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  "path": "/abs/2604.04830v1",
  "publishedAt": "2026-04-07T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Jan Krajicek"
  ],
  "textContent": "**Authors:** Jan Krajicek\n\nA propositional proof system $P$ has the strong feasible disjunction property iff there is a constant $c \\geq 1$ such that whenever $P$ admits a size $s$ proof of $\\bigvee_i α_i$ with no two $α_i$ sharing an atom then one of $α_i$ has a $P$-proof of size $\\le s^c$. It was proved by K. (2025) that no proof system strong enough admits this property assuming a computational complexity conjecture and a conjecture about proof complexity generators. Here we build on Ilango (2025) and Ren et al. (2025) and prove the same result under two purely computational complexity hypotheses: - there exists a language in class E that requires exponential size circuits even if they are allowed to query an NP oracle, - there exists a P/poly demi-bit in the sense of Rudich (1997).",
  "title": "Failure of the strong feasible disjunction property"
}