%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU560^2 : TPTP v9.2.0. Released v3.7.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n001.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 08:01:54 PM UTC 2025 % Result : Theorem 3.62s 3.82s % Output : Proof 3.62s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.13 % Problem : SEU560^2 : TPTP v9.2.0. Released v3.7.0. % 0.03/0.14 % Command : duper %s % 0.14/0.35 % Computer : n001.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 06:33:23 EDT 2025 % 0.14/0.35 % CPUTime : % 3.62/3.82 SZS status Theorem for theBenchmark.p % 3.62/3.82 SZS output start Proof for theBenchmark.p % 3.62/3.82 Clause #1 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True % 3.62/3.82 Clause #2 (by assumption #[]): Eq (Not (subsetI1 → ∀ (A B : Iota), Eq A B → subset B A)) True % 3.62/3.82 Clause #3 (by clausification #[2]): Eq (subsetI1 → ∀ (A B : Iota), Eq A B → subset B A) False % 3.62/3.82 Clause #4 (by clausification #[3]): Eq subsetI1 True % 3.62/3.82 Clause #5 (by clausification #[3]): Eq (∀ (A B : Iota), Eq A B → subset B A) False % 3.62/3.82 Clause #6 (by clausification #[5]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), Eq (skS.0 0 a) B → subset B (skS.0 0 a))) True % 3.62/3.82 Clause #7 (by clausification #[6]): ∀ (a : Iota), Eq (∀ (B : Iota), Eq (skS.0 0 a) B → subset B (skS.0 0 a)) False % 3.62/3.82 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Eq (Not (Eq (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 1 a a_1) (skS.0 0 a))) True % 3.62/3.82 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1) → subset (skS.0 1 a a_1) (skS.0 0 a)) False % 3.62/3.82 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (Eq (skS.0 0 a) (skS.0 1 a a_1)) True % 3.62/3.82 Clause #11 (by clausification #[9]): ∀ (a a_1 : Iota), Eq (subset (skS.0 1 a a_1) (skS.0 0 a)) False % 3.62/3.82 Clause #12 (by clausification #[10]): ∀ (a a_1 : Iota), Eq (skS.0 0 a) (skS.0 1 a a_1) % 3.62/3.82 Clause #13 (by clausification #[1]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.62/3.82 Clause #14 (by forward demodulation #[13, 4]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) % 3.62/3.82 Clause #15 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True % 3.62/3.82 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True % 3.62/3.82 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True) % 3.62/3.82 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Iota), % 3.62/3.82 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) % 3.62/3.82 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 → in (skS.0 2 a a_1 a_2) a_1) False) % 3.62/3.82 Clause #20 (by clausification #[19]): ∀ (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) % 3.62/3.82 Clause #21 (by clausification #[19]): ∀ (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) % 3.62/3.82 Clause #28 (by forward demodulation #[11, 12]): ∀ (a : Iota), Eq (subset (skS.0 0 a) (skS.0 0 a)) False % 3.62/3.82 Clause #45 (by superposition #[21, 20]): ∀ (a : Iota), Or (Eq (subset a a) True) (Or (Eq (subset a a) True) (Eq False True)) % 3.62/3.82 Clause #47 (by clausification #[45]): ∀ (a : Iota), Or (Eq (subset a a) True) (Eq (subset a a) True) % 3.62/3.82 Clause #48 (by eliminate duplicate literals #[47]): ∀ (a : Iota), Eq (subset a a) True % 3.62/3.82 Clause #49 (by superposition #[48, 28]): Eq True False % 3.62/3.82 Clause #51 (by clausification #[49]): False % 3.62/3.82 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------