%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SET991+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n027.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 08:00:47 PM UTC 2025 % Result : Theorem 11.66s 11.90s % Output : Proof 11.74s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.09/0.11 % Problem : SET991+1 : TPTP v9.2.0. Released v3.2.0. % 0.09/0.12 % Command : duper %s % 0.11/0.33 % Computer : n027.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 300 % 0.11/0.33 % DateTime : Thu Oct 2 14:13:38 EDT 2025 % 0.11/0.33 % CPUTime : % 11.66/11.90 SZS status Theorem for theBenchmark.p % 11.66/11.90 SZS output start Proof for theBenchmark.p % 11.66/11.90 Clause #29 (by assumption #[]): Eq (Not (∀ (A B : Iota), And (relation B) (function B) → in A (relation_dom B) → in (apply B A) (relation_rng B))) True % 11.66/11.90 Clause #30 (by assumption #[]): Eq % 11.66/11.90 (∀ (A : Iota), % 11.66/11.90 And (relation A) (function A) → % 11.66/11.90 ∀ (B : Iota), % 11.66/11.90 Iff (Eq B (relation_rng A)) % 11.66/11.90 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom A)) (Eq C (apply A D))))) % 11.66/11.90 True % 11.66/11.90 Clause #225 (by clausification #[29]): Eq (∀ (A B : Iota), And (relation B) (function B) → in A (relation_dom B) → in (apply B A) (relation_rng B)) False % 11.66/11.90 Clause #226 (by clausification #[225]): ∀ (a : Iota), % 11.66/11.90 Eq % 11.66/11.90 (Not % 11.66/11.90 (∀ (B : Iota), % 11.66/11.90 And (relation B) (function B) → in (skS.0 9 a) (relation_dom B) → in (apply B (skS.0 9 a)) (relation_rng B))) % 11.66/11.90 True % 11.66/11.90 Clause #227 (by clausification #[226]): ∀ (a : Iota), % 11.66/11.90 Eq % 11.66/11.90 (∀ (B : Iota), % 11.66/11.90 And (relation B) (function B) → in (skS.0 9 a) (relation_dom B) → in (apply B (skS.0 9 a)) (relation_rng B)) % 11.66/11.90 False % 11.66/11.90 Clause #228 (by clausification #[227]): ∀ (a a_1 : Iota), % 11.66/11.90 Eq % 11.66/11.90 (Not % 11.66/11.90 (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1)) → % 11.66/11.90 in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) → % 11.66/11.90 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1)))) % 11.66/11.90 True % 11.66/11.90 Clause #229 (by clausification #[228]): ∀ (a a_1 : Iota), % 11.66/11.90 Eq % 11.66/11.90 (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1)) → % 11.66/11.90 in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) → % 11.66/11.90 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) % 11.66/11.90 False % 11.66/11.90 Clause #230 (by clausification #[229]): ∀ (a a_1 : Iota), Eq (And (relation (skS.0 10 a a_1)) (function (skS.0 10 a a_1))) True % 11.66/11.90 Clause #231 (by clausification #[229]): ∀ (a a_1 : Iota), % 11.66/11.90 Eq % 11.66/11.90 (in (skS.0 9 a) (relation_dom (skS.0 10 a a_1)) → % 11.66/11.90 in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) % 11.66/11.90 False % 11.66/11.90 Clause #232 (by clausification #[230]): ∀ (a a_1 : Iota), Eq (function (skS.0 10 a a_1)) True % 11.66/11.90 Clause #233 (by clausification #[230]): ∀ (a a_1 : Iota), Eq (relation (skS.0 10 a a_1)) True % 11.66/11.90 Clause #243 (by clausification #[30]): ∀ (a : Iota), % 11.66/11.90 Eq % 11.66/11.90 (And (relation a) (function a) → % 11.66/11.90 ∀ (B : Iota), % 11.66/11.90 Iff (Eq B (relation_rng a)) % 11.66/11.90 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D))))) % 11.66/11.90 True % 11.66/11.90 Clause #244 (by clausification #[243]): ∀ (a : Iota), % 11.66/11.90 Or (Eq (And (relation a) (function a)) False) % 11.66/11.90 (Eq % 11.66/11.90 (∀ (B : Iota), % 11.66/11.90 Iff (Eq B (relation_rng a)) % 11.66/11.90 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D))))) % 11.66/11.90 True) % 11.66/11.90 Clause #245 (by clausification #[244]): ∀ (a : Iota), % 11.66/11.90 Or % 11.66/11.90 (Eq % 11.66/11.90 (∀ (B : Iota), % 11.66/11.90 Iff (Eq B (relation_rng a)) % 11.66/11.90 (∀ (C : Iota), Iff (in C B) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D))))) % 11.66/11.90 True) % 11.66/11.90 (Or (Eq (relation a) False) (Eq (function a) False)) % 11.66/11.90 Clause #246 (by clausification #[245]): ∀ (a a_1 : Iota), % 11.66/11.90 Or (Eq (relation a) False) % 11.66/11.90 (Or (Eq (function a) False) % 11.66/11.90 (Eq % 11.66/11.90 (Iff (Eq a_1 (relation_rng a)) % 11.66/11.90 (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D))))) % 11.66/11.90 True)) % 11.66/11.90 Clause #248 (by clausification #[246]): ∀ (a a_1 : Iota), % 11.66/11.90 Or (Eq (relation a) False) % 11.66/11.90 (Or (Eq (function a) False) % 11.66/11.90 (Or (Eq (Eq a_1 (relation_rng a)) False) % 11.66/11.90 (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))) True))) % 11.66/11.90 Clause #363 (by clausification #[231]): ∀ (a a_1 : Iota), Eq (in (skS.0 9 a) (relation_dom (skS.0 10 a a_1))) True % 11.66/11.90 Clause #364 (by clausification #[231]): ∀ (a a_1 : Iota), Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) False % 11.66/11.90 Clause #399 (by clausification #[248]): ∀ (a a_1 : Iota), % 11.66/11.90 Or (Eq (relation a) False) % 11.66/11.90 (Or (Eq (function a) False) % 11.66/11.90 (Or (Eq (∀ (C : Iota), Iff (in C a_1) (Exists fun D => And (in D (relation_dom a)) (Eq C (apply a D)))) True) % 11.74/11.94 (Ne a_1 (relation_rng a)))) % 11.74/11.94 Clause #400 (by clausification #[399]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Ne a_1 (relation_rng a)) % 11.74/11.94 (Eq (Iff (in a_2 a_1) (Exists fun D => And (in D (relation_dom a)) (Eq a_2 (apply a D)))) True))) % 11.74/11.94 Clause #401 (by clausification #[400]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Ne a_1 (relation_rng a)) % 11.74/11.94 (Or (Eq (in a_2 a_1) True) (Eq (Exists fun D => And (in D (relation_dom a)) (Eq a_2 (apply a D))) False)))) % 11.74/11.94 Clause #403 (by clausification #[401]): ∀ (a a_1 a_2 a_3 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Ne a_1 (relation_rng a)) % 11.74/11.94 (Or (Eq (in a_2 a_1) True) (Eq (And (in a_3 (relation_dom a)) (Eq a_2 (apply a a_3))) False)))) % 11.74/11.94 Clause #404 (by clausification #[403]): ∀ (a a_1 a_2 a_3 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Ne a_1 (relation_rng a)) % 11.74/11.94 (Or (Eq (in a_2 a_1) True) (Or (Eq (in a_3 (relation_dom a)) False) (Eq (Eq a_2 (apply a a_3)) False))))) % 11.74/11.94 Clause #405 (by clausification #[404]): ∀ (a a_1 a_2 a_3 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Ne a_1 (relation_rng a)) % 11.74/11.94 (Or (Eq (in a_2 a_1) True) (Or (Eq (in a_3 (relation_dom a)) False) (Ne a_2 (apply a a_3)))))) % 11.74/11.94 Clause #406 (by destructive equality resolution #[405]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) % 11.74/11.94 (Or (Eq (in a_1 (relation_rng a)) True) (Or (Eq (in a_2 (relation_dom a)) False) (Ne a_1 (apply a a_2))))) % 11.74/11.94 Clause #407 (by destructive equality resolution #[406]): ∀ (a a_1 : Iota), % 11.74/11.94 Or (Eq (relation a) False) % 11.74/11.94 (Or (Eq (function a) False) (Or (Eq (in (apply a a_1) (relation_rng a)) True) (Eq (in a_1 (relation_dom a)) False))) % 11.74/11.94 Clause #412 (by superposition #[407, 233]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (function (skS.0 10 a a_1)) False) % 11.74/11.94 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True) % 11.74/11.94 (Or (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False) (Eq False True))) % 11.74/11.94 Clause #615 (by clausification #[412]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (function (skS.0 10 a a_1)) False) % 11.74/11.94 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True) % 11.74/11.94 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False)) % 11.74/11.94 Clause #616 (by forward demodulation #[615, 232]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq True False) % 11.74/11.94 (Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True) % 11.74/11.94 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False)) % 11.74/11.94 Clause #617 (by clausification #[616]): ∀ (a a_1 a_2 : Iota), % 11.74/11.94 Or (Eq (in (apply (skS.0 10 a a_1) a_2) (relation_rng (skS.0 10 a a_1))) True) % 11.74/11.94 (Eq (in a_2 (relation_dom (skS.0 10 a a_1))) False) % 11.74/11.94 Clause #618 (by superposition #[617, 363]): ∀ (a a_1 : Iota), Or (Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) True) (Eq False True) % 11.74/11.94 Clause #621 (by clausification #[618]): ∀ (a a_1 : Iota), Eq (in (apply (skS.0 10 a a_1) (skS.0 9 a)) (relation_rng (skS.0 10 a a_1))) True % 11.74/11.94 Clause #622 (by superposition #[621, 364]): Eq True False % 11.74/11.94 Clause #628 (by clausification #[622]): False % 11.74/11.94 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------