Inequalities for the triangle scenario (classical case), Case 2

In the following we provide the inequalities obtained from the calculation labelled Case 2 in Section III of the article "Non - Shannon inequalities in the entropy vector approach to causal structures". These inequalities are of the form a H (X) + b H (Y) + c H (Z) + d H (XY) + e H (XZ) + f H (YZ) + g H (XYZ) >= 0. The coefficients a, b, c, d, e, f and g of all irredundant inequalities are in the following listed as the rows of a matrix.

{{0, 0, 0, 0, 0, -1, 1}, {0, 0, 0, 0, -1, 0, 1}, {0, 0, 0, -1, 0, 0, 1}, 
 {1, 1, 0, -1, 0, 0, 0}, {1, 0, 1, 0, -1, 0, 0}, {0, 1, 1, 0, 0, -1, 0}, 
 {-1, -1, -1, 1, 1, 0, 0}, {-1, -1, -1, 1, 0, 1, 0}, 
 {-1, -1, -1, 0, 1, 1, 0}, {0, 0, -1, 0, 1, 1, -1}, {0, -1, 0, 1, 0, 1, -1}, 
 {-1, 0, 0, 1, 1, 0, -1}, {-4, -4, -4, 4, 3, 3, -2}, 
 {-4, -4, -4, 3, 4, 3, -2}, {-4, -4, -4, 3, 3, 4, -2}, 
 {-7, -7, -7, 7, 6, 4, -3}, {-7, -7, -7, 7, 4, 6, -3}, 
 {-7, -7, -7, 6, 7, 4, -3}, {-7, -7, -7, 6, 4, 7, -3}, 
 {-7, -7, -7, 4, 7, 6, -3}, {-7, -7, -7, 4, 6, 7, -3}, 
 {-2, -2, -2, 3, 3, 3, -4}, {-6, -7, -7, 7, 6, 6, -5}, 
 {-6, -7, -7, 6, 7, 6, -5}, {-7, -6, -7, 7, 6, 6, -5}, 
 {-7, -6, -7, 6, 6, 7, -5}, {-7, -7, -6, 6, 7, 6, -5}, 
 {-7, -7, -6, 6, 6, 7, -5}, {-8, -8, -8, 7, 7, 7, -5}, 
 {-12, -12, -12, 11, 11, 9, -7}, {-12, -12, -12, 11, 9, 11, -7}, 
 {-12, -12, -12, 9, 11, 11, -7}, {-3, -5, -5, 6, 6, 8, -9}, 
 {-4, -5, -7, 6, 7, 9, -9}, {-4, -7, -5, 7, 6, 9, -9}, 
 {-5, -3, -5, 6, 8, 6, -9}, {-5, -4, -7, 6, 9, 7, -9}, 
 {-5, -5, -3, 8, 6, 6, -9}, {-5, -7, -4, 9, 6, 7, -9}, 
 {-7, -4, -5, 7, 9, 6, -9}, {-7, -5, -4, 9, 7, 6, -9}, 
 {-7, -8, -8, 9, 8, 9, -9}, {-7, -8, -8, 8, 9, 9, -9}, 
 {-8, -7, -8, 9, 9, 8, -9}, {-8, -7, -8, 8, 9, 9, -9}, 
 {-8, -8, -7, 9, 9, 8, -9}, {-8, -8, -7, 9, 8, 9, -9}, 
 {-10, -11, -11, 12, 9, 12, -10}, {-10, -11, -11, 9, 12, 12, -10}, 
 {-11, -10, -11, 12, 12, 9, -10}, {-11, -10, -11, 9, 12, 12, -10}, 
 {-11, -11, -10, 12, 12, 9, -10}, {-11, -11, -10, 12, 9, 12, -10}, 
 {-11, -13, -13, 12, 12, 13, -11}, {-13, -11, -13, 12, 13, 12, -11}, 
 {-13, -13, -11, 13, 12, 12, -11}, {-18, -18, -18, 17, 15, 15, -11}, 
 {-18, -18, -18, 15, 17, 15, -11}, {-18, -18, -18, 15, 15, 17, -11}, 
 {-20, -21, -21, 20, 15, 20, -13}, {-20, -21, -21, 15, 20, 20, -13}, 
 {-21, -20, -21, 20, 20, 15, -13}, {-21, -20, -21, 15, 20, 20, -13}, 
 {-21, -21, -20, 20, 20, 15, -13}, {-21, -21, -20, 20, 15, 20, -13}, 
 {-7, -9, -9, 11, 11, 12, -14}, {-9, -7, -9, 11, 12, 11, -14}, 
 {-9, -9, -7, 12, 11, 11, -14}, {-27, -27, -27, 26, 24, 18, -14}, 
 {-27, -27, -27, 26, 18, 24, -14}, {-27, -27, -27, 24, 26, 18, -14}, 
 {-27, -27, -27, 24, 18, 26, -14}, {-27, -27, -27, 18, 26, 24, -14}, 
