%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU219+1 : TPTP v9.2.0. Released v3.3.0. % 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 08:01:09 PM UTC 2025 % Result : Theorem 87.23s 87.45s % Output : Proof 87.32s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU219+1 : TPTP v9.2.0. Released v3.3.0. % 0.03/0.13 % 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 05:15:53 EDT 2025 % 0.14/0.35 % CPUTime : % 87.23/87.45 SZS status Theorem for theBenchmark.p % 87.23/87.45 SZS output start Proof for theBenchmark.p % 87.23/87.45 Clause #0 (by assumption #[]): Eq (∀ (A : Iota), And (relation A) (function A) → one_to_one A → Eq (function_inverse A) (relation_inverse A)) True % 87.23/87.45 Clause #8 (by assumption #[]): Eq % 87.23/87.45 (∀ (A : Iota), % 87.23/87.45 relation A → % 87.23/87.45 And (Eq (relation_rng A) (relation_dom (relation_inverse A))) % 87.23/87.45 (Eq (relation_dom A) (relation_rng (relation_inverse A)))) % 87.23/87.45 True % 87.23/87.45 Clause #9 (by assumption #[]): Eq % 87.23/87.45 (Not % 87.23/87.45 (∀ (A : Iota), % 87.23/87.45 And (relation A) (function A) → % 87.23/87.45 one_to_one A → % 87.23/87.45 And (Eq (relation_rng A) (relation_dom (function_inverse A))) % 87.23/87.45 (Eq (relation_dom A) (relation_rng (function_inverse A))))) % 87.23/87.45 True % 87.23/87.45 Clause #20 (by clausification #[0]): ∀ (a : Iota), Eq (And (relation a) (function a) → one_to_one a → Eq (function_inverse a) (relation_inverse a)) True % 87.23/87.45 Clause #21 (by clausification #[20]): ∀ (a : Iota), % 87.23/87.45 Or (Eq (And (relation a) (function a)) False) (Eq (one_to_one a → Eq (function_inverse a) (relation_inverse a)) True) % 87.23/87.46 Clause #22 (by clausification #[21]): ∀ (a : Iota), % 87.23/87.46 Or (Eq (one_to_one a → Eq (function_inverse a) (relation_inverse a)) True) % 87.23/87.46 (Or (Eq (relation a) False) (Eq (function a) False)) % 87.23/87.46 Clause #23 (by clausification #[22]): ∀ (a : Iota), % 87.23/87.46 Or (Eq (relation a) False) % 87.23/87.46 (Or (Eq (function a) False) (Or (Eq (one_to_one a) False) (Eq (Eq (function_inverse a) (relation_inverse a)) True))) % 87.23/87.46 Clause #24 (by clausification #[23]): ∀ (a : Iota), % 87.23/87.46 Or (Eq (relation a) False) % 87.23/87.46 (Or (Eq (function a) False) (Or (Eq (one_to_one a) False) (Eq (function_inverse a) (relation_inverse a)))) % 87.23/87.46 Clause #49 (by clausification #[8]): ∀ (a : Iota), % 87.23/87.46 Eq % 87.23/87.46 (relation a → % 87.23/87.46 And (Eq (relation_rng a) (relation_dom (relation_inverse a))) % 87.23/87.46 (Eq (relation_dom a) (relation_rng (relation_inverse a)))) % 87.23/87.46 True % 87.23/87.46 Clause #50 (by clausification #[49]): ∀ (a : Iota), % 87.23/87.46 Or (Eq (relation a) False) % 87.23/87.46 (Eq % 87.23/87.46 (And (Eq (relation_rng a) (relation_dom (relation_inverse a))) % 87.23/87.46 (Eq (relation_dom a) (relation_rng (relation_inverse a)))) % 87.23/87.46 True) % 87.23/87.46 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (Eq (relation_dom a) (relation_rng (relation_inverse a))) True) % 87.23/87.46 Clause #52 (by clausification #[50]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (Eq (relation_rng a) (relation_dom (relation_inverse a))) True) % 87.23/87.46 Clause #53 (by clausification #[51]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (relation_dom a) (relation_rng (relation_inverse a))) % 87.23/87.46 Clause #56 (by clausification #[52]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (relation_rng a) (relation_dom (relation_inverse a))) % 87.23/87.46 Clause #84 (by clausification #[9]): Eq % 87.23/87.46 (∀ (A : Iota), % 87.23/87.46 And (relation A) (function A) → % 87.23/87.46 one_to_one A → % 87.23/87.46 And (Eq (relation_rng A) (relation_dom (function_inverse A))) % 87.23/87.46 (Eq (relation_dom A) (relation_rng (function_inverse A)))) % 87.23/87.46 False % 87.23/87.46 Clause #85 (by clausification #[84]): ∀ (a : Iota), % 87.23/87.46 Eq % 87.23/87.46 (Not % 87.23/87.46 (And (relation (skS.0 2 a)) (function (skS.0 2 a)) → % 87.23/87.46 one_to_one (skS.0 2 a) → % 87.23/87.46 And (Eq (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.23/87.46 (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))))) % 87.23/87.46 True % 87.23/87.46 Clause #86 (by clausification #[85]): ∀ (a : Iota), % 87.23/87.46 Eq % 87.23/87.46 (And (relation (skS.0 2 a)) (function (skS.0 2 a)) → % 87.23/87.46 one_to_one (skS.0 2 a) → % 87.23/87.46 And (Eq (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.23/87.46 (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a))))) % 87.23/87.46 False % 87.23/87.46 Clause #87 (by clausification #[86]): ∀ (a : Iota), Eq (And (relation (skS.0 2 a)) (function (skS.0 2 a))) True % 87.23/87.46 Clause #88 (by clausification #[86]): ∀ (a : Iota), % 87.23/87.46 Eq % 87.23/87.46 (one_to_one (skS.0 2 a) → % 87.23/87.46 And (Eq (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.23/87.46 (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a))))) % 87.23/87.46 False % 87.23/87.46 Clause #89 (by clausification #[87]): ∀ (a : Iota), Eq (function (skS.0 2 a)) True % 87.32/87.50 Clause #90 (by clausification #[87]): ∀ (a : Iota), Eq (relation (skS.0 2 a)) True % 87.32/87.50 Clause #93 (by superposition #[90, 24]): ∀ (a : Iota), % 87.32/87.50 Or (Eq True False) % 87.32/87.50 (Or (Eq (function (skS.0 2 a)) False) % 87.32/87.50 (Or (Eq (one_to_one (skS.0 2 a)) False) (Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a))))) % 87.32/87.50 Clause #96 (by superposition #[90, 53]): ∀ (a : Iota), Or (Eq True False) (Eq (relation_dom (skS.0 2 a)) (relation_rng (relation_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #97 (by superposition #[90, 56]): ∀ (a : Iota), Or (Eq True False) (Eq (relation_rng (skS.0 2 a)) (relation_dom (relation_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #278 (by clausification #[96]): ∀ (a : Iota), Eq (relation_dom (skS.0 2 a)) (relation_rng (relation_inverse (skS.0 2 a))) % 87.32/87.50 Clause #281 (by clausification #[97]): ∀ (a : Iota), Eq (relation_rng (skS.0 2 a)) (relation_dom (relation_inverse (skS.0 2 a))) % 87.32/87.50 Clause #881 (by clausification #[88]): ∀ (a : Iota), Eq (one_to_one (skS.0 2 a)) True % 87.32/87.50 Clause #882 (by clausification #[88]): ∀ (a : Iota), % 87.32/87.50 Eq % 87.32/87.50 (And (Eq (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.32/87.50 (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a))))) % 87.32/87.50 False % 87.32/87.50 Clause #895 (by clausification #[93]): ∀ (a : Iota), % 87.32/87.50 Or (Eq (function (skS.0 2 a)) False) % 87.32/87.50 (Or (Eq (one_to_one (skS.0 2 a)) False) (Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #896 (by forward demodulation #[895, 89]): ∀ (a : Iota), % 87.32/87.50 Or (Eq True False) % 87.32/87.50 (Or (Eq (one_to_one (skS.0 2 a)) False) (Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #897 (by clausification #[896]): ∀ (a : Iota), Or (Eq (one_to_one (skS.0 2 a)) False) (Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a))) % 87.32/87.50 Clause #898 (by superposition #[897, 881]): ∀ (a : Iota), Or (Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a))) (Eq False True) % 87.32/87.50 Clause #899 (by clausification #[898]): ∀ (a : Iota), Eq (function_inverse (skS.0 2 a)) (relation_inverse (skS.0 2 a)) % 87.32/87.50 Clause #6205 (by clausification #[882]): ∀ (a : Iota), % 87.32/87.50 Or (Eq (Eq (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) False) % 87.32/87.50 (Eq (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))) False) % 87.32/87.50 Clause #6206 (by clausification #[6205]): ∀ (a : Iota), % 87.32/87.50 Or (Eq (Eq (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))) False) % 87.32/87.50 (Ne (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #6207 (by clausification #[6206]): ∀ (a : Iota), % 87.32/87.50 Or (Ne (relation_rng (skS.0 2 a)) (relation_dom (function_inverse (skS.0 2 a)))) % 87.32/87.50 (Ne (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #6208 (by forward demodulation #[6207, 899]): ∀ (a : Iota), % 87.32/87.50 Or (Ne (relation_rng (skS.0 2 a)) (relation_dom (relation_inverse (skS.0 2 a)))) % 87.32/87.50 (Ne (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #6209 (by forward demodulation #[6208, 281]): ∀ (a : Iota), % 87.32/87.50 Or (Ne (relation_rng (skS.0 2 a)) (relation_rng (skS.0 2 a))) % 87.32/87.50 (Ne (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a)))) % 87.32/87.50 Clause #6210 (by eliminate resolved literals #[6209]): ∀ (a : Iota), Ne (relation_dom (skS.0 2 a)) (relation_rng (function_inverse (skS.0 2 a))) % 87.32/87.50 Clause #6211 (by forward demodulation #[6210, 899]): ∀ (a : Iota), Ne (relation_dom (skS.0 2 a)) (relation_rng (relation_inverse (skS.0 2 a))) % 87.32/87.50 Clause #6212 (by forward demodulation #[6211, 278]): ∀ (a : Iota), Ne (relation_dom (skS.0 2 a)) (relation_dom (skS.0 2 a)) % 87.32/87.50 Clause #6213 (by eliminate resolved literals #[6212]): False % 87.32/87.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------