| 0 | | inference rule with conclusion upper X and 1 premise |
| 1 | AX | inference rule with conclusion upper X and 1 premise |
| 2 | X | inference rule with conclusion upper X and 1 premise |
| 3 | XN | inference rule label upper N with conclusion upper X and 1 premise |
| 4 | A | axiom upper A |
| 5 | | empty axiom |
| 6 | AXN | inference rule label upper N with conclusion upper X and 1 premise |
| 7 | ABXN | inference rule label upper N with conclusion upper X and 2 premises |
| 8 | ABCXN | inference rule label upper N with conclusion upper X and 3 premises |
| 9 | NAX | inference rule label upper N with conclusion upper X and 1 premise |
| 10 | NABX | inference rule label upper N with conclusion upper X and 2 premises |
| 11 | NABCX | inference rule label upper N with conclusion upper X and 3 premises |
| 12 | AX | 1st premise axiom upper A |
| 13 | ABX | 1st premise axiom upper A 2nd premise axiom upper B |
| 14 | ABCX | 1st premise axiom upper A 2nd premise axiom upper B 3rd premise axiom upper C |