 {-27, -27, -27, 18, 24, 26, -14}, {-21, -23, -23, 23, 18, 20, -15}, 
 {-21, -23, -23, 18, 23, 20, -15}, {-23, -21, -23, 23, 20, 18, -15}, 
 {-23, -21, -23, 18, 20, 23, -15}, {-23, -23, -21, 20, 23, 18, -15}, 
 {-23, -23, -21, 20, 18, 23, -15}, {-8, -8, -11, 11, 14, 13, -16}, 
 {-8, -8, -11, 11, 13, 14, -16}, {-8, -11, -8, 14, 11, 13, -16}, 
 {-8, -11, -8, 13, 11, 14, -16}, {-11, -8, -8, 14, 13, 11, -16}, 
 {-11, -8, -8, 13, 14, 11, -16}, {-11, -11, -12, 14, 14, 14, -16}, 
 {-11, -12, -11, 14, 14, 14, -16}, {-12, -11, -11, 14, 14, 14, -16}, 
 {-10, -12, -14, 14, 15, 17, -18}, {-10, -14, -12, 15, 14, 17, -18}, 
 {-12, -10, -14, 14, 17, 15, -18}, {-12, -14, -10, 17, 14, 15, -18}, 
 {-14, -10, -12, 15, 17, 14, -18}, {-14, -12, -10, 17, 15, 14, -18}, 
 {-12, -15, -15, 17, 16, 18, -19}, {-12, -15, -15, 16, 17, 18, -19}, 
 {-15, -12, -15, 17, 18, 16, -19}, {-15, -12, -15, 16, 18, 17, -19}, 
 {-15, -15, -12, 18, 17, 16, -19}, {-15, -15, -12, 18, 16, 17, -19}, 
 {-24, -27, -27, 26, 24, 24, -20}, {-24, -27, -27, 24, 26, 24, -20}, 
 {-27, -24, -27, 26, 24, 24, -20}, {-27, -24, -27, 24, 24, 26, -20}, 
 {-27, -27, -24, 24, 26, 24, -20}, {-27, -27, -24, 24, 24, 26, -20}, 
 {-16, -19, -19, 22, 21, 22, -24}, {-16, -19, -19, 21, 22, 22, -24}, 
 {-19, -16, -19, 22, 22, 21, -24}, {-19, -16, -19, 21, 22, 22, -24}, 
 {-19, -19, -16, 22, 22, 21, -24}, {-19, -19, -16, 22, 21, 22, -24}, 
 {-16, -18, -19, 22, 22, 23, -26}, {-16, -19, -18, 22, 22, 23, -26}, 
 {-18, -16, -19, 22, 23, 22, -26}, {-18, -19, -16, 23, 22, 22, -26}, 
 {-19, -16, -18, 22, 23, 22, -26}, {-19, -18, -16, 23, 22, 22, -26}, 
 {-15, -19, -21, 22, 23, 26, -28}, {-15, -21, -19, 23, 22, 26, -28}, 
 {-19, -15, -21, 22, 26, 23, -28}, {-19, -21, -15, 26, 22, 23, -28}, 
 {-21, -15, -19, 23, 26, 22, -28}, {-21, -19, -15, 26, 23, 22, -28}, 
 {-20, -22, -23, 27, 27, 27, -31}, {-20, -23, -22, 27, 27, 27, -31}, 
 {-22, -20, -23, 27, 27, 27, -31}, {-22, -23, -20, 27, 27, 27, -31}, 
 {-23, -20, -22, 27, 27, 27, -31}, {-23, -22, -20, 27, 27, 27, -31}, 
 {-19, -23, -25, 27, 28, 30, -33}, {-19, -25, -23, 28, 27, 30, -33}, 
 {-23, -19, -25, 27, 30, 28, -33}, {-23, -25, -19, 30, 27, 28, -33}, 
 {-25, -19, -23, 28, 30, 27, -33}, {-25, -23, -19, 30, 28, 27, -33}, 
 {-30, -32, -33, 35, 35, 33, -34}, {-30, -33, -32, 35, 35, 33, -34}, 
 {-32, -30, -33, 35, 33, 35, -34}, {-32, -33, -30, 33, 35, 35, -34}, 
 {-33, -30, -32, 35, 33, 35, -34}, {-33, -32, -30, 33, 35, 35, -34}, 
 {-42, -46, -46, 41, 41, 45, -35}, {-46, -42, -46, 41, 45, 41, -35}, 
 {-46, -46, -42, 45, 41, 41, -35}, {-19, -23, -29, 27, 30, 36, -37}, 
 {-19, -29, -23, 30, 27, 36, -37}, {-23, -19, -29, 27, 36, 30, -37}, 
