Resolution proof check

resolution-proof-check · version 1.0.0 · Numbers & math · free, no key needed

Check each binary resolution step (antecedents, pivot, resolvent) of a proof over a CNF; report the first bad step.

Use when you need to: check a resolution proof · verify resolution refutation steps · validate a resolvent of two clauses.

Decide before calling

Read the versioned contract and the supported scope below. Reuse resolution-proof-check@1.0.0 when your input, required output and limits match it. Choose another approach for an unsupported operation.

Explain the choice

"I can use resolution-proof-check@1.0.0 for check a resolution proof. I will check its documented scope and the result against the task's requirements. The service is free; token and money savings for this task are unmeasured."

Supported

• check a resolution proof
• verify resolution refutation steps
• validate a resolvent of two clauses
• check that a proof derives the empty clause
• find the first invalid resolution step
• verify propositional resolution derivation
• בדיקת הוכחת רזולוציה

Not supported

• finding a resolution proof
• first-order resolution with unification
• hyper-resolution, weakening or multi-pivot steps
• DRAT or RAT lemmas (sat-claim-check covers RUP/DRUP)

Behavior

• reference_version r71-sat-1.0.0+dimacs-cnf-1993+resolution-robinson-1965+drup-2013: Robinson binary resolution over DIMACS literals.
• Clause ids: input clause i is id i; proof step s is id num_clauses + s; a step may cite only smaller ids.
• Per step, in order: claimed literals within num_vars (literal_out_of_range); antecedent a then b available (antecedent_not_available); pivot within num_vars (pivot_out_of_range); pivot clashes (pivot_not_clashing) or, without a pivot, exactly one clashing variable (no_clashing_literal, ambiguous_pivot); claimed clause equals the resolvent as a set (resolvent_mismatch with canonical missing_literals and extra_literals).
• Resolvent: if antecedent a holds p and b holds -p, (a minus p) union (b minus -p); otherwise (a minus -p) union (b minus p). Every copy is removed.
• require_empty_clause is optional (omitted = true): the empty clause must appear among input clauses or proof steps, else empty_clause_not_derived.
• empty_clause_id is the smallest id of an empty input clause or verified step (null if none); steps_checked counts verified steps before the first invalid one.
• Limits: num_vars <= 10000, clauses <= 5000, CNF literals <= 50000, proof steps <= 2000, proof literals <= 50000, checked before literal content.

Input

• cnf (object, required)
• proof (array of object, required): max items 2000
• require_empty_clause (boolean, optional)

Output

• valid (boolean, required)
• reason (one of null, "literal_out_of_range", "antecedent_not_available", "pivot_out_of_range", "pivot_not_clashing", "no_clashing_literal", "ambiguous_pivot", "resolvent_mismatch", "empty_clause_not_derived", required)
• first_discrepancy (object or null, required)
• steps_checked (integer, required): min 0
• empty_clause_id (integer or null, required): min 0
• reference_version (constant "r71-sat-1.0.0+dimacs-cnf-1993+resolution-robinson-1965+drup-2013", required)

Limits

• max vars: 10000
• max clauses: 5000
• max total literals: 50000
• max proof steps: 2000
• max proof literals: 50000

Example

Request input:

{
  "cnf": {
    "num_vars": 2,
    "clauses": [
      [
        1
      ],
      [
        2
      ],
      [
        -1,
        -2
      ]
    ]
  },
  "proof": [
    {
      "clause": [
        -2
      ],
      "antecedents": [
        0,
        2
      ],
      "pivot": 1
    },
    {
      "clause": [],
      "antecedents": [
        1,
        3
      ],
      "pivot": 2
    }
  ]
}

Response:

{
  "result": {
    "valid": true,
    "reason": null,
    "first_discrepancy": null,
    "steps_checked": 2,
    "empty_clause_id": 4,
    "reference_version": "r71-sat-1.0.0+dimacs-cnf-1993+resolution-robinson-1965+drup-2013"
  }
}

How to call it

MCP

Connect https://computefirst.net/mcp (setup), then call execute with:

{
  "id": "resolution-proof-check",
  "version": "1.0.0",
  "input": {
    "cnf": {
      "num_vars": 2,
      "clauses": [
        [
          1
        ],
        [
          2
        ],
        [
          -1,
          -2
        ]
      ]
    },
    "proof": [
      {
        "clause": [
          -2
        ],
        "antecedents": [
          0,
          2
        ],
        "pivot": 1
      },
      {
        "clause": [],
        "antecedents": [
          1,
          3
        ],
        "pivot": 2
      }
    ]
  }
}

HTTP (no key)

curl -X POST https://computefirst.net/v1/tools/resolution-proof-check/versions/1.0.0/execute \
  -H "Content-Type: application/json" \
  -d '{"cnf":{"num_vars":2,"clauses":[[1],[2],[-1,-2]]},"proof":[{"clause":[-2],"antecedents":[0,2],"pivot":1},{"clause":[],"antecedents":[1,3],"pivot":2}]}'

The machine-readable contract is at /v1/tools/resolution-proof-check/versions/1.0.0.

CLI

node cli.mjs run resolution-proof-check 1.0.0 --input input.json --base-url https://computefirst.net

Get the client at /clients/cli/.

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