%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU096+1 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n024.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 08:00:52 PM UTC 2025 % Result : Theorem 119.62s 119.84s % Output : Proof 119.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SEU096+1 : TPTP v9.2.0. Released v3.2.0. % 0.13/0.13 % Command : duper %s % 0.13/0.34 % Computer : n024.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Oct 3 05:24:23 EDT 2025 % 0.13/0.34 % CPUTime : % 119.62/119.84 SZS status Theorem for theBenchmark.p % 119.62/119.84 SZS output start Proof for theBenchmark.p % 119.62/119.84 Clause #14 (by assumption #[]): Eq (∀ (A B : Iota), And (And (relation A) (function A)) (finite B) → finite (relation_image A B)) True % 119.62/119.84 Clause #49 (by assumption #[]): Eq % 119.62/119.84 (∀ (A B : Iota), % 119.62/119.84 And (relation B) (function B) → subset A (relation_rng B) → Eq (relation_image B (relation_inverse_image B A)) A) % 119.62/119.84 True % 119.62/119.84 Clause #52 (by assumption #[]): Eq % 119.62/119.84 (Not % 119.62/119.84 (∀ (A B : Iota), % 119.62/119.84 And (relation B) (function B) → And (subset A (relation_rng B)) (finite (relation_inverse_image B A)) → finite A)) % 119.62/119.84 True % 119.62/119.84 Clause #134 (by clausification #[14]): ∀ (a : Iota), Eq (∀ (B : Iota), And (And (relation a) (function a)) (finite B) → finite (relation_image a B)) True % 119.62/119.84 Clause #135 (by clausification #[134]): ∀ (a a_1 : Iota), Eq (And (And (relation a) (function a)) (finite a_1) → finite (relation_image a a_1)) True % 119.62/119.84 Clause #136 (by clausification #[135]): ∀ (a a_1 : Iota), % 119.62/119.84 Or (Eq (And (And (relation a) (function a)) (finite a_1)) False) (Eq (finite (relation_image a a_1)) True) % 119.62/119.84 Clause #137 (by clausification #[136]): ∀ (a a_1 : Iota), % 119.62/119.84 Or (Eq (finite (relation_image a a_1)) True) (Or (Eq (And (relation a) (function a)) False) (Eq (finite a_1) False)) % 119.62/119.84 Clause #138 (by clausification #[137]): ∀ (a a_1 : Iota), % 119.62/119.84 Or (Eq (finite (relation_image a a_1)) True) % 119.62/119.84 (Or (Eq (finite a_1) False) (Or (Eq (relation a) False) (Eq (function a) False))) % 119.62/119.84 Clause #145 (by clausification #[52]): Eq % 119.62/119.84 (∀ (A B : Iota), % 119.62/119.84 And (relation B) (function B) → And (subset A (relation_rng B)) (finite (relation_inverse_image B A)) → finite A) % 119.62/119.84 False % 119.62/119.84 Clause #146 (by clausification #[145]): ∀ (a : Iota), % 119.62/119.84 Eq % 119.62/119.84 (Not % 119.62/119.84 (∀ (B : Iota), % 119.62/119.84 And (relation B) (function B) → % 119.62/119.84 And (subset (skS.0 2 a) (relation_rng B)) (finite (relation_inverse_image B (skS.0 2 a))) → % 119.62/119.84 finite (skS.0 2 a))) % 119.62/119.84 True % 119.62/119.84 Clause #147 (by clausification #[146]): ∀ (a : Iota), % 119.62/119.84 Eq % 119.62/119.84 (∀ (B : Iota), % 119.62/119.84 And (relation B) (function B) → % 119.62/119.84 And (subset (skS.0 2 a) (relation_rng B)) (finite (relation_inverse_image B (skS.0 2 a))) → finite (skS.0 2 a)) % 119.62/119.84 False % 119.62/119.84 Clause #148 (by clausification #[147]): ∀ (a a_1 : Iota), % 119.62/119.84 Eq % 119.62/119.84 (Not % 119.62/119.84 (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1)) → % 119.62/119.84 