N_sol;

        clock_t times[ 10 ];

        times[ 0 ] = clock( );

        N_sol = N1 - N2;

        times[ 1 ] = clock( );
        cout << "La diferencia ha durado: " << ( float )( times[ 1 ] - times[ 0
] ) / CLOCKS_PER_SEC << endl;

        fich1 = fopen( "c:\\temp\\caja1.off" ,"w" );
                
        if(N_sol.is_simple()) {
                N_sol.convert_to_Polyhedron( SOL1 );
        }
        else {
                fstream fs("c:\\temp\\caja1.off", ios::in | ios::out |
ios::trunc);
                fs << N_sol;
                fs.close();
        }

        SaveOFF( "c:\\temp\\solution2.off", SOL1 );
}
//The main:
int main( int argc, char **argv) 
{
        TEST3( );

        getchar( );

    return 0;
}


//-----------------------------------------------------

And here we are the two balls:
OFF
1627 3250 0

-386.887 150.288 -13.2468
-383.348 147.95 -15.9947
-385.68 144.401 -14.2008
-388.514 146.81 -11.908
-400.378 143.309 5.11721
-400.691 148.499 5.60586
-399.15 148.38 2.06703
-401.87 145.944 8.9095
-400.948 149.166 39.6836
-400.762 144.832 40.1094
-399.197 148.66 43.7863
-399.129 145.134 43.8635
-388.643 147.423 57.8135
-385.758 144.298 60.1324
-386.234 148.36 59.8172
-383.063 147.646 62.1938
-379.109 145.047 64.4889
-378.449 148.838 64.8509
-370.527 145.999 -22.0489
-369.58 149.792 -22.2462
-366.82 146.701 -22.9855
-387.808 142.32 -12.2988
-391.006 146.883 -9.56544
-393.97 143.428 -5.92109
-393.998 147.888 -6.06821
-396.799 147.138 -2.11039
-398.37 143.121 0.865172
-402.603 143.194 12.1474
-402.748 146.836 12.0449
-403.327 142.719 15.885
-403.573 146.983 16.2609
-403.809 144.069 19.7682
-403.984 147.054 20.66
-403.887 143.255 23.0736
-404.025 146.941 23.7702
-403.736 143.637 27.2688
-403.844 147.164 27.4315
-403.047 144.453 32.4303
-403.161 146.736 32.1873
-401.918 145.198 36.8746
-396.831 145.274 48.016
-394.342 144.671 51.5013
-393.984 147.641 52.1123
-391.236 143.738 55.1189
-390.895 147.502 55.605
-375.07 146.207 66.4434
-363.251 144.621 69.5673
-358.428 147.043 70.0588
-362.291 148.787 69.6935
-381 144.184 -17.403
-396.086 141.537 -2.59681
-401.473 142.295 8.4286
-397.3 141.255 46.6302
-388.23 143.231 57.9656
-403.435 140.208 19.7177
-402.674 139.431 31.5472
-403.213 139.048 27.2386
-401.672 139.638 35.9058
-400.535 140.699 39.7121
-399.221 141.051 42.877
-394.059 140.251 51.2714
-382 142.26 62.5993
-366.648 143.23 -22.9018
-363.573 146.829 -23.5789
-390.597 141.271 -9.42091
-402.213 139.899 12.1648
-400.499 137.683 7.52484
-403.388 139.113 23.1785
-366.958 148.908 68.9849
-367.9 144.552 68.7254
-371.546 142.942 -21.5541
-374.811 146.043 -20.534
-393.169 139.411 -6.15304
-397.451 139.306 0.263241
-398.768 137.674 3.39784
-402.77 138.627 16.1059
-390.416 139.99 55.3671
-372.534 143.556 67.2635
-371.699 147.383 67.6751
-374.395 141.503 -20.3606
-377.441 145.51 -19.3651
-380.546 140.641 -17.2272
-383.418 141.017 -15.4436
-387.768 140.111 57.9008
-385.447 140.834 59.9313
-376.988 140.853 65.1897
-395.914 136.531 -1.35784
-401.607 136.656 12.2318
-402.259 136.134 16.1025
-402.608 136.006 19.7723
-398.535 137.357 42.8377
-399.626 136.713 40.0001
-396.486 137.417 46.7662
-377.229 139.96 -18.9021
-385.376 138.633 -13.5814
-389.012 136.708 -9.96591
-402.645 135.675 23.1257
-402.122 134.26 27.2074
-401.55 134.397 31.409
-400.764 135.113 35.5854
-391.968 135.889 52.4688
-389.654 136.704 55.2717
-384.178 138.01 60.3363
-381.26 138.863 62.4566
