%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU812^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n013.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 3.95s 4.12s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU812^2 : TPTP v9.2.0. Released v3.7.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n013.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 300 % 0.14/0.35 % DateTime : Fri Oct 3 05:49:38 EDT 2025 % 0.14/0.35 % CPUTime : % 3.95/4.12 SZS status Theorem for theBenchmark.p % 3.95/4.12 SZS output start Proof for theBenchmark.p % 3.95/4.12 Clause #0 (by assumption #[]): Eq (Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A) True % 3.95/4.12 Clause #1 (by assumption #[]): Eq (Not (∀ (X : Iota), transitiveset X → ∀ (A : Iota), in A X → subset A X)) True % 3.95/4.12 Clause #2 (by clausification #[1]): Eq (∀ (X : Iota), transitiveset X → ∀ (A : Iota), in A X → subset A X) False % 3.95/4.12 Clause #3 (by clausification #[2]): ∀ (a : Iota), Eq (Not (transitiveset (skS.0 0 a) → ∀ (A : Iota), in A (skS.0 0 a) → subset A (skS.0 0 a))) True % 3.95/4.12 Clause #4 (by clausification #[3]): ∀ (a : Iota), Eq (transitiveset (skS.0 0 a) → ∀ (A : Iota), in A (skS.0 0 a) → subset A (skS.0 0 a)) False % 3.95/4.12 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (transitiveset (skS.0 0 a)) True % 3.95/4.12 Clause #6 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (A : Iota), in A (skS.0 0 a) → subset A (skS.0 0 a)) False % 3.95/4.12 Clause #7 (by clausification #[0]): Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A % 3.95/4.12 Clause #8 (by argument congruence #[7]): ∀ (a : Iota), Eq (transitiveset a) ((fun A => ∀ (X : Iota), in X A → subset X A) a) % 3.95/4.12 Clause #9 (by betaEtaReduce #[8]): ∀ (a : Iota), Eq (transitiveset a) (∀ (X : Iota), in X a → subset X a) % 3.95/4.12 Clause #11 (by clausify Prop equality #[9]): ∀ (a : Iota), Or (Eq (transitiveset a) False) (Eq (∀ (X : Iota), in X a → subset X a) True) % 3.95/4.12 Clause #13 (by clausification #[11]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (in a_1 a → subset a_1 a) True) % 3.95/4.12 Clause #14 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True)) % 3.95/4.12 Clause #15 (by superposition #[14, 5]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Or (Eq (subset a (skS.0 0 a_1)) True) (Eq False True)) % 3.95/4.12 Clause #20 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Not (in (skS.0 2 a a_1) (skS.0 0 a) → subset (skS.0 2 a a_1) (skS.0 0 a))) True % 3.95/4.12 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a a_1) (skS.0 0 a) → subset (skS.0 2 a a_1) (skS.0 0 a)) False % 3.95/4.12 Clause #22 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (in (skS.0 2 a a_1) (skS.0 0 a)) True % 3.95/4.12 Clause #23 (by clausification #[21]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a a_1) (skS.0 0 a)) False % 3.95/4.12 Clause #24 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 0 a_1)) False) (Eq (subset a (skS.0 0 a_1)) True) % 3.95/4.12 Clause #25 (by superposition #[24, 22]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 2 a a_1) (skS.0 0 a)) True) (Eq False True) % 3.95/4.12 Clause #27 (by clausification #[25]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a a_1) (skS.0 0 a)) True % 3.95/4.12 Clause #28 (by superposition #[27, 23]): Eq True False % 3.95/4.12 Clause #31 (by clausification #[28]): False % 3.95/4.12 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------