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Nevertheless, it still remains unclear how good LLMs are for reasoning tasks, especially for long-chain ones. In this paper, we evaluate LLMs' performance on the simplest yet long-chain reasoning task, namely the Equivalence Class Problem (ECP), i.e., determining whether two variables are equal given a set of randomly generated equivalence relations. We consider both reasoning and non-reasoning representative LLMs over a large variety of problem instances, ranging over different numbers of variables, connectivity probabilities, prompts, and other factors. The experimental results show that non-reasoning LLMs fail ECP, while reasoning models are significantly better but still struggle to completely solve this problem. 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Interestingly, considering various connectivity probabilities with a fixed number of variables, we observe that, for non-reasoning models, the ha","title":"How Well Do LLMs Perform on the Simplest Long-Chain Reasoning Tasks: An Empirical Study on the Equivalence Class Problem","vendor":"arxiv_cs_ai"},"confidence":{"method":"deterministic"},"decision":"POSITIVE","issued_at":"2026-05-11T04:43:50Z","notes":"Spider vendor_press (news) news.vendor_press.v1","object":{"captured_by":"crovia.spider.vendor_press","primary_source_url":"https://arxiv.org/abs/2605.06882"},"predecessors":[],"schema":"crovia.axiom.v1","signature":"ed25519:b74ded5a4108ed687f1b01b02530d3c31e585daefd87f72975e70aaf963d35ee37d28b6ae469fc64aebdcf8af9f44742252a267843c6bab5f62a13c75c722a05","signer":"crovia.substrate","subject":{"observed_at":"2026-05-11T04:43:50Z","source_collector":"spider:vendor_press","target_id":"https://arxiv.org/abs/2605.06882"},"tsa":{"authority":"crovia.substrate.bootstrap","rfc3161_token":"{\"kind\":\"crovia.bootstrap.tsa\",\"source_jsonl\":\"/opt/crovia/spider/data/news/vendor_press_v1.jsonl\",\"source_seal_merkle_root\":\"spider_vendor_press_v1\",\"upgrade_path\":\"Sessione H \\u2014 OpenTimestamps weekly anchor\"}"},"zk_mode":"clear","zk_proof":null},"ledger":{"leaf_hash":"ccccce4a99546f55903aff6f6edcfa31a008e51b9230925e250d7e9c32cf86ab","leaf_index":126278,"ledger_path":"/opt/crovia/substrate/axiom_ledger.jsonl"},"merkle_proof":{"hash_alg":"sha256","leaf_prefix":"0x00","node_prefix":"0x01","odd_leaf_rule":"duplicate_last","path":[{"sibling":"459fb51f8919442df24b48e534803c395467bb89ce20e4d57105dfd5c566cec1","side":"right"},{"sibling":"fe39a4625b220f172467ab0762778105949a66fc00b070d8b0eba85c0794cb04","side":"left"},{"sibling":"8b9b5f617738703f9daed34d83e216c7e0072f7e4f50625035549c8f56f4d237","side":"left"},{"sibling":"578798444351c7abe3fe172a61e9e7fa3b0a130f83aac7c82edab0deee2531e8","side":"right"},{"sibling":"1f9e715ff55277a862426e13474f6a5f7610ad79e46b937840fda8aee486a286","side":"right"},{"sibling":"e0ffecde4fe410b22b6171f01b4edeeaa4340bdb4efebffc857ff26922b18ad4","side":"right"},{"sibling":"04569d59306be014888bbb09868ab1d810d758344e57c06e8192441d524059d1","side":"left"},{"sibling":"fd62d742789ec2a4ad0baaf30412885f0f707ff8c8186d2dd2d66fddc87a651a","side":"right"},{"sibling":"d2135da61742c6387f57e5dbeb0f84ba6602653b50838e32a22e26e69c963d0c","side":"left"},{"sibling":"fe7cf0b54f5bf9492865fdc338944ef352cdca1a4f9f377e2991ace599a3bb58","side":"right"},{"sibling":"1a581be91236d1f25e8d47fe5efa0e2b51b7f0f6d706ef76a9093067688e5d56","side":"left"},{"sibling":"878cc30108509c9fa1fc52705a216f519d73b647916fcbdfc30a389934d3364b","side":"left"},{"sibling":"ae7dfff36ba07d9f48c36c28a341482ef244ee13cd0efd49aee2bbef2fd65f87","side":"right"},{"sibling":"62ac6554017807bd83187f5a3e5f4f72d6c482616429c2780e9fff1f4845fa04","side":"left"},{"sibling":"3a5e69cf0803f4c91f3895ed7c9a95748fef240bec4422e167c05300f79f06c0","side":"left"},{"sibling":"f2817ab288b5324fe49770372c7a10f33f7cd11005f8d4c0a730316f5229dc98","side":"left"},{"sibling":"725fac972e772ca0dc598810ea1abc70df472f72d2d6ab8a0baee2b80e5d2f4c","side":"left"},{"sibling":"98fc57dfef8873b512edc8340f7181df57302bb96777625e072235c62d7c5895","side":"right"}]},"schema":"crovia.axiom_proof.v1","seal":{"first_collector_run_id":"","first_receipt_hash":"","jsonl_path":"/opt/crovia/substrate/axiom_ledger.jsonl","key_id":"430895f101d38164","last_collector_run_id":"","last_receipt_hash":"","leaf_count":134292,"merkle_root":"77fc9c28fae777b81da5b495b3115474df6592dfac590333213d3bdf8b94a9b3","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","run_id":"hourly_json_retrofit_20260515T023701Z","schema":"crovia.seal.v1","seal_family_version":"crovia-seal-family/1","seal_kind":"substrate_batch","sealed_at":"2026-05-15T02:37:25Z","sig_algorithm":"ed25519","signature":"68107a834b00b24f5d4501e5ec727445311f132a486567ecc4c72a4e6dff24c8c21f2de3105293353ba5fdbe370d032819af6aa70f694e2e39b6af6737507009","signer_version":"1.1.0"},"trust_root":{"key_id":"430895f101d38164","public_key_hex":"cf742e26f75669dc673cb5c0786a1ae23ae8ca19c347317192ce40c28a7ff25c","signature_algorithm":"ed25519","url":"/registry/canon/TRUST_ROOT.md"},"verifier":{"spec":"/registry/canon/AXIOM_RECEIPT_v1.md","url":"/v/axm_6baf71019ab5f1de19e834017178c4cc00c57bb8aff766e41bf5938f21468970"}}