-381.742 135.837 -15.465
-391.351 133.959 -6.4374
-393.918 134.024 -3.16681
-399.098 132.536 7.62034
-396.743 132.411 2.39965
-400.297 132.277 11.8513
-401.172 132.262 16.1561
-401.459 132.009 19.5202
-401.605 132.015 22.6595
-399.164 133.047 38.4871
-397.865 132.779 41.5029
-396.637 133.37 44.3837
-394.313 134.172 48.6383
-386.784 136.707 57.9144
-369.704 140.809 67.8743
-400.72 130.106 27.206
-400.065 130.005 31.3966
-399.664 131.17 34.8886
-372.555 139.102 66.7056
-385.231 134.712 -12.568
-389.093 132.973 54.4018
-360.639 146.244 -23.8941
-362.432 142.364 -23.4911
-379.303 136.225 -16.9972
-399.414 128.048 15.4625
-399.805 127.83 19.4299
-399.541 126.81 22.5865
-398 129.407 37.9053
-393.843 130.027 46.8749
-391.704 131.919 50.9409
-386.531 133.273 56.9408
-383.447 134.188 59.7668
-379.671 135.838 62.6859
-376.837 137.076 64.4933
-369.729 139.629 -21.7087
-387.597 132.111 -9.47978
-393.294 129.546 -1.32287
-395.237 129.227 2.17949
-395.853 127.652 4.77084
-397.271 127.419 8.53947
-398.084 127.148 11.4598
-398.699 125.741 28.1374
-398.247 126.883 33.4156
-395.974 128.867 42.1306
-365.224 140.77 68.9013
-391.18 129.946 -4.42546
-372.864 137.078 -20.1716
-384.119 131.758 -12.3179
-389.039 128.794 -6.28239
-396.602 126.313 37.7805
-389.854 127.836 50.7146
-387.917 129.575 53.9186
-364.173 139.574 -22.9114
-375.748 136.15 -18.7393
-392.529 125.859 0.534116
-397.955 124.623 16.9442
-394.249 125.778 42.3637
-392.901 127.856 46.653
-390.792 126.782 -2.71228
-396.447 122.961 14.1606
-384.77 129.931 56.9055
-381.613 129.113 58.9153
-379.209 132.333 61.8118
-359.914 142.838 69.761
-394.732 123.808 7.14525
-395.657 123.103 10.8807
-397.047 122.424 21.0826
-395.725 120.425 19.5383
-397.029 122.36 24.9803
-396.283 123.26 33.3591
-396.276 121.847 29.0773
-393.682 123.152 40.3333
-358.818 142.941 -23.8251
-376.818 132.213 -17.0363
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-381.873 129.496 -12.8742
-385.991 128.429 -9.04334
-393.099 124.103 3.41689
-394.304 122.094 37.1748
-391.674 123.528 44.4572
-390.46 124.911 47.5914
-371.807 135.531 66.1788
-375.796 134.244 64.1764
-372.598 133.28 -19.2311
-383.383 127.568 -10.7369
-385.477 125.188 -7.45407
-388.402 124.36 -3.74789
-389.16 121.793 -0.394115
-391.506 121.68 3.48486
-392.916 121.056 7.14732
-394.062 120.429 11.4113
-394.705 119.898 15.5526
-395.478 119.991 24.81
-394.225 120.023 33.0395
-394.35 119.07 29.1216
-387.512 123.619 50.1256
-386.48 125.408 52.5924
-383.896 126.381 55.6524
-367.749 137.378 67.7728
-392.076 118.183 35.4491
-391.051 119.596 40.4301
-389.836 120.634 43.9658
-388.242 121.42 47.1293
-378.687 128.97 60.6355
-372.483 131.874 64.786
-368.647 135.456 -21.0892
-391.794 117.457 11.5444
-392.873 117.486 15.5997
-393.182 117.05 20.1022
-393.209 116.993 24.8724
-375.17 129.866 62.8764
-365.818 137.205 -22.1466
-379.116 127.258 -13.5148
-381.637 125.209 -10.6446
-384.579 120.57 -4.51963
-389.504 119.407 3.17121
-390.942 118.625 7.01299
-391.778 116.075 29.9769
-383.458 123.304 53.8722
-385.353 120.627 49.7349
-382.627 121.722 -7.30856
-379.072 124.288 57.8382
-372.242 130.202 -18.2194
-375.655 128.338 -15.9333
-385.323 118.782 -1.79115
-385.921 117.042 1.05653
-388.336 116.794 5.15913
-388.808 114.75 10.1378
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-390.74 114.364 19.5073
-390.24 113.733 25.2573
-389.276 114.965 35.2405
-388.14 115.927 39.7399
-386.859 117.586 44.4485
