%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU567^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:01:55 PM UTC 2025 % Result : Theorem 3.91s 4.08s % Output : Proof 3.91s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.13 % Problem : SEU567^2 : TPTP v9.2.0. Released v3.7.0. % 0.04/0.14 % Command : duper %s % 0.15/0.36 % Computer : n024.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 04:58:53 EDT 2025 % 0.15/0.36 % CPUTime : % 3.91/4.08 SZS status Theorem for theBenchmark.p % 3.91/4.08 SZS output start Proof for theBenchmark.p % 3.91/4.08 Clause #0 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.91/4.08 Clause #1 (by assumption #[]): Eq (Not (subsetI1 → ∀ (A B : Iota), Not (subset A B) → Ne A B)) True % 3.91/4.08 Clause #2 (by clausification #[1]): Eq (subsetI1 → ∀ (A B : Iota), Not (subset A B) → Ne A B) False % 3.91/4.08 Clause #3 (by clausification #[2]): Eq subsetI1 True % 3.91/4.08 Clause #4 (by clausification #[2]): Eq (∀ (A B : Iota), Not (subset A B) → Ne A B) False % 3.91/4.08 Clause #5 (by clausification #[4]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Not (subset (skS.0 0 a) B) → Ne (skS.0 0 a) B)) True % 3.91/4.08 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (subset (skS.0 0 a) B) → Ne (skS.0 0 a) B) False % 3.91/4.08 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (Not (Not (subset (skS.0 0 a) (skS.0 1 a a_1)) → Ne (skS.0 0 a) (skS.0 1 a a_1))) True % 3.91/4.08 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (skS.0 1 a a_1)) → Ne (skS.0 0 a) (skS.0 1 a a_1)) False % 3.91/4.08 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Not (subset (skS.0 0 a) (skS.0 1 a a_1))) True % 3.91/4.08 Clause #10 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Ne (skS.0 0 a) (skS.0 1 a a_1)) False % 3.91/4.08 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (subset (skS.0 0 a) (skS.0 1 a a_1)) False % 3.91/4.08 Clause #12 (by clausification #[0]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.91/4.08 Clause #13 (by forward demodulation #[12, 3]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.91/4.08 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 3.91/4.08 Clause #15 (by clausification #[14]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 3.91/4.08 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 3.91/4.08 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Iota), % 3.91/4.08 Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1)) True) % 3.91/4.08 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a → in (skS.0 2 a a_1 a_2) a_1) False) % 3.91/4.08 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a) True) % 3.91/4.08 Clause #20 (by clausification #[18]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 2 a a_1 a_2) a_1) False) % 3.91/4.08 Clause #21 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 1 a a_1) % 3.91/4.08 Clause #22 (by backward demodulation #[21, 11]): ∀ (a : Iota), Eq (subset (skS.0 0 a) (skS.0 0 a)) False % 3.91/4.08 Clause #23 (by superposition #[20, 19]): ∀ (a : Iota), Or (Eq (subset a a) True) (Or (Eq (subset a a) True) (Eq False True)) % 3.91/4.08 Clause #24 (by clausification #[23]): ∀ (a : Iota), Or (Eq (subset a a) True) (Eq (subset a a) True) % 3.91/4.08 Clause #25 (by eliminate duplicate literals #[24]): ∀ (a : Iota), Eq (subset a a) True % 3.91/4.08 Clause #26 (by superposition #[25, 22]): Eq True False % 3.91/4.08 Clause #27 (by clausification #[26]): False % 3.91/4.08 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------