Question 32744: Checking Both Inverse Identities

Original question and givens

The declared total function f:A→B has A={-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1}, B={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39}, and table {(-20, 39), (-19, 1), (-18, 3), (-17, 5), (-16, 7), (-15, 9), (-14, 11), (-13, 13), (-12, 15), (-11, 17), (-10, 19), (-9, 21), (-8, 23), (-7, 25), (-6, 27), (-5, 29), (-4, 31), (-3, 33), (-2, 35), (-1, 37)}. The function has been confirmed bijective. The candidate total g:B→A has table {(1, -19), (3, -18), (5, -17), (7, -16), (9, -15), (11, -14), (13, -13), (15, -12), (17, -11), (19, -10), (21, -9), (23, -8), (25, -7), (27, -6), (29, -5), (31, -4), (33, -3), (35, -2), (37, -1), (39, -20)}. Check both identities to decide whether g is the inverse of f.

• G001 — The declared total function f:A→B has A={-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1}, B={1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39}, and table {(-20, 39), (-19, 1), (-18, 3), (-17, 5), (-16, 7), (-15, 9), (-14, 11), (-13, 13), (-12, 15), (-11, 17), (-10, 19), (-9, 21), (-8, 23), (-7, 25), (-6, 27), (-5, 29), (-4, 31), (-3, 33), (-2, 35), (-1, 37)}. The function has been confirmed bijective. The candidate total g:B→A has table {(1, -19), (3, -18), (5, -17), (7, -16), (9, -15), (11, -14), (13, -13), (15, -12), (17, -11), (19, -10), (21, -9), (23, -8), (25, -7), (27, -6), (29, -5), (31, -4), (33, -3), (35, -2), (37, -1), (39, -20)}. Check both identities to decide whether g is the inverse of f.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-inverse-function

Step-by-step derivation

source roles = [qf-inverse-function-candidate, inverse_candidate, no-required-domain, []]

derived = [[BOTH_restorations_YesNo_STRING]]

source roles = [ORIGINAL f domain, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [[-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

source roles = [ORIGINAL f codomain, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

source roles = [ORIGINAL f, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

source roles = [ORIGINAL f, 0, -20, 39, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 1, -19, 1, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 2, -18, 3, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 3, -17, 5, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 4, -16, 7, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 5, -15, 9, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 6, -14, 11, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 7, -13, 13, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 8, -12, 15, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 9, -11, 17, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 10, -10, 19, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 11, -9, 21, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 12, -8, 23, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 13, -7, 25, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 14, -6, 27, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 15, -5, 29, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 16, -4, 31, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 17, -3, 33, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 18, -2, 35, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, 19, -1, 37, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [Yes, Yes, Yes]

source roles = [ORIGINAL f, -20, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -19, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -18, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -17, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -16, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -15, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -14, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -13, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -12, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -11, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -10, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -9, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -8, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -7, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -6, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -5, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -4, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -3, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -2, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, -1, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [ORIGINAL f, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], Yes]

source roles = [ORIGINAL f, 1, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-19], 1]

source roles = [ORIGINAL f, 3, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-18], 1]

source roles = [ORIGINAL f, 5, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-17], 1]

source roles = [ORIGINAL f, 7, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-16], 1]

source roles = [ORIGINAL f, 9, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-15], 1]

source roles = [ORIGINAL f, 11, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-14], 1]

source roles = [ORIGINAL f, 13, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-13], 1]

source roles = [ORIGINAL f, 15, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-12], 1]

source roles = [ORIGINAL f, 17, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-11], 1]

source roles = [ORIGINAL f, 19, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-10], 1]

source roles = [ORIGINAL f, 21, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-9], 1]

source roles = [ORIGINAL f, 23, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-8], 1]

source roles = [ORIGINAL f, 25, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-7], 1]

source roles = [ORIGINAL f, 27, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-6], 1]

source roles = [ORIGINAL f, 29, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-5], 1]