-375.012 126.182 61.1735
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-378.965 122.68 -10.7863
-386.18 114.547 5.4126
-389.299 113.502 29.9191
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-351.416 130.226 -20.6126
-344.708 101.704 26.4824
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-346.932 107.809 46.9858
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-350.491 126.889 65.0608
-352.379 139.342 -23.1913
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-346.011 106.343 2.06755
-344.802 105.248 5.03875
-344.991 101.609 20.1849
-344.277 101.718 23.4292
-348.498 119.701 60.3806
-348.246 120.724 -15.0274
-346.978 115.364 -10.3283
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-343.335 102.588 15.4609
-342.934 104.105 9.67654
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-342.599 104.067 35.771
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-343.186 108.974 47.0061
-344.598 112.916 52.9425
-346.849 123.991 62.7742
-348.373 126.691 -18.5418
-340.279 103.682 15.2804
-339.912 103.176 24.1091
-339.103 103.79 28.495
-341.572 111.498 49.8057
-349.722 133.844 -21.5894
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-345.566 123.016 -15.8504
-341.819 116.513 -9.48884
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-345.318 120.194 59.8694
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-342.466 120.289 -12.917
-339.848 111.652 -2.849
-339.104 110.096 -0.0596179
-338.309 109.878 45.1199
-341.486 115.057 53.8744
-347.193 130.33 -19.8697
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3  0 1 2
3  2 3 0
3  4 5 6
3  7 5 4
3  8 9 10
3  11 10 9
3  12 13 14
3  15 14 13
3  16 17 15
3  18 19 20
3  21 3 2
3  22 3 21
3  23 24 22
3  24 23 25
3  6 25 26
3  6 26 4
3  27 28 7
3  29 30 28
3  27 29 28
3  31 32 30
3  30 29 31
3  33 32 31
3  33 34 32
3  35 36 34
3  33 35 34
3  37 38 36
3  36 35 37
3  39 38 37
3  39 9 8
3  40 41 42
3  42 41 43
3  43 44 42
3  12 44 43
3  45 17 16
3  46 47 48
3  1 49 2
3  23 50 25
3  50 26 25
3  4 51 7
3  7 51 27
3  40 11 52
3  53 12 43
3  12 53 13
3  29 54 31
3  33 31 54
3  55 37 35
3  35 56 55
3  37 55 57
3  57 39 37
3  58 9 39
3  57 58 39
3  11 9 59
3  58 59 9
3  11 59 52
3  40 52 60
3  60 41 40
3  41 60 43
3  13 61 15
3  61 16 15
3  62 20 63
3  21 64 22
3  23 22 64
3  65 27 51
3  51 66 65
3  29 27 65
3  54 67 33
3  56 35 33
3  33 67 56
3  68 69 46
3  62 18 20
3  18 70 71
3  72 23 64
3  23 72 50
3  26 50 73
3  26 73 74
3  4 26 74
3  74 66 4
3  66 51 4
3  65 75 29
3  54 29 75
3  43 76 53
3  45 77 78
3  78 77 69
3  70 79 71
3  80 71 79
3  49 81 82
3  49 82 2
3  21 2 82
3  76 43 60
3  83 53 76
3  13 53 84
3  53 83 84
3  61 13 84
3  85 16 61
3  45 16 85
3  85 77 45
3  72 86 50
3  86 73 50
3  66 87 65
3  88 75 65
3  87 88 65
3  89 54 75
3  75 88 89
3  67 54 89
3  90 59 58
3  58 91 90
3  92 52 59
3  59 90 92
3  60 52 92
3  79 93 80
3  49 80 93
3  93 81 49
3  94 21 82
3  64 21 95
3  72 64 95
3  74 73 86
3  89 96 67
3  97 56 67
3  67 96 97
3  55 56 98
3  56 97 98
3  99 57 55
3  55 98 99
3  91 58 57
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3  60 100 76
3  70 18 62
3  21 94 95
3  100 101 76
3  84 102 61
3  102 103 61
3  81 104 82
3  95 105 72
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3  110 88 87
3  109 110 87
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3  135 134 164
3  135 165 166
3  166 136 135
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3  78 69 68

