%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU264+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n003.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 08:01:15 PM UTC 2025 % Result : Theorem 44.78s 44.95s % Output : Proof 44.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SEU264+1 : TPTP v9.2.0. Released v3.3.0. % 0.06/0.13 % Command : duper %s % 0.12/0.34 % Computer : n003.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 300 % 0.12/0.34 % DateTime : Fri Oct 3 04:27:38 EDT 2025 % 0.12/0.34 % CPUTime : % 44.78/44.95 SZS status Theorem for theBenchmark.p % 44.78/44.95 SZS output start Proof for theBenchmark.p % 44.78/44.95 Clause #8 (by assumption #[]): Eq (∀ (A B C : Iota), relation_of2_as_subset C A B → And (subset (relation_dom C) A) (subset (relation_rng C) B)) True % 44.78/44.95 Clause #9 (by assumption #[]): Eq (∀ (A B C D : Iota), relation_of2_as_subset D C A → subset (relation_rng D) B → relation_of2_as_subset D C B) True % 44.78/44.95 Clause #10 (by assumption #[]): Eq (Not (∀ (A B C D : Iota), relation_of2_as_subset D C A → subset A B → relation_of2_as_subset D C B)) True % 44.78/44.95 Clause #11 (by assumption #[]): Eq (∀ (A B C : Iota), And (subset A B) (subset B C) → subset A C) True % 44.78/44.95 Clause #19 (by clausification #[11]): ∀ (a : Iota), Eq (∀ (B C : Iota), And (subset a B) (subset B C) → subset a C) True % 44.78/44.95 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota), Eq (∀ (C : Iota), And (subset a a_1) (subset a_1 C) → subset a C) True % 44.78/44.95 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota), Eq (And (subset a a_1) (subset a_1 a_2) → subset a a_2) True % 44.78/44.95 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a_2)) False) (Eq (subset a a_2) True) % 44.78/44.95 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Or (Eq (subset a a_2) False) (Eq (subset a_2 a_1) False)) % 44.78/44.95 Clause #40 (by clausification #[9]): ∀ (a : Iota), % 44.78/44.95 Eq (∀ (B C D : Iota), relation_of2_as_subset D C a → subset (relation_rng D) B → relation_of2_as_subset D C B) True % 44.78/44.95 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), % 44.78/44.95 Eq (∀ (C D : Iota), relation_of2_as_subset D C a → subset (relation_rng D) a_1 → relation_of2_as_subset D C a_1) True % 44.78/44.95 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota), % 44.78/44.95 Eq (∀ (D : Iota), relation_of2_as_subset D a a_1 → subset (relation_rng D) a_2 → relation_of2_as_subset D a a_2) True % 44.78/44.95 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota), % 44.78/44.95 Eq (relation_of2_as_subset a a_1 a_2 → subset (relation_rng a) a_3 → relation_of2_as_subset a a_1 a_3) True % 44.78/44.95 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota), % 44.78/44.95 Or (Eq (relation_of2_as_subset a a_1 a_2) False) % 44.78/44.95 (Eq (subset (relation_rng a) a_3 → relation_of2_as_subset a a_1 a_3) True) % 44.78/44.95 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), % 44.78/44.95 Or (Eq (relation_of2_as_subset a a_1 a_2) False) % 44.78/44.95 (Or (Eq (subset (relation_rng a) a_3) False) (Eq (relation_of2_as_subset a a_1 a_3) True)) % 44.78/44.95 Clause #65 (by clausification #[8]): ∀ (a : Iota), % 44.78/44.95 Eq (∀ (B C : Iota), relation_of2_as_subset C a B → And (subset (relation_dom C) a) (subset (relation_rng C) B)) True % 44.78/44.95 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), % 44.78/44.95 Eq (∀ (C : Iota), relation_of2_as_subset C a a_1 → And (subset (relation_dom C) a) (subset (relation_rng C) a_1)) True % 44.78/44.95 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), % 44.78/44.95 Eq (relation_of2_as_subset a a_1 a_2 → And (subset (relation_dom a) a_1) (subset (relation_rng a) a_2)) True % 44.78/44.95 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 : Iota), % 44.78/44.95 Or (Eq (relation_of2_as_subset a a_1 a_2) False) % 44.78/44.95 (Eq (And (subset (relation_dom a) a_1) (subset (relation_rng a) a_2)) True) % 44.78/44.95 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Or (Eq (relation_of2_as_subset a a_1 a_2) False) (Eq (subset (relation_rng a) a_2) True) % 44.78/44.95 Clause #73 (by clausification #[10]): Eq (∀ (A B C D : Iota), relation_of2_as_subset D C A → subset A B → relation_of2_as_subset D C B) False % 44.78/44.95 Clause #74 (by clausification #[73]): ∀ (a : Iota), % 44.78/44.95 Eq % 44.78/44.95 (Not % 44.78/44.95 (∀ (B C D : Iota), relation_of2_as_subset D C (skS.0 3 a) → subset (skS.0 