%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU198+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n008.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 08:01:06 PM UTC 2025 % Result : Theorem 55.27s 55.50s % Output : Proof 55.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU198+1 : TPTP v9.2.0. Released v3.3.0. % 0.11/0.13 % Command : duper %s % 0.14/0.34 % Computer : n008.cluster.edu % 0.14/0.34 % Model : x86_64 x86_64 % 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.34 % Memory : 8042.1875MB % 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.34 % CPULimit : 300 % 0.14/0.34 % WCLimit : 300 % 0.14/0.34 % DateTime : Fri Oct 3 06:02:23 EDT 2025 % 0.14/0.34 % CPUTime : % 55.27/55.50 SZS status Theorem for theBenchmark.p % 55.27/55.50 SZS output start Proof for theBenchmark.p % 55.27/55.50 Clause #2 (by assumption #[]): Eq (∀ (A B : Iota), Iff (subset A B) (∀ (C : Iota), in C A → in C B)) True % 55.27/55.50 Clause #18 (by assumption #[]): Eq % 55.27/55.50 (∀ (A B C : Iota), % 55.27/55.50 relation C → Iff (in A (relation_rng (relation_rng_restriction B C))) (And (in A B) (in A (relation_rng C)))) % 55.27/55.50 True % 55.27/55.50 Clause #19 (by assumption #[]): Eq (Not (∀ (A B : Iota), relation B → subset (relation_rng (relation_rng_restriction A B)) A)) True % 55.27/55.50 Clause #51 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (B : Iota), Iff (subset a B) (∀ (C : Iota), in C a → in C B)) True % 55.27/55.50 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (C : Iota), in C a → in C a_1)) True % 55.27/55.50 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (C : Iota), in C a → in C a_1) False) % 55.27/55.50 Clause #55 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), % 55.27/55.50 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) % 55.27/55.50 Clause #56 (by clausification #[55]): ∀ (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) % 55.27/55.50 Clause #57 (by clausification #[56]): ∀ (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) % 55.27/55.50 Clause #58 (by clausification #[56]): ∀ (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) % 55.27/55.50 Clause #162 (by clausification #[18]): ∀ (a : Iota), % 55.27/55.50 Eq % 55.27/55.50 (∀ (B C : Iota), % 55.27/55.50 relation C → Iff (in a (relation_rng (relation_rng_restriction B C))) (And (in a B) (in a (relation_rng C)))) % 55.27/55.50 True % 55.27/55.50 Clause #163 (by clausification #[162]): ∀ (a a_1 : Iota), % 55.27/55.50 Eq % 55.27/55.50 (∀ (C : Iota), % 55.27/55.50 relation C → Iff (in a (relation_rng (relation_rng_restriction a_1 C))) (And (in a a_1) (in a (relation_rng C)))) % 55.27/55.50 True % 55.27/55.50 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 : Iota), % 55.27/55.50 Eq % 55.27/55.50 (relation a → % 55.27/55.50 Iff (in a_1 (relation_rng (relation_rng_restriction a_2 a))) (And (in a_1 a_2) (in a_1 (relation_rng a)))) % 55.27/55.50 True % 55.27/55.50 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 : Iota), % 55.27/55.50 Or (Eq (relation a) False) % 55.27/55.50 (Eq (Iff (in a_1 (relation_rng (relation_rng_restriction a_2 a))) (And (in a_1 a_2) (in a_1 (relation_rng a)))) % 55.27/55.50 True) % 55.27/55.50 Clause #167 (by clausification #[165]): ∀ (a a_1 a_2 : Iota), % 55.27/55.50 Or (Eq (relation a) False) % 55.27/55.50 (Or (Eq (in a_1 (relation_rng (relation_rng_restriction a_2 a))) False) % 55.27/55.50 (Eq (And (in a_1 a_2) (in a_1 (relation_rng a))) True)) % 55.27/55.50 Clause #177 (by clausification #[19]): Eq (∀ (A B : Iota), relation B → subset (relation_rng (relation_rng_restriction A B)) A) False % 55.27/55.50 Clause #178 (by clausification #[177]): ∀ (a : Iota), % 55.27/55.50 Eq (Not (∀ (B : Iota), relation B → subset (relation_rng (relation_rng_restriction (skS.0 8 a) B)) (skS.0 8 a))) True % 55.27/55.50 Clause #179 (by clausification #[178]): ∀ (a : Iota), % 55.27/55.50 Eq (∀ (B : Iota), relation B → subset (relation_rng (relation_rng_restriction (skS.0 8 a) B)) (skS.0 8 a)) False % 55.27/55.50 Clause #180 (by clausification #[179]): ∀ (a a_1 : Iota), % 55.27/55.50 Eq % 55.27/55.50 (Not % 55.27/55.50 (relation (skS.0 9 a a_1) → % 55.27/55.50 subset (relation_rng (relation_rng_restriction (skS.0 8 a) (skS.0 9 a a_1))) (skS.0 8 a))) % 55.27/55.50 True % 55.27/55.50 Clause #181 (by clausification #[180]): ∀ (a a_1 : Iota), % 55.27/55.50 Eq % 55.27/55.50 (relation (skS.0 9 a a_1) → % 55.27/55.50 subset (relation_rng (relation_rng_restriction (skS.0 8 a) (skS.0 9 a a_1))) (skS.0 8 a)) % 55.27/55.50 False % 55.27/55.50 Clause #182 (by clausification #[181]): ∀ (a a_1 : Iota), Eq (relation (skS.0 9 a a_1)) True % 55.27/55.50 Clause #183 (by clausification #[181]): ∀ (a a_1 : Iota), Eq (subset (relation_rng (relation_rng_restriction (skS.0 8 a) (skS.0 9 a a_1))) (skS.0 8 a)) False % 55.27/55.50 Clause #337 (by clausification #[167]): ∀ (a a_1 a_2 : Iota), % 55.27/55.50 Or (Eq (relation a) False) % 55.27/55.50 (Or (Eq (in a_1 (relation_rng (relation_rng_restriction a_2 a))) False) (Eq (in a_1 a_2) True)) % 55.27/55.50 Clause #358 (by superposition #[337, 182]): ∀ (a a_1 a_2 a_3 : Iota), % 55.27/55.50 Or (Eq (in a (relation_rng (relation_rng_restriction a_1 (skS.0 9 a_2 a_3)))) False) % 55.36/55.58 (Or (Eq (in a a_1) True) (Eq False True)) % 55.36/55.58 Clause #554 (by clausification #[358]): ∀ (a a_1 a_2 a_3 : Iota), % 55.36/55.58 Or (Eq (in a (relation_rng (relation_rng_restriction a_1 (skS.0 9 a_2 a_3)))) False) (Eq (in a a_1) True) % 55.36/55.58 Clause #555 (by superposition #[554, 57]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 55.36/55.58 Or (Eq (in (skS.0 2 (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a_3 a_4) a) True) % 55.36/55.58 (Or (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a_3) True) (Eq False True)) % 55.36/55.58 Clause #2617 (by clausification #[555]): ∀ (a a_1 a_2 a_3 a_4 : Iota), % 55.36/55.58 Or (Eq (in (skS.0 2 (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a_3 a_4) a) True) % 55.36/55.58 (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a_3) True) % 55.36/55.58 Clause #2655 (by superposition #[2617, 58]): ∀ (a a_1 a_2 : Iota), % 55.36/55.58 Or (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a) True) % 55.36/55.58 (Or (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a) True) (Eq True False)) % 55.36/55.58 Clause #8986 (by clausification #[2655]): ∀ (a a_1 a_2 : Iota), % 55.36/55.58 Or (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a) True) % 55.36/55.58 (Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a) True) % 55.36/55.58 Clause #8987 (by eliminate duplicate literals #[8986]): ∀ (a a_1 a_2 : Iota), Eq (subset (relation_rng (relation_rng_restriction a (skS.0 9 a_1 a_2))) a) True % 55.36/55.58 Clause #8988 (by superposition #[8987, 183]): Eq True False % 55.36/55.58 Clause #8991 (by clausification #[8988]): False % 55.36/55.58 SZS output end Proof for theBenchmark.p 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