%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU188+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:01:04 PM UTC 2025 % Result : Theorem 4.31s 4.55s % Output : Proof 4.42s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : SEU188+1 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.13 % Command : duper %s % 0.12/0.34 % Computer : n014.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 05:21:23 EDT 2025 % 0.12/0.34 % CPUTime : % 4.31/4.55 SZS status Theorem for theBenchmark.p % 4.31/4.55 SZS output start Proof for theBenchmark.p % 4.31/4.55 Clause #8 (by assumption #[]): Eq (empty empty_set) True % 4.31/4.55 Clause #13 (by assumption #[]): Eq (∀ (A : Iota), And (Not (empty A)) (relation A) → Not (empty (relation_dom A))) True % 4.31/4.55 Clause #14 (by assumption #[]): Eq (∀ (A : Iota), And (Not (empty A)) (relation A) → Not (empty (relation_rng A))) True % 4.31/4.55 Clause #23 (by assumption #[]): Eq (∀ (A : Iota), relation A → (∀ (B C : Iota), Not (in (ordered_pair B C) A)) → Eq A empty_set) True % 4.31/4.55 Clause #24 (by assumption #[]): Eq % 4.31/4.55 (Not (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set)) % 4.31/4.55 True % 4.31/4.55 Clause #26 (by assumption #[]): Eq (∀ (A B : Iota), Not (And (in A B) (empty B))) True % 4.31/4.55 Clause #41 (by clausification #[14]): ∀ (a : Iota), Eq (And (Not (empty a)) (relation a) → Not (empty (relation_rng a))) True % 4.31/4.55 Clause #42 (by clausification #[41]): ∀ (a : Iota), Or (Eq (And (Not (empty a)) (relation a)) False) (Eq (Not (empty (relation_rng a))) True) % 4.31/4.55 Clause #43 (by clausification #[42]): ∀ (a : Iota), Or (Eq (Not (empty (relation_rng a))) True) (Or (Eq (Not (empty a)) False) (Eq (relation a) False)) % 4.31/4.55 Clause #44 (by clausification #[43]): ∀ (a : Iota), Or (Eq (Not (empty a)) False) (Or (Eq (relation a) False) (Eq (empty (relation_rng a)) False)) % 4.31/4.55 Clause #45 (by clausification #[44]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (empty (relation_rng a)) False) (Eq (empty a) True)) % 4.31/4.55 Clause #47 (by clausification #[13]): ∀ (a : Iota), Eq (And (Not (empty a)) (relation a) → Not (empty (relation_dom a))) True % 4.31/4.55 Clause #48 (by clausification #[47]): ∀ (a : Iota), Or (Eq (And (Not (empty a)) (relation a)) False) (Eq (Not (empty (relation_dom a))) True) % 4.31/4.55 Clause #49 (by clausification #[48]): ∀ (a : Iota), Or (Eq (Not (empty (relation_dom a))) True) (Or (Eq (Not (empty a)) False) (Eq (relation a) False)) % 4.31/4.55 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (Not (empty a)) False) (Or (Eq (relation a) False) (Eq (empty (relation_dom a)) False)) % 4.31/4.55 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (empty (relation_dom a)) False) (Eq (empty a) True)) % 4.31/4.55 Clause #67 (by clausification #[23]): ∀ (a : Iota), Eq (relation a → (∀ (B C : Iota), Not (in (ordered_pair B C) a)) → Eq a empty_set) True % 4.31/4.55 Clause #68 (by clausification #[67]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq ((∀ (B C : Iota), Not (in (ordered_pair B C) a)) → Eq a empty_set) True) % 4.31/4.55 Clause #69 (by clausification #[68]): ∀ (a : Iota), % 4.31/4.55 Or (Eq (relation a) False) (Or (Eq (∀ (B C : Iota), Not (in (ordered_pair B C) a)) False) (Eq (Eq a empty_set) True)) % 4.31/4.55 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), % 4.31/4.55 Or (Eq (relation a) False) % 4.31/4.55 (Or (Eq (Eq a empty_set) True) (Eq (Not (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a))) True)) % 4.31/4.55 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), % 4.31/4.55 Or (Eq (relation a) False) % 4.31/4.55 (Or (Eq (Not (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a))) True) (Eq a empty_set)) % 4.31/4.55 Clause #72 (by clausification #[71]): ∀ (a a_1 : Iota), % 4.31/4.55 Or (Eq (relation a) False) % 4.31/4.55 (Or (Eq a empty_set) (Eq (∀ (C : Iota), Not (in (ordered_pair (skS.0 2 a a_1) C) a)) False)) % 4.31/4.55 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota), % 4.31/4.55 Or (Eq (relation a) False) % 4.31/4.55 (Or (Eq a empty_set) (Eq (Not (Not (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a))) True)) % 4.31/4.55 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota), % 4.31/4.55 Or (Eq (relation a) False) % 4.31/4.55 (Or (Eq a empty_set) (Eq (Not (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a)) False)) % 4.31/4.55 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota), % 4.31/4.55 Or (Eq (relation a) False) (Or (Eq a empty_set) (Eq (in (ordered_pair (skS.0 2 a a_1) (skS.0 3 a a_1 a_2)) a) True)) % 4.31/4.55 Clause #99 (by clausification #[24]): Eq (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set) % 4.31/4.55 False % 4.31/4.55 Clause #100 (by clausification #[99]): ∀ (a : Iota), % 4.31/4.55 Eq % 4.31/4.55 (Not % 4.31/4.55 (relation (skS.0 6 a) → % 4.42/4.58 Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) → % 4.42/4.58 Eq (skS.0 6 a) empty_set)) % 4.42/4.58 True % 4.42/4.58 Clause #101 (by clausification #[100]): ∀ (a : Iota), % 4.42/4.58 Eq % 4.42/4.58 (relation (skS.0 6 a) → % 4.42/4.58 Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) → Eq (skS.0 6 a) empty_set) % 4.42/4.58 False % 4.42/4.58 Clause #102 (by clausification #[101]): ∀ (a : Iota), Eq (relation (skS.0 6 a)) True % 4.42/4.58 Clause #103 (by clausification #[101]): ∀ (a : Iota), % 4.42/4.58 Eq (Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) → Eq (skS.0 6 a) empty_set) % 4.42/4.58 False % 4.42/4.58 Clause #104 (by superposition #[102, 45]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True)) % 4.42/4.58 Clause #105 (by superposition #[102, 51]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True)) % 4.42/4.58 Clause #106 (by superposition #[102, 75]): ∀ (a a_1 a_2 : Iota), % 4.42/4.58 Or (Eq True False) % 4.42/4.58 (Or (Eq (skS.0 6 a) empty_set) % 4.42/4.58 (Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True)) % 4.42/4.58 Clause #207 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B : Iota), Not (And (in a B) (empty B))) True % 4.42/4.58 Clause #208 (by clausification #[207]): ∀ (a a_1 : Iota), Eq (Not (And (in a a_1) (empty a_1))) True % 4.42/4.58 Clause #209 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (And (in a a_1) (empty a_1)) False % 4.42/4.58 Clause #210 (by clausification #[209]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (empty a_1) False) % 4.42/4.58 Clause #214 (by clausification #[103]): ∀ (a : Iota), Eq (Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set)) True % 4.42/4.58 Clause #215 (by clausification #[103]): ∀ (a : Iota), Eq (Eq (skS.0 6 a) empty_set) False % 4.42/4.58 Clause #216 (by clausification #[214]): ∀ (a : Iota), Or (Eq (Eq (relation_dom (skS.0 6 a)) empty_set) True) (Eq (Eq (relation_rng (skS.0 6 a)) empty_set) True) % 4.42/4.58 Clause #217 (by clausification #[216]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 6 a)) empty_set) True) (Eq (relation_dom (skS.0 6 a)) empty_set) % 4.42/4.58 Clause #218 (by clausification #[217]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 6 a)) empty_set) (Eq (relation_rng (skS.0 6 a)) empty_set) % 4.42/4.58 Clause #226 (by clausification #[215]): ∀ (a : Iota), Ne (skS.0 6 a) empty_set % 4.42/4.58 Clause #311 (by clausification #[104]): ∀ (a : Iota), Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True) % 4.42/4.58 Clause #336 (by clausification #[105]): ∀ (a : Iota), Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq (empty (skS.0 6 a)) True) % 4.42/4.58 Clause #366 (by clausification #[106]): ∀ (a a_1 a_2 : Iota), % 4.42/4.58 Or (Eq (skS.0 6 a) empty_set) % 4.42/4.58 (Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True) % 4.42/4.58 Clause #367 (by forward contextual literal cutting #[366, 226]): ∀ (a a_1 a_2 : Iota), Eq (in (ordered_pair (skS.0 2 (skS.0 6 a) a_1) (skS.0 3 (skS.0 6 a) a_1 a_2)) (skS.0 6 a)) True % 4.42/4.58 Clause #370 (by superposition #[367, 210]): ∀ (a : Iota), Or (Eq True False) (Eq (empty (skS.0 6 a)) False) % 4.42/4.58 Clause #371 (by clausification #[370]): ∀ (a : Iota), Eq (empty (skS.0 6 a)) False % 4.42/4.58 Clause #372 (by backward demodulation #[371, 311]): ∀ (a : Iota), Or (Eq (empty (relation_rng (skS.0 6 a))) False) (Eq False True) % 4.42/4.58 Clause #373 (by backward demodulation #[371, 336]): ∀ (a : Iota), Or (Eq (empty (relation_dom (skS.0 6 a))) False) (Eq False True) % 4.42/4.58 Clause #374 (by clausification #[373]): ∀ (a : Iota), Eq (empty (relation_dom (skS.0 6 a))) False % 4.42/4.58 Clause #375 (by superposition #[374, 218]): ∀ (a : Iota), Or (Eq (relation_rng (skS.0 6 a)) empty_set) (Eq (empty empty_set) False) % 4.42/4.58 Clause #376 (by forward demodulation #[375, 8]): ∀ (a : Iota), Or (Eq (relation_rng (skS.0 6 a)) empty_set) (Eq True False) % 4.42/4.58 Clause #377 (by clausification #[376]): ∀ (a : Iota), Eq (relation_rng (skS.0 6 a)) empty_set % 4.42/4.58 Clause #379 (by clausification #[372]): ∀ (a : Iota), Eq (empty (relation_rng (skS.0 6 a))) False % 4.42/4.58 Clause #380 (by forward demodulation #[379, 377]): Eq (empty empty_set) False % 4.42/4.58 Clause #381 (by superposition #[380, 8]): Eq False True % 4.42/4.58 Clause #383 (by clausification #[381]): False % 4.42/4.58 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------