3 a) B → relation_of2_as_subset D C B)) % 44.78/44.95 True % 44.78/44.95 Clause #75 (by clausification #[74]): ∀ (a : Iota), % 44.78/44.95 Eq (∀ (B C D : Iota), relation_of2_as_subset D C (skS.0 3 a) → subset (skS.0 3 a) B → relation_of2_as_subset D C B) % 44.78/44.95 False % 44.78/44.95 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), % 44.78/44.95 Eq % 44.78/44.95 (Not % 44.78/44.95 (∀ (C D : Iota), % 44.78/44.95 relation_of2_as_subset D C (skS.0 3 a) → % 44.78/44.95 subset (skS.0 3 a) (skS.0 4 a a_1) → relation_of2_as_subset D C (skS.0 4 a a_1))) % 44.82/45.01 True % 44.82/45.01 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (∀ (C D : Iota), % 44.82/45.01 relation_of2_as_subset D C (skS.0 3 a) → % 44.82/45.01 subset (skS.0 3 a) (skS.0 4 a a_1) → relation_of2_as_subset D C (skS.0 4 a a_1)) % 44.82/45.01 False % 44.82/45.01 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (Not % 44.82/45.01 (∀ (D : Iota), % 44.82/45.01 relation_of2_as_subset D (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 44.82/45.01 subset (skS.0 3 a) (skS.0 4 a a_1) → relation_of2_as_subset D (skS.0 5 a a_1 a_2) (skS.0 4 a a_1))) % 44.82/45.01 True % 44.82/45.01 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (∀ (D : Iota), % 44.82/45.01 relation_of2_as_subset D (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 44.82/45.01 subset (skS.0 3 a) (skS.0 4 a a_1) → relation_of2_as_subset D (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) % 44.82/45.01 False % 44.82/45.01 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (Not % 44.82/45.01 (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 44.82/45.01 subset (skS.0 3 a) (skS.0 4 a a_1) → % 44.82/45.01 relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_1))) % 44.82/45.01 True % 44.82/45.01 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 3 a) → % 44.82/45.01 subset (skS.0 3 a) (skS.0 4 a a_1) → % 44.82/45.01 relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) % 44.82/45.01 False % 44.82/45.01 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 3 a)) True % 44.82/45.01 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), % 44.82/45.01 Eq % 44.82/45.01 (subset (skS.0 3 a) (skS.0 4 a a_1) → % 44.82/45.01 relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) % 44.82/45.01 False % 44.82/45.01 Clause #85 (by superposition #[82, 45]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq True False) % 44.82/45.01 (Or (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) a_4) False) % 44.82/45.01 (Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) a_4) True)) % 44.82/45.01 Clause #87 (by superposition #[82, 69]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) (skS.0 3 a)) True) % 44.82/45.01 Clause #121 (by clausification #[83]): ∀ (a a_1 : Iota), Eq (subset (skS.0 3 a) (skS.0 4 a a_1)) True % 44.82/45.01 Clause #122 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_1)) False % 44.82/45.01 Clause #143 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) a_4) False) % 44.82/45.01 (Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) a_4) True) % 44.82/45.01 Clause #168 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) (skS.0 3 a)) True % 44.82/45.01 Clause #170 (by superposition #[168, 23]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) a_4) True) % 44.82/45.01 (Or (Eq True False) (Eq (subset (skS.0 3 a) a_4) False)) % 44.82/45.01 Clause #387 (by clausification #[170]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) a_4) True) (Eq (subset (skS.0 3 a) a_4) False) % 44.82/45.01 Clause #388 (by superposition #[387, 121]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) (skS.0 4 a a_4)) True) (Eq False True) % 44.82/45.01 Clause #390 (by clausification #[388]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (subset (relation_rng (skS.0 6 a a_1 a_2 a_3)) (skS.0 4 a a_4)) True % 44.82/45.01 Clause #391 (by superposition #[390, 143]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Or (Eq True False) (Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_4)) True) % 44.82/45.01 Clause #6056 (by clausification #[391]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 44.82/45.01 Eq (relation_of2_as_subset (skS.0 6 a a_1 a_2 a_3) (skS.0 5 a a_1 a_2) (skS.0 4 a a_4)) True % 44.82/45.01 Clause #6057 (by superposition #[6056, 122]): Eq True False % 44.82/45.01 Clause #6060 (by clausification #[6057]): False % 44.82/45.01 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------