%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU817^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n028.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 08:02:30 PM UTC 2025 % Result : Theorem 4.77s 4.93s % Output : Proof 4.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU817^2 : TPTP v9.2.0. Released v3.7.0. % 0.06/0.13 % Command : duper %s % 0.13/0.34 % Computer : n028.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:15:38 EDT 2025 % 0.13/0.34 % CPUTime : % 4.77/4.93 SZS status Theorem for theBenchmark.p % 4.77/4.93 SZS output start Proof for theBenchmark.p % 4.77/4.93 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True % 4.77/4.93 Clause #2 (by assumption #[]): Eq (Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A) True % 4.77/4.93 Clause #5 (by assumption #[]): Eq (Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) True % 4.77/4.93 Clause #6 (by assumption #[]): Eq (Not (subsetE → ∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X)) True % 4.77/4.93 Clause #18 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.77/4.93 Clause #36 (by clausification #[2]): Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A % 4.77/4.93 Clause #37 (by argument congruence #[36]): ∀ (a : Iota), Eq (transitiveset a) ((fun A => ∀ (X : Iota), in X A → subset X A) a) % 4.77/4.93 Clause #41 (by betaEtaReduce #[37]): ∀ (a : Iota), Eq (transitiveset a) (∀ (X : Iota), in X a → subset X a) % 4.77/4.93 Clause #43 (by clausify Prop equality #[41]): ∀ (a : Iota), Or (Eq (transitiveset a) False) (Eq (∀ (X : Iota), in X a → subset X a) True) % 4.77/4.93 Clause #47 (by clausification #[43]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (in a_1 a → subset a_1 a) True) % 4.77/4.93 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True)) % 4.77/4.93 Clause #75 (by clausification #[5]): Eq ordinal fun Xx => And (transitiveset Xx) (wellorderedByIn Xx) % 4.77/4.93 Clause #76 (by argument congruence #[75]): ∀ (a : Iota), Eq (ordinal a) ((fun Xx => And (transitiveset Xx) (wellorderedByIn Xx)) a) % 4.77/4.93 Clause #77 (by betaEtaReduce #[76]): ∀ (a : Iota), Eq (ordinal a) (And (transitiveset a) (wellorderedByIn a)) % 4.77/4.93 Clause #78 (by identity loobHoist #[77]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) True)) (Eq (wellorderedByIn a) False) % 4.77/4.93 Clause #79 (by identity boolHoist #[77]): ∀ (a : Iota), Or (Eq (ordinal a) (And (transitiveset a) False)) (Eq (wellorderedByIn a) True) % 4.77/4.93 Clause #80 (by bool simp #[78]): ∀ (a : Iota), Or (Eq (ordinal a) (transitiveset a)) (Eq (wellorderedByIn a) False) % 4.77/4.93 Clause #81 (by clausification #[6]): Eq (subsetE → ∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X) False % 4.77/4.93 Clause #82 (by clausification #[81]): Eq subsetE True % 4.77/4.93 Clause #83 (by clausification #[81]): Eq (∀ (X : Iota), ordinal X → ∀ (Xx A : Iota), in A X → in Xx A → in Xx X) False % 4.77/4.93 Clause #84 (by backward demodulation #[82, 18]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B) % 4.77/4.93 Clause #87 (by clausification #[84]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True % 4.77/4.93 Clause #88 (by clausification #[87]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True % 4.77/4.93 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True % 4.77/4.93 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True) % 4.77/4.93 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True)) % 4.77/4.93 Clause #92 (by bool simp #[79]): ∀ (a : Iota), Or (Eq (ordinal a) False) (Eq (wellorderedByIn a) True) % 4.77/4.93 Clause #93 (by clausification #[83]): ∀ (a : Iota), Eq (Not (ordinal (skS.0 4 a) → ∀ (Xx A : Iota), in A (skS.0 4 a) → in