| [ |
| { |
| "id": "a01", |
| "description": "Single positive atom P", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 1 |
| }, |
| { |
| "id": "a02", |
| "description": "Single negative atom \u00acP", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 1 |
| }, |
| { |
| "id": "a03", |
| "description": "Direct contradiction P \u2227 \u00acP", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 1 |
| }, |
| { |
| "id": "a04", |
| "description": "Disjunction P \u2228 Q", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "a05", |
| "description": "Force false: \u00acP \u2227 \u00acQ \u2227 (P \u2228 Q)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "a06", |
| "description": "Conjunction P \u2227 Q", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "a07", |
| "description": "Both true but at-most-one: P \u2227 Q \u2227 (\u00acP \u2228 \u00acQ)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "a08", |
| "description": "XOR plus equivalence: 4-clause UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "b01", |
| "description": "Modus ponens premise: (\u00acP \u2228 Q) \u2227 P", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "b02", |
| "description": "Modus ponens contradiction: above \u2227 \u00acQ", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "b03", |
| "description": "Two-step MP chain: (\u00acP \u2228 Q) \u2227 (\u00acQ \u2228 R) \u2227 P", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "b04", |
| "description": "Two-step MP contradiction: above \u2227 \u00acR", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "b05", |
| "description": "Modus tollens setup: (\u00acP \u2228 Q) \u2227 \u00acQ (forces \u00acP)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "b06", |
| "description": "Modus tollens contradiction: above \u2227 P", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "c01", |
| "description": "Three-step chain SAT: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227(\u00acC\u2228D)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "D", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "c02", |
| "description": "Three-step chain UNSAT: above \u2227 A \u2227 \u00acD", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "D", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "D", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "c03", |
| "description": "Redundant transitivity: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227(\u00acA\u2228C)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "c04", |
| "description": "Transitive trigger: (\u00acA\u2228B)\u2227(\u00acB\u2228C)\u2227A", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "c05", |
| "description": "Transitive contradiction: above \u2227 \u00acC", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "C", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "c06", |
| "description": "Cyclic implications: (\u00acA\u2228B)\u2227(\u00acB\u2228A)\u2227A", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "B", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "A", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d01", |
| "description": "Resolves Q: (P\u2228Q) \u2227 (\u00acP\u2228Q)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d02", |
| "description": "Resolution UNSAT: above \u2227 \u00acQ", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d03", |
| "description": "Resolves P: (P\u2228Q) \u2227 (P\u2228\u00acQ)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d04", |
| "description": "Resolution UNSAT: above \u2227 \u00acP", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d05", |
| "description": "Three-clause resolution SAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "d06", |
| "description": "Four-corner UNSAT (full XOR contradiction)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "e01", |
| "description": "2-pigeon-1-hole UNSAT (each pigeon needs a hole, but only one hole)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "e02", |
| "description": "2-pigeon-2-hole SAT (place pigeons in distinct holes)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "e03", |
| "description": "3-pigeon-2-hole UNSAT (classic pigeonhole)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 6 |
| }, |
| { |
| "id": "e04", |
| "description": "3-pigeon-3-hole SAT (a perfect matching exists)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P1H3", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P2H3", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "P3H3", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H1", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H1", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H2", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H2", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H3", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P2H3", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P1H3", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H3", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P2H3", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "P3H3", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 9 |
| }, |
| { |
| "id": "f01", |
| "description": "Cat(Tom)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 1 |
| }, |
| { |
| "id": "f02", |
| "description": "Cat(Tom) \u2227 \u00acCat(Tom)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 1 |
| }, |
| { |
| "id": "f03", |
| "description": "Cat(Tom) \u2227 HasFur(Tom)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "HasFur", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "f04", |
| "description": "Modus ponens grounded: (\u00acCat(Tom) \u2228 HasFur(Tom)) \u2227 Cat(Tom)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "HasFur", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "f05", |
| "description": "Grounded MP UNSAT: above \u2227 \u00acHasFur(Tom)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "HasFur", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "HasFur", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "f06", |
| "description": "Two birds, one negated: Bird(Robin) \u2227 Bird(Tweety) \u2227 \u00acBird(Tweety)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Robin" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 2 |
| }, |
| { |
| "id": "f07", |
| "description": "Universal grounded over 2 constants \u2014 SAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Robin" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Flies", |
| "args": [ |
| "Robin" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Flies", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Robin" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "f08", |
| "description": "Above + \u00acFlies(Tweety) \u2014 UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Robin" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Flies", |
| "args": [ |
| "Robin" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Flies", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Robin" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Bird", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Flies", |
| "args": [ |
| "Tweety" |
| ], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "f09", |
| "description": "Three-step grounded chain SAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Animal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Animal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Mortal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "f10", |
| "description": "Three-step grounded chain UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Animal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Animal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| }, |
| { |
| "predicate": "Mortal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Cat", |
| "args": [ |
| "Tom" |
| ], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Mortal", |
| "args": [ |
| "Tom" |
| ], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g01", |
| "description": "Three-way OR with two negated: (P\u2228Q\u2228R) \u2227 \u00acP \u2227 \u00acQ", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g02", |
| "description": "Above with all negated: UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g03", |
| "description": "Two-pair OR with at-most-one cross: (P\u2228Q)\u2227(R\u2228S)\u2227(\u00acP\u2228\u00acR)", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "S", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 4 |
| }, |
| { |
| "id": "g04", |
| "description": "Three asserted, three-clause exclusion UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g05", |
| "description": "At-most-one of {P,Q,R}", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g06", |
| "description": "Exactly-one of {P,Q,R}: at-most-1 + at-least-1", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "consistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g07", |
| "description": "Exactly-one of {P,Q,R} but force two true: UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| }, |
| { |
| "id": "g08", |
| "description": "Six-atom forced inconsistency: cover all six and refute their conjunction", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "S", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "T", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "U", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "U", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 6 |
| }, |
| { |
| "id": "g09", |
| "description": "Six-atom UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "S", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "T", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "U", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "S", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "T", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "U", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 6 |
| }, |
| { |
| "id": "g10", |
| "description": "Five-atom resolution UNSAT", |
| "rendered_cnf": { |
| "clauses": [ |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": false |
| }, |
| { |
| "predicate": "Q", |
| "args": [], |
| "negated": true |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": false |
| } |
| ], |
| [ |
| { |
| "predicate": "P", |
| "args": [], |
| "negated": true |
| }, |
| { |
| "predicate": "R", |
| "args": [], |
| "negated": true |
| } |
| ] |
| ] |
| }, |
| "label": "inconsistent", |
| "mode": "consistency", |
| "atom_count": 3 |
| } |
| ] |