And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) % 119.62/119.84 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) → % 119.62/119.84 finite (skS.0 2 a))) % 119.62/119.84 True % 119.62/119.84 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), % 119.62/119.84 Eq % 119.62/119.84 (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1)) → % 119.62/119.84 And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) % 119.62/119.84 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) → % 119.62/119.84 finite (skS.0 2 a)) % 119.62/119.84 False % 119.62/119.84 Clause #150 (by clausification #[149]): ∀ (a a_1 : Iota), Eq (And (relation (skS.0 3 a a_1)) (function (skS.0 3 a a_1))) True % 119.62/119.84 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota), % 119.62/119.84 Eq % 119.62/119.84 (And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) % 119.62/119.84 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) → % 119.62/119.84 finite (skS.0 2 a)) % 119.62/119.84 False % 119.62/119.84 Clause #152 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (function (skS.0 3 a a_1)) True % 119.62/119.84 Clause #153 (by clausification #[150]): ∀ (a a_1 : Iota), Eq (relation (skS.0 3 a a_1)) True % 119.62/119.84 Clause #202 (by clausification #[151]): ∀ (a a_1 : Iota), % 119.62/119.84 Eq % 119.62/119.84 (And (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) % 119.62/119.84 (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a)))) % 119.62/119.84 True % 119.62/119.84 Clause #203 (by clausification #[151]): ∀ (a : Iota), Eq (finite (skS.0 2 a)) False % 119.62/119.84 Clause #204 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (finite (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) True % 119.62/119.84 Clause #205 (by clausification #[202]): ∀ (a a_1 : Iota), Eq (subset (skS.0 2 a) (relation_rng (skS.0 3 a a_1))) True % 119.62/119.84 Clause #207 (by superposition #[204, 138]): ∀ (a a_1 a_2 : Iota), % 119.62/119.84 Or (Eq (finite (relation_image a (relation_inverse_image (skS.0 3 a_1 a_2) (skS.0 2 a_1)))) True) % 119.62/119.84 (Or (Eq True False) (Or (Eq (relation a) False) (Eq (function a) False))) % 119.71/119.89 Clause #475 (by clausification #[49]): ∀ (a : Iota), % 119.71/119.89 Eq % 119.71/119.89 (∀ (B : Iota), % 119.71/119.89 And (relation B) (function B) → subset a (relation_rng B) → Eq (relation_image B (relation_inverse_image B a)) a) % 119.71/119.89 True % 119.71/119.89 Clause #476 (by clausification #[475]): ∀ (a a_1 : Iota), % 119.71/119.89 Eq % 119.71/119.89 (And (relation a) (function a) → % 119.71/119.89 subset a_1 (relation_rng a) → Eq (relation_image a (relation_inverse_image a a_1)) a_1) % 119.71/119.89 True % 119.71/119.89 Clause #477 (by clausification #[476]): ∀ (a a_1 : Iota), % 119.71/119.89 Or (Eq (And (relation a) (function a)) False) % 119.71/119.89 (Eq (subset a_1 (relation_rng a) → Eq (relation_image a (relation_inverse_image a a_1)) a_1) True) % 119.71/119.89 Clause #478 (by clausification #[477]): ∀ (a a_1 : Iota), % 119.71/119.89 Or (Eq (subset a (relation_rng a_1) → Eq (relation_image a_1 (relation_inverse_image a_1 a)) a) True) % 119.71/119.89 (Or (Eq (relation a_1) False) (Eq (function a_1) False)) % 119.71/119.89 Clause #479 (by clausification #[478]): ∀ (a a_1 : Iota), % 119.71/119.89 Or (Eq (relation a) False) % 119.71/119.89 (Or (Eq (function a) False) % 119.71/119.89 (Or (Eq (subset