"proof system" meaning in English

{
  "forms": [
    {
      "form": "proof systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "proof system (plural proof systems)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
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          "parents": [],
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          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Polish translations",
          "parents": [],
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        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Logic",
          "orig": "en:Logic",
          "parents": [
            "Formal sciences",
            "Philosophy",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them."
      ],
      "id": "en-proof_system-en-noun-b~kp0T64",
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "inference rule",
          "inference rule"
        ],
        [
          "tautologies",
          "tautologies"
        ],
        [
          "proof",
          "proof"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "Translations",
          "word": "todistusjärjestelmä"
        },
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "Beweissystem"
        },
        {
          "code": "pl",
          "lang": "Polish",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "grupa aksjomatów"
        }
      ]
    }
  ],
  "word": "proof system"
}

{
  "forms": [
    {
      "form": "proof systems",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "proof system (plural proof systems)",
      "name": "en-noun"
    }
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Finnish translations",
        "Terms with German translations",
        "Terms with Polish translations",
        "Translation table header lacks gloss",
        "en:Logic"
      ],
      "glosses": [
        "A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them."
      ],
      "links": [
        [
          "logic",
          "logic"
        ],
        [
          "axiom",
          "axiom"
        ],
        [
          "inference rule",
          "inference rule"
        ],
        [
          "tautologies",
          "tautologies"
        ],
        [
          "proof",
          "proof"
        ]
      ],
      "raw_glosses": [
        "(logic) A set of axioms and a set of inference rules which are jointly used to deduce tautologies, thereby providing proofs of them."
      ],
      "topics": [
        "human-sciences",
        "logic",
        "mathematics",
        "philosophy",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "Translations",
      "word": "todistusjärjestelmä"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "Beweissystem"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "grupa aksjomatów"
    }
  ],
  "word": "proof system"
}