 {-23, -29, -19, 36, 27, 30, -37}, {-29, -19, -23, 30, 36, 27, -37}, 
 {-29, -23, -19, 36, 30, 27, -37}, {-29, -33, -39, 35, 36, 44, -40}, 
 {-29, -39, -33, 36, 35, 44, -40}, {-33, -29, -39, 35, 44, 36, -40}, 
 {-33, -39, -29, 44, 35, 36, -40}, {-39, -29, -33, 36, 44, 35, -40}, 
 {-39, -33, -29, 44, 36, 35, -40}, {-61, -63, -63, 58, 48, 60, -40}, 
 {-61, -63, -63, 48, 58, 60, -40}, {-63, -61, -63, 58, 60, 48, -40}, 
 {-63, -61, -63, 48, 60, 58, -40}, {-63, -63, -61, 60, 58, 48, -40}, 
 {-63, -63, -61, 60, 48, 58, -40}, {-33, -39, -39, 41, 39, 42, -41}, 
 {-33, -39, -39, 39, 41, 42, -41}, {-39, -33, -39, 41, 42, 39, -41}, 
 {-39, -33, -39, 39, 42, 41, -41}, {-39, -39, -33, 42, 41, 39, -41}, 
 {-39, -39, -33, 42, 39, 41, -41}, {-57, -63, -63, 59, 57, 57, -47}, 
 {-57, -63, -63, 57, 59, 57, -47}, {-63, -57, -63, 59, 57, 57, -47}, 
 {-63, -57, -63, 57, 57, 59, -47}, {-63, -63, -57, 57, 59, 57, -47}, 
 {-63, -63, -57, 57, 57, 59, -47}, {-36, -43, -43, 48, 43, 50, -50}, 
 {-36, -43, -43, 43, 48, 50, -50}, {-43, -36, -43, 48, 50, 43, -50}, 
 {-43, -36, -43, 43, 50, 48, -50}, {-43, -43, -36, 50, 48, 43, -50}, 
 {-43, -43, -36, 50, 43, 48, -50}, {-45, -51, -51, 56, 54, 54, -56}, 
 {-45, -51, -51, 54, 56, 54, -56}, {-51, -45, -51, 56, 54, 54, -56}, 
 {-51, -45, -51, 54, 54, 56, -56}, {-51, -51, -45, 54, 56, 54, -56}, 
 {-51, -51, -45, 54, 54, 56, -56}, {-79, -87, -87, 82, 72, 85, -65}, 
 {-79, -87, -87, 72, 82, 85, -65}, {-87, -79, -87, 82, 85, 72, -65}, 
 {-87, -79, -87, 72, 85, 82, -65}, {-87, -87, -79, 85, 82, 72, -65}, 
 {-87, -87, -79, 85, 72, 82, -65}, {-45, -51, -63, 56, 60, 72, -68}, 
 {-45, -63, -51, 60, 56, 72, -68}, {-51, -45, -63, 56, 72, 60, -68}, 
 {-51, -63, -45, 72, 56, 60, -68}, {-63, -45, -51, 60, 72, 56, -68}, 
 {-63, -51, -45, 72, 60, 56, -68}, {-93, -99, -99, 94, 84, 90, -70}, 
 {-93, -99, -99, 84, 94, 90, -70}, {-99, -93, -99, 94, 90, 84, -70}, 
 {-99, -93, -99, 84, 90, 94, -70}, {-99, -99, -93, 90, 94, 84, -70}, 
 {-99, -99, -93, 90, 84, 94, -70}, {-56, -58, -63, 73, 73, 75, -85}, 
 {-56, -63, -58, 73, 73, 75, -85}, {-58, -56, -63, 73, 75, 73, -85}, 
 {-58, -63, -56, 75, 73, 73, -85}, {-63, -56, -58, 73, 75, 73, -85}, 
 {-63, -58, -56, 75, 73, 73, -85}, {-51, -63, -73, 73, 78, 90, -95}, 
 {-51, -73, -63, 78, 73, 90, -95}, {-63, -51, -73, 73, 90, 78, -95}, 
 {-63, -73, -51, 90, 73, 78, -95}, {-73, -51, -63, 78, 90, 73, -95}, 
 {-73, -63, -51, 90, 78, 73, -95}, {-139, -157, -157, 147, 137, 155, -125}, 
 {-139, -157, -157, 137, 147, 155, -125}, {-157, -139, -157, 147, 155, 137, 
  -125}, {-157, -139, -157, 137, 155, 147, -125}, 
 {-157, -157, -139, 155, 147, 137, -125}, {-157, -157, -139, 155, 137, 147, 
  -125}}