//-----------------------------------------------------
And the other ball:

OFF
1627 3250 0

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3  0 1 2
3  2 3 0
3  4 5 6
3  7 5 4
3  8 9 10
3  11 10 9
3  12 13 14
3  15 14 13
3  16 17 15
3  18 19 20
3  21 3 2
3  22 3 21
3  23 24 22
3  24 23 25
3  6 25 26
3  6 26 4
3  27 28 7
3  29 30 28
3  27 29 28
3  31 32 30
3  30 29 31
3  33 32 31
3  33 34 32
3  35 36 34
3  33 35 34
3  37 38 36
3  36 35 37
3  39 38 37
3  39 9 8
3  40 41 42
3  42 41 43
3  43 44 42
3  12 44 43
3  45 17 16
3  46 47 48
3  1 49 2
3  23 50 25
3  50 26 25
3  4 51 7
3  7 51 27
3  40 11 52
3  53 12 43
3  12 53 13
3  29 54 31
3  33 31 54
3  55 37 35
3  35 56 55
3  37 55 57
3  57 39 37
3  58 9 39
3  57 58 39
3  11 9 59
3  58 59 9
3  11 59 52
3  40 52 60
3  60 41 40
3  41 60 43
3  13 61 15
3  61 16 15
3  62 20 63
3  21 64 22
3  23 22 64
3  65 27 51
3  51 66 65
3  29 27 65
3  54 67 33
3  56 35 33
3  33 67 56
3  68 69 46
3  62 18 20
3  18 70 71
3  72 23 64
3  23 72 50
3  26 50 73
3  26 73 74
3  4 26 74
3  74 66 4
3  66 51 4
3  65 75 29
3  54 29 75
3  43 76 53
3  45 77 78
3  78 77 69
3  70 79 71
3  80 71 79
3  49 81 82
3  49 82 2
3  21 2 82
3  76 43 60
3  83 53 76
3  13 53 84
3  53 83 84
3  61 13 84
3  85 16 61
3  45 16 85
3  85 77 45
3  72 86 50
3  86 73 50
3  66 87 65
3  88 75 65
3  87 88 65
3  89 54 75
3  75 88 89
3  67 54 89
3  90 59 58
3  58 91 90
3  92 52 59
3  59 90 92
3  60 52 92
3  79 93 80
3  49 80 93
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