%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU818^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:02:31 PM UTC 2025 % Result : Theorem 4.28s 4.46s % Output : Proof 4.28s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.02/0.12 % Problem : SEU818^2 : TPTP v9.2.0. Released v3.7.0. % 0.02/0.13 % Command : duper %s % 0.14/0.34 % Computer : n010.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 06:08:08 EDT 2025 % 0.14/0.34 % CPUTime : % 4.28/4.46 SZS status Theorem for theBenchmark.p % 4.28/4.46 SZS output start Proof for theBenchmark.p % 4.28/4.46 Clause #2 (by assumption #[]): Eq (Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A) True % 4.28/4.46 Clause #5 (by assumption #[]): Eq (Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) True % 4.28/4.46 Clause #7 (by assumption #[]): Eq (Not (subsetI1 → ordinalTransSet → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → subset A X)) True % 4.28/4.46 Clause #29 (by clausification #[2]): Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A % 4.28/4.46 Clause #30 (by argument congruence #[29]): ∀ (a : Iota), Eq (transitiveset a) ((fun A => ∀ (X : Iota), in X A → subset X A) a) % 4.28/4.46 Clause #58 (by betaEtaReduce #[30]): ∀ (a : Iota), Eq (transitiveset a) (∀ (X : Iota), in X a → subset X a) % 4.28/4.46 Clause #60 (by clausify Prop equality #[58]): ∀ (a : Iota), Or (Eq (transitiveset a) False) (Eq (∀ (X : Iota), in X a → subset X a) True) % 4.28/4.46 Clause #64 (by clausification #[60]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (in a_1 a → subset a_1 a) True) % 4.28/4.46 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True)) % 4.28/4.46 Clause #76 (by clausification #[5]): Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx) % 4.28/4.46 Clause #77 (by argument congruence #[76]): ∀ (a : Iota), Eq (ordinal a) ((fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) a) % 4.28/4.46 Clause #78 (by betaEtaReduce #[77]): ∀ (a : Iota), Eq (ordinal a) (And (transitiveset a) (wellorderedByIn a)) % 4.28/4.46 Clause #79 (by identity loobHoist #[78]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) True)) (Eq (wellorderedByIn a) False) % 4.28/4.46 Clause #80 (by identity boolHoist #[78]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) False)) (Eq (wellorderedByIn a) True) % 4.28/4.46 Clause #81 (by bool simp #[79]): ∀ (a : Iota), Or (Eq (ordinal a) (transitiveset a)) (Eq (wellorderedByIn a) False) % 4.28/4.46 Clause #82 (by bool simp #[80]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (wellorderedByIn a) True) % 4.28/4.46 Clause #87 (by clausification #[7]): Eq (subsetI1 → ordinalTransSet → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → subset A X) False % 4.28/4.46 Clause #89 (by clausification #[87]): Eq (ordinalTransSet → ∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → subset A X) False % 4.28/4.46 Clause #103 (by clausification #[89]): Eq (∀ (X : Iota), ordinal X → ∀ (A : Iota), in A X → subset A X) False % 4.28/4.46 Clause #109 (by clausification #[103]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 5 a) → ∀ (A : Iota), in A (skS.0 5 a) → subset A (skS.0 5 a))) True % 4.28/4.46 Clause #110 (by clausification #[109]): ∀ (a : Iota), Eq (ordinal (skS.0 5 a) → ∀ (A : Iota), in A (skS.0 5 a) → subset A (skS.0 5 a)) False % 4.28/4.46 Clause #111 (by clausification #[110]): ∀ (a : Iota), Eq (ordinal (skS.0 5 a)) True % 4.28/4.46 Clause #112 (by clausification #[110]): ∀ (a : Iota), Eq (∀ (A : Iota), in A (skS.0 5 a) → subset A (skS.0 5 a)) False % 4.28/4.46 Clause #113 (by superposition #[111, 82]): ∀ (a : Iota), Or (Eq True False) (Eq (wellorderedByIn (skS.0 5 a)) True) % 4.28/4.46 Clause #116 (by clausification #[113]): ∀ (a : Iota), Eq (wellorderedByIn (skS.0 5 a)) True % 4.28/4.46 Clause #117 (by superposition #[116, 81]): ∀ (a : Iota), Or (Eq (ordinal (skS.0 5 a)) (transitiveset (skS.0 5 a))) (Eq True False) % 4.28/4.46 Clause #127 (by clausification #[112]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 6 a a_1) (skS.0 5 a) → subset (skS.0 6 a a_1) (skS.0 5 a))) True % 4.28/4.46 Clause #128 (by clausification #[127]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a) → subset (skS.0 6 a a_1) (skS.0 5 a)) False % 4.28/4.46 Clause #129 (by clausification #[128]): ∀ (a a_1 : Iota), Eq (in (skS.0 6 a a_1) (skS.0 5 a)) True % 4.28/4.46 Clause #130 (by clausification #[128]): ∀ (a a_1 : Iota), Eq (subset (skS.0 6 a a_1) (skS.0 5 a)) False % 4.28/4.46 Clause #170 (by clausification #[117]): ∀ (a : Iota), Eq (ordinal (skS.0 5 a)) (transitiveset (skS.0 5 a)) % 4.28/4.46 Clause #171 (by forward demodulation #[170, 111]): ∀ (a : Iota), Eq True (transitiveset (skS.0 5 a)) % 4.28/4.46 Clause #174 (by superposition #[171, 65]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1)) False) (Eq (subset a (skS.0 5 a_1)) True)) % 4.28/4.46 Clause #253 (by clausification #[174]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 5 a_1)) False) (Eq (subset a (skS.0 5 a_1)) True) % 4.28/4.46 Clause #254 (by superposition #[253, 129]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 6 a a_1) (skS.0 5 a)) True) (Eq False True) % 4.28/4.46 Clause #263 (by clausification #[254]): ∀ (a a_1 : Iota), Eq (subset (skS.0 6 a a_1) (skS.0 5 a)) True % 4.28/4.46 Clause #264 (by superposition #[263, 130]): Eq True False % 4.28/4.46 Clause #274 (by clausification #[264]): False % 4.28/4.46 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------