source roles = [ORIGINAL f, 31, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-4], 1]

source roles = [ORIGINAL f, 33, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-3], 1]

source roles = [ORIGINAL f, 35, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-2], 1]

source roles = [ORIGINAL f, 37, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-1], 1]

source roles = [ORIGINAL f, 39, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [[-20], 1]

source roles = [ORIGINAL f, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[-19], [-18], [-17], [-16], [-15], [-14], [-13], [-12], [-11], [-10], [-9], [-8], [-7], [-6], [-5], [-4], [-3], [-2], [-1], [-20]]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g domain, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

derived = [[1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39]]

source roles = [CANDIDATE g codomain, [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [[-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

source roles = [CANDIDATE g, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

source roles = [CANDIDATE g, 0, 1, -19, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 1, 3, -18, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 2, 5, -17, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 3, 7, -16, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 4, 9, -15, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 5, 11, -14, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 6, 13, -13, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 7, 15, -12, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 8, 17, -11, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 9, 19, -10, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 10, 21, -9, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 11, 23, -8, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 12, 25, -7, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 13, 27, -6, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 14, 29, -5, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 15, 31, -4, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 16, 33, -3, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 17, 35, -2, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 18, 37, -1, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 19, 39, -20, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1]]

derived = [Yes, Yes, Yes]

source roles = [CANDIDATE g, 1, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 3, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 5, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 7, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 9, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 11, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 13, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 15, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 17, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 19, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 21, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 23, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 25, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 27, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 29, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 31, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 33, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 35, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 37, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, 39, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [1, Yes]

source roles = [CANDIDATE g, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], Yes]

source roles = [CANDIDATE g, -20, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[39], 1]

source roles = [CANDIDATE g, -19, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[1], 1]

source roles = [CANDIDATE g, -18, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[3], 1]

source roles = [CANDIDATE g, -17, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[5], 1]

source roles = [CANDIDATE g, -16, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[7], 1]

source roles = [CANDIDATE g, -15, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[9], 1]

source roles = [CANDIDATE g, -14, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[11], 1]

source roles = [CANDIDATE g, -13, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[13], 1]

source roles = [CANDIDATE g, -12, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[15], 1]

source roles = [CANDIDATE g, -11, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[17], 1]

source roles = [CANDIDATE g, -10, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[19], 1]

source roles = [CANDIDATE g, -9, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[21], 1]

source roles = [CANDIDATE g, -8, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[23], 1]

source roles = [CANDIDATE g, -7, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[25], 1]

source roles = [CANDIDATE g, -6, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[27], 1]

source roles = [CANDIDATE g, -5, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[29], 1]

source roles = [CANDIDATE g, -4, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[31], 1]

source roles = [CANDIDATE g, -3, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[33], 1]

source roles = [CANDIDATE g, -2, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[35], 1]

source roles = [CANDIDATE g, -1, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[37], 1]

source roles = [CANDIDATE g, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [[39], [1], [3], [5], [7], [9], [11], [13], [15], [17], [19], [21], [23], [25], [27], [29], [31], [33], [35], [37]]]

derived = [Yes, Yes, Yes]

source roles = [-20, 39, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-20, Yes]

source roles = [-19, 1, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-19, Yes]

source roles = [-18, 3, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-18, Yes]

source roles = [-17, 5, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-17, Yes]

source roles = [-16, 7, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-16, Yes]

source roles = [-15, 9, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-15, Yes]

source roles = [-14, 11, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-14, Yes]

source roles = [-13, 13, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-13, Yes]

source roles = [-12, 15, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-12, Yes]

source roles = [-11, 17, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-11, Yes]

source roles = [-10, 19, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-10, Yes]

source roles = [-9, 21, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-9, Yes]

source roles = [-8, 23, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-8, Yes]

source roles = [-7, 25, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-7, Yes]

source roles = [-6, 27, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-6, Yes]

source roles = [-5, 29, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-5, Yes]

source roles = [-4, 31, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-4, Yes]

