%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU189+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n017.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 08:01:05 PM UTC 2025 % Result : Theorem 3.91s 4.09s % Output : Proof 3.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.09 % Problem : SEU189+1 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.11 % Command : duper %s % 0.11/0.30 % Computer : n017.cluster.edu % 0.11/0.30 % Model : x86_64 x86_64 % 0.11/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.30 % Memory : 8042.1875MB % 0.11/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.30 % CPULimit : 300 % 0.11/0.30 % WCLimit : 300 % 0.11/0.30 % DateTime : Fri Oct 3 05:20:23 EDT 2025 % 0.11/0.31 % CPUTime : % 3.91/4.09 SZS status Theorem for theBenchmark.p % 3.91/4.09 SZS output start Proof for theBenchmark.p % 3.91/4.09 Clause #10 (by assumption #[]): Eq (∀ (A : Iota), empty A → And (empty (relation_dom A)) (relation (relation_dom A))) True % 3.91/4.09 Clause #11 (by assumption #[]): Eq (∀ (A : Iota), empty A → And (empty (relation_rng A)) (relation (relation_rng A))) True % 3.91/4.09 Clause #17 (by assumption #[]): Eq (empty empty_set) True % 3.91/4.09 Clause #18 (by assumption #[]): Eq (∀ (A : Iota), empty A → Eq A empty_set) True % 3.91/4.09 Clause #19 (by assumption #[]): Eq (Not (∀ (A : Iota), relation A → Iff (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set))) True % 3.91/4.09 Clause #21 (by assumption #[]): Eq (∀ (A : Iota), relation A → Or (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set) → Eq A empty_set) True % 3.91/4.09 Clause #45 (by clausification #[18]): ∀ (a : Iota), Eq (empty a → Eq a empty_set) True % 3.91/4.09 Clause #46 (by clausification #[45]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (Eq a empty_set) True) % 3.91/4.09 Clause #47 (by clausification #[46]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq a empty_set) % 3.91/4.09 Clause #63 (by clausification #[21]): ∀ (a : Iota), Eq (relation a → Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set) → Eq a empty_set) True % 3.91/4.09 Clause #64 (by clausification #[63]): ∀ (a : Iota), % 3.91/4.09 Or (Eq (relation a) False) % 3.91/4.09 (Eq (Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set) → Eq a empty_set) True) % 3.91/4.09 Clause #65 (by clausification #[64]): ∀ (a : Iota), % 3.91/4.09 Or (Eq (relation a) False) % 3.91/4.09 (Or (Eq (Or (Eq (relation_dom a) empty_set) (Eq (relation_rng a) empty_set)) False) (Eq (Eq a empty_set) True)) % 3.91/4.09 Clause #66 (by clausification #[65]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq (relation_rng a) empty_set) False)) % 3.91/4.09 Clause #67 (by clausification #[65]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq a empty_set) True) (Eq (Eq (relation_dom a) empty_set) False)) % 3.91/4.09 Clause #68 (by clausification #[66]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq (relation_rng a) empty_set) False) (Eq a empty_set)) % 3.91/4.09 Clause #69 (by clausification #[68]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq a empty_set) (Ne (relation_rng a) empty_set)) % 3.91/4.09 Clause #93 (by clausification #[11]): ∀ (a : Iota), Eq (empty a → And (empty (relation_rng a)) (relation (relation_rng a))) True % 3.91/4.09 Clause #94 (by clausification #[93]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (And (empty (relation_rng a)) (relation (relation_rng a))) True) % 3.91/4.09 Clause #96 (by clausification #[94]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (empty (relation_rng a)) True) % 3.91/4.09 Clause #102 (by superposition #[96, 17]): Or (Eq (empty (relation_rng empty_set)) True) (Eq False True) % 3.91/4.09 Clause #103 (by clausification #[10]): ∀ (a : Iota), Eq (empty a → And (empty (relation_dom a)) (relation (relation_dom a))) True % 3.91/4.09 Clause #104 (by clausification #[103]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (And (empty (relation_dom a)) (relation (relation_dom a))) True) % 3.91/4.09 Clause #106 (by clausification #[104]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (empty (relation_dom a)) True) % 3.91/4.09 Clause #112 (by clausification #[102]): Eq (empty (relation_rng empty_set)) True % 3.91/4.09 Clause #114 (by superposition #[112, 47]): Or (Eq True False) (Eq (relation_rng empty_set) empty_set) % 3.91/4.09 Clause #118 (by clausification #[114]): Eq (relation_rng empty_set) empty_set % 3.91/4.09 Clause #124 (by superposition #[106, 17]): Or (Eq (empty (relation_dom empty_set)) True) (Eq False True) % 3.91/4.09 Clause #125 (by clausification #[124]): Eq (empty (relation_dom empty_set)) True % 3.91/4.09 Clause #127 (by superposition #[125, 47]): Or (Eq True False) (Eq (relation_dom empty_set) empty_set) % 3.91/4.09 Clause #132 (by clausification #[127]): Eq (relation_dom empty_set) empty_set % 3.91/4.09 Clause #145 (by clausification #[19]): Eq (∀ (A : Iota), relation A → Iff (Eq (relation_dom A) empty_set) (Eq (relation_rng A) empty_set)) False % 3.91/4.09 Clause #146 (by clausification #[145]): ∀ (a : Iota), % 3.91/4.09 Eq % 3.91/4.09 (Not % 3.91/4.09 (relation (skS.0 5 a) → Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set))) % 3.91/4.09 True % 3.91/4.09 Clause #147 (by clausification #[146]): ∀ (a : Iota), % 3.95/4.11 Eq (relation (skS.0 5 a) → Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set)) % 3.95/4.11 False % 3.95/4.11 Clause #148 (by clausification #[147]): ∀ (a : Iota), Eq (relation (skS.0 5 a)) True % 3.95/4.11 Clause #149 (by clausification #[147]): ∀ (a : Iota), Eq (Iff (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set)) False % 3.95/4.11 Clause #152 (by superposition #[148, 69]): ∀ (a : Iota), Or (Eq True False) (Or (Eq (skS.0 5 a) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set)) % 3.95/4.11 Clause #173 (by clausification #[67]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq (Eq (relation_dom a) empty_set) False) (Eq a empty_set)) % 3.95/4.11 Clause #174 (by clausification #[173]): ∀ (a : Iota), Or (Eq (relation a) False) (Or (Eq a empty_set) (Ne (relation_dom a) empty_set)) % 3.95/4.11 Clause #177 (by superposition #[174, 148]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Or (Ne (relation_dom (skS.0 5 a)) empty_set) (Eq False True)) % 3.95/4.11 Clause #186 (by clausification #[177]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Ne (relation_dom (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #195 (by clausification #[152]): ∀ (a : Iota), Or (Eq (skS.0 5 a) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #206 (by clausification #[149]): ∀ (a : Iota), % 3.95/4.11 Or (Eq (Eq (relation_dom (skS.0 5 a)) empty_set) False) (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) False) % 3.95/4.11 Clause #207 (by clausification #[149]): ∀ (a : Iota), Or (Eq (Eq (relation_dom (skS.0 5 a)) empty_set) True) (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) True) % 3.95/4.11 Clause #208 (by clausification #[206]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) False) (Ne (relation_dom (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #209 (by clausification #[208]): ∀ (a : Iota), Or (Ne (relation_dom (skS.0 5 a)) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #210 (by clausification #[207]): ∀ (a : Iota), Or (Eq (Eq (relation_rng (skS.0 5 a)) empty_set) True) (Eq (relation_dom (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #211 (by clausification #[210]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (relation_rng (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #212 (by superposition #[211, 195]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Or (Eq (skS.0 5 a) empty_set) (Ne empty_set empty_set)) % 3.95/4.11 Clause #214 (by eliminate resolved literals #[212]): ∀ (a : Iota), Or (Eq (relation_dom (skS.0 5 a)) empty_set) (Eq (skS.0 5 a) empty_set) % 3.95/4.11 Clause #215 (by forward contextual literal cutting #[214, 186]): ∀ (a : Iota), Eq (skS.0 5 a) empty_set % 3.95/4.11 Clause #220 (by backward demodulation #[215, 209]): ∀ (a : Iota), Or (Ne (relation_dom empty_set) empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #223 (by forward demodulation #[220, 132]): ∀ (a : Iota), Or (Ne empty_set empty_set) (Ne (relation_rng (skS.0 5 a)) empty_set) % 3.95/4.11 Clause #224 (by eliminate resolved literals #[223]): ∀ (a : Iota), Ne (relation_rng (skS.0 5 a)) empty_set % 3.95/4.11 Clause #225 (by forward demodulation #[224, 215]): Ne (relation_rng empty_set) empty_set % 3.95/4.11 Clause #226 (by forward demodulation #[225, 118]): Ne empty_set empty_set % 3.95/4.11 Clause #227 (by eliminate resolved literals #[226]): False % 3.95/4.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------