a_1 (relation_rng a)) False) % 119.71/119.89 (Eq (Eq (relation_image a (relation_inverse_image a a_1)) a_1) True))) % 119.71/119.89 Clause #480 (by clausification #[479]): ∀ (a a_1 : Iota), % 119.71/119.89 Or (Eq (relation a) False) % 119.71/119.89 (Or (Eq (function a) False) % 119.71/119.89 (Or (Eq (subset a_1 (relation_rng a)) False) (Eq (relation_image a (relation_inverse_image a a_1)) a_1))) % 119.71/119.89 Clause #484 (by superposition #[480, 153]): ∀ (a a_1 a_2 : Iota), % 119.71/119.89 Or (Eq (function (skS.0 3 a a_1)) False) % 119.71/119.89 (Or (Eq (subset a_2 (relation_rng (skS.0 3 a a_1))) False) % 119.71/119.89 (Or (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) a_2)) a_2) (Eq False True))) % 119.71/119.89 Clause #682 (by clausification #[207]): ∀ (a a_1 a_2 : Iota), % 119.71/119.89 Or (Eq (finite (relation_image a (relation_inverse_image (skS.0 3 a_1 a_2) (skS.0 2 a_1)))) True) % 119.71/119.89 (Or (Eq (relation a) False) (Eq (function a) False)) % 119.71/119.89 Clause #686 (by superposition #[682, 153]): ∀ (a a_1 a_2 a_3 : Iota), % 119.71/119.89 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True) % 119.71/119.90 (Or (Eq (function (skS.0 3 a a_1)) False) (Eq False True)) % 119.71/119.90 Clause #1247 (by clausification #[484]): ∀ (a a_1 a_2 : Iota), % 119.71/119.90 Or (Eq (function (skS.0 3 a a_1)) False) % 119.71/119.90 (Or (Eq (subset a_2 (relation_rng (skS.0 3 a a_1))) False) % 119.71/119.90 (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) a_2)) a_2)) % 119.71/119.90 Clause #1248 (by forward demodulation #[1247, 152]): ∀ (a a_1 a_2 : Iota), % 119.71/119.90 Or (Eq True False) % 119.71/119.90 (Or (Eq (subset a (relation_rng (skS.0 3 a_1 a_2))) False) % 119.71/119.90 (Eq (relation_image (skS.0 3 a_1 a_2) (relation_inverse_image (skS.0 3 a_1 a_2) a)) a)) % 119.71/119.90 Clause #1249 (by clausification #[1248]): ∀ (a a_1 a_2 : Iota), % 119.71/119.90 Or (Eq (subset a (relation_rng (skS.0 3 a_1 a_2))) False) % 119.71/119.90 (Eq (relation_image (skS.0 3 a_1 a_2) (relation_inverse_image (skS.0 3 a_1 a_2) a)) a) % 119.71/119.90 Clause #1250 (by superposition #[1249, 205]): ∀ (a a_1 : Iota), % 119.71/119.90 Or (Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) (skS.0 2 a)) % 119.71/119.90 (Eq False True) % 119.71/119.90 Clause #1873 (by clausification #[686]): ∀ (a a_1 a_2 a_3 : Iota), % 119.71/119.90 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True) % 119.71/119.90 (Eq (function (skS.0 3 a a_1)) False) % 119.71/119.90 Clause #1874 (by forward demodulation #[1873, 152]): ∀ (a a_1 a_2 a_3 : Iota), % 119.71/119.90 Or (Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True) % 119.71/119.90 (Eq True False) % 119.71/119.90 Clause #1875 (by clausification #[1874]): ∀ (a a_1 a_2 a_3 : Iota), % 119.71/119.90 Eq (finite (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a_2 a_3) (skS.0 2 a_2)))) True % 119.71/119.90 Clause #5579 (by clausification #[1250]): ∀ (a a_1 : Iota), Eq (relation_image (skS.0 3 a a_1) (relation_inverse_image (skS.0 3 a a_1) (skS.0 2 a))) (skS.0 2 a) % 119.71/119.90 Clause #5580 (by superposition #[5579, 1875]): ∀ (a : Iota), Eq (finite (skS.0 2 a)) True % 119.71/119.90 Clause #5581 (by superposition #[5580, 203]): Eq True False % 119.71/119.90 Clause #5584 (by clausification #[5581]): False % 119.71/119.90 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------