source roles = [-3, 33, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-3, Yes]

source roles = [-2, 35, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-2, Yes]

source roles = [-1, 37, [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [-1, Yes]

source roles = [1, -19, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [1, Yes]

source roles = [3, -18, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [3, Yes]

source roles = [5, -17, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [5, Yes]

source roles = [7, -16, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [7, Yes]

source roles = [9, -15, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [9, Yes]

source roles = [11, -14, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [11, Yes]

source roles = [13, -13, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [13, Yes]

source roles = [15, -12, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [15, Yes]

source roles = [17, -11, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [17, Yes]

source roles = [19, -10, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [19, Yes]

source roles = [21, -9, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [21, Yes]

source roles = [23, -8, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [23, Yes]

source roles = [25, -7, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [25, Yes]

source roles = [27, -6, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [27, Yes]

source roles = [29, -5, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [29, Yes]

source roles = [31, -4, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [31, Yes]

source roles = [33, -3, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [33, Yes]

source roles = [35, -2, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [35, Yes]

source roles = [37, -1, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [37, Yes]

source roles = [39, -20, [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]]]

derived = [39, Yes]

source roles = [[-20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9, -8, -7, -6, -5, -4, -3, -2, -1], [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39], [[-20, 39], [-19, 1], [-18, 3], [-17, 5], [-16, 7], [-15, 9], [-14, 11], [-13, 13], [-12, 15], [-11, 17], [-10, 19], [-9, 21], [-8, 23], [-7, 25], [-6, 27], [-5, 29], [-4, 31], [-3, 33], [-2, 35], [-1, 37]], [[1, -19], [3, -18], [5, -17], [7, -16], [9, -15], [11, -14], [13, -13], [15, -12], [17, -11], [19, -10], [21, -9], [23, -8], [25, -7], [27, -6], [29, -5], [31, -4], [33, -3], [35, -2], [37, -1], [39, -20]]]

derived = [[Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], [Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes, Yes], Yes]

Reverse checks

• S172 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S171 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S170 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S169 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S168 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S167 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S166 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S165 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S164 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S163 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S162 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S161 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S160 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S159 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S158 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S157 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S156 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S155 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S154 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S153 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S152 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S151 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S150 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S149 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S148 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S147 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S146 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S145 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S144 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S143 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S142 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S141 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S140 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S139 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S138 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S137 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S136 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S135 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S134 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S133 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S132 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S131 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S130 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S129 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S128 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S127 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S126 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S125 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S124 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S123 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S122 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S121 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S120 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S119 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S118 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S117 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S116 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S115 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S114 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S113 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S112 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S111 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S110 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S109 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S108 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S107 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S106 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S105 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S104 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S103 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S102 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S101 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S100 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S099 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S098 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S097 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S096 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S095 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S094 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S093 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S092 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S091 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S090 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S089 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S088 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S087 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S086 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S085 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S084 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S083 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S082 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S081 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S080 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S079 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S078 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S077 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S076 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S075 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S074 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S073 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S072 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S071 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S070 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S069 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S068 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S067 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S066 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S065 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S064 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S063 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S062 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S061 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S060 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S059 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S058 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S057 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S056 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S055 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S054 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S053 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S052 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S051 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S050 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S049 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S048 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S047 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S046 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S045 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S044 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S043 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S042 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S041 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S040 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S039 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S038 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S037 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S036 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S035 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S034 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S033 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S032 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S031 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S030 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S029 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S028 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S027 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S026 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S025 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S024 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S023 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S022 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S021 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S020 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S019 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S018 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S017 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S016 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S015 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S014 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S013 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S012 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S011 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S010 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S009 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S008 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S007 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S006 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S005 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S004 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S003 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S002 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.
• S001 · premise_and_result_audit — Reverse-check ORIGINAL data,field roles,types,domain and premises;the conclusion need not uniquely recover its premises.Keep source-bound candidates,independent review,formal proof and publication separate.

Result

Yes

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.