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As explained in the application description, we are trying to find a sum-free partition of the integers 1-167 into 5 sets. This is the best sum-free partition found so far:
Set 1: 12 14 17 20 22 23 48 56 59 61 69 72 77 80 101 105 106 108 114 116 128 129 130 132 135 137 138 145 150 152 154 156 166 167
Set 2: 3 4 9 11 19 25 27 32 37 39 45 53 55 60 68 75 83 89 91 96 103 104 109 117 119 125 127 131 133 134 151 155 161 165
Set 3: 5 6 8 15 18 28 31 40 42 51 52 54 63 64 65 76 86 87 88 90 97 99 100 111 113 120 122 123 124 142 144 147 148 153 159 162 163 164
Set 4: 2 7 10 21 26 29 34 35 38 43 46 49 57 62 66 71 74 79 82 85 93 94 102 118 121 126 140 141 143 146 149 158
Set 5: 1 13 16 24 30 33 36 41 44 47 50 58 67 70 73 78 81 84 92 95 98 107 110 112 115 136 139 157 160
Sum-Free up to 127