Xx A → in Xx (skS.0 4 a))) True % 4.77/4.93 Clause #94 (by clausification #[93]): ∀ (a : Iota), Eq (ordinal (skS.0 4 a) → ∀ (Xx A : Iota), in A (skS.0 4 a) → in Xx A → in Xx (skS.0 4 a)) False % 4.77/4.93 Clause #95 (by clausification #[94]): ∀ (a : Iota), Eq (ordinal (skS.0 4 a)) True % 4.77/4.93 Clause #96 (by clausification #[94]): ∀ (a : Iota), Eq (∀ (Xx A : Iota), in A (skS.0 4 a) → in Xx A → in Xx (skS.0 4 a)) False % 4.77/4.93 Clause #97 (by superposition #[95, 92]): ∀ (a : Iota), Or (Eq True False) (Eq (wellorderedByIn (skS.0 4 a)) True) % 4.77/4.93 Clause #100 (by clausification #[97]): ∀ (a : Iota), Eq (wellorderedByIn (skS.0 4 a)) True % 4.77/4.93 Clause #101 (by superposition #[100, 80]): ∀ (a : Iota), Or (Eq (ordinal (skS.0 4 a)) (transitiveset (skS.0 4 a))) (Eq True False) % 4.77/4.95 Clause #104 (by clausification #[96]): ∀ (a a_1 : Iota), Eq (Not (∀ (A : Iota), in A (skS.0 4 a) → in (skS.0 5 a a_1) A → in (skS.0 5 a a_1) (skS.0 4 a))) True % 4.77/4.95 Clause #105 (by clausification #[104]): ∀ (a a_1 : Iota), Eq (∀ (A : Iota), in A (skS.0 4 a) → in (skS.0 5 a a_1) A → in (skS.0 5 a a_1) (skS.0 4 a)) False % 4.77/4.95 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 : Iota), % 4.77/4.95 Eq % 4.77/4.95 (Not (in (skS.0 6 a a_1 a_2) (skS.0 4 a) → in (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → in (skS.0 5 a a_1) (skS.0 4 a))) % 4.77/4.95 True % 4.77/4.95 Clause #107 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 4.77/4.95 Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a) → in (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → in (skS.0 5 a a_1) (skS.0 4 a)) % 4.77/4.95 False % 4.77/4.95 Clause #108 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 6 a a_1 a_2) (skS.0 4 a)) True % 4.77/4.95 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → in (skS.0 5 a a_1) (skS.0 4 a)) False % 4.77/4.95 Clause #148 (by clausification #[101]): ∀ (a : Iota), Eq (ordinal (skS.0 4 a)) (transitiveset (skS.0 4 a)) % 4.77/4.95 Clause #149 (by forward demodulation #[148, 95]): ∀ (a : Iota), Eq True (transitiveset (skS.0 4 a)) % 4.77/4.95 Clause #152 (by superposition #[149, 48]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 4 a_1)) False) (Eq (subset a (skS.0 4 a_1)) True)) % 4.77/4.95 Clause #164 (by clausification #[109]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True % 4.77/4.95 Clause #165 (by clausification #[109]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 4 a)) False % 4.77/4.95 Clause #211 (by clausification #[152]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 4 a_1)) False) (Eq (subset a (skS.0 4 a_1)) True) % 4.77/4.95 Clause #212 (by superposition #[211, 108]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset (skS.0 6 a a_1 a_2) (skS.0 4 a)) True) (Eq False True) % 4.77/4.95 Clause #227 (by clausification #[212]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 6 a a_1 a_2) (skS.0 4 a)) True % 4.77/4.95 Clause #228 (by superposition #[227, 91]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 6 a_1 a_2 a_3)) False) (Eq (in a (skS.0 4 a_1)) True)) % 4.77/4.95 Clause #292 (by clausification #[228]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 6 a_1 a_2 a_3)) False) (Eq (in a (skS.0 4 a_1)) True) % 4.77/4.95 Clause #293 (by superposition #[292, 164]): ∀ (a a_1 : Iota), Or (Eq (in (skS.0 5 a a_1) (skS.0 4 a)) True) (Eq False True) % 4.77/4.95 Clause #302 (by clausification #[293]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (skS.0 4 a)) True % 4.77/4.95 Clause #303 (by superposition #[302, 165]): Eq True False % 4.77/4.95 Clause #312 (by clausification #[303]): False % 4.77/4.95 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------