%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU303+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 08:01:20 PM UTC 2025 % Result : Theorem 4.01s 4.24s % Output : Proof 4.01s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.13 % Problem : SEU303+1 : TPTP v9.2.0. Released v3.3.0. % 0.08/0.15 % Command : duper %s % 0.15/0.36 % Computer : n001.cluster.edu % 0.15/0.36 % Model : x86_64 x86_64 % 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.15/0.36 % Memory : 8042.1875MB % 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 % 0.15/0.36 % CPULimit : 300 % 0.15/0.36 % WCLimit : 300 % 0.15/0.36 % DateTime : Fri Oct 3 06:31:08 EDT 2025 % 0.15/0.36 % CPUTime : % 4.01/4.24 SZS status Theorem for theBenchmark.p % 4.01/4.24 SZS output start Proof for theBenchmark.p % 4.01/4.24 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), And (And (relation A) (function A)) (finite B) → finite (relation_image A B)) True % 4.01/4.24 Clause #3 (by assumption #[]): Eq (∀ (A : Iota), relation A → Eq (relation_image A (relation_dom A)) (relation_rng A)) True % 4.01/4.24 Clause #5 (by assumption #[]): Eq (Not (∀ (A : Iota), And (relation A) (function A) → finite (relation_dom A) → finite (relation_rng A))) True % 4.01/4.24 Clause #6 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), And (And (relation a) (function a)) (finite B) → finite (relation_image a B)) True % 4.01/4.24 Clause #7 (by clausification #[6]): ∀ (a a_1 : Iota), Eq (And (And (relation a) (function a)) (finite a_1) → finite (relation_image a a_1)) True % 4.01/4.24 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (And (And (relation a) (function a)) (finite a_1)) False) (Eq (finite (relation_image a a_1)) True) % 4.01/4.24 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image a a_1)) True) (Or (Eq (And (relation a) (function a)) False) (Eq (finite a_1) False)) % 4.01/4.24 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image a a_1)) True) % 4.01/4.24 (Or (Eq (finite a_1) False) (Or (Eq (relation a) False) (Eq (function a) False))) % 4.01/4.24 Clause #11 (by clausification #[5]): Eq (∀ (A : Iota), And (relation A) (function A) → finite (relation_dom A) → finite (relation_rng A)) False % 4.01/4.24 Clause #12 (by clausification #[11]): ∀ (a : Iota), % 4.01/4.24 Eq % 4.01/4.24 (Not % 4.01/4.24 (And (relation (skS.0 0 a)) (function (skS.0 0 a)) → % 4.01/4.24 finite (relation_dom (skS.0 0 a)) → finite (relation_rng (skS.0 0 a)))) % 4.01/4.24 True % 4.01/4.24 Clause #13 (by clausification #[12]): ∀ (a : Iota), % 4.01/4.24 Eq % 4.01/4.24 (And (relation (skS.0 0 a)) (function (skS.0 0 a)) → % 4.01/4.24 finite (relation_dom (skS.0 0 a)) → finite (relation_rng (skS.0 0 a))) % 4.01/4.24 False % 4.01/4.24 Clause #14 (by clausification #[13]): ∀ (a : Iota), Eq (And (relation (skS.0 0 a)) (function (skS.0 0 a))) True % 4.01/4.24 Clause #15 (by clausification #[13]): ∀ (a : Iota), Eq (finite (relation_dom (skS.0 0 a)) → finite (relation_rng (skS.0 0 a))) False % 4.01/4.24 Clause #16 (by clausification #[14]): ∀ (a : Iota), Eq (function (skS.0 0 a)) True % 4.01/4.24 Clause #17 (by clausification #[14]): ∀ (a : Iota), Eq (relation (skS.0 0 a)) True % 4.01/4.24 Clause #21 (by clausification #[3]): ∀ (a : Iota), Eq (relation a → Eq (relation_image a (relation_dom a)) (relation_rng a)) True % 4.01/4.24 Clause #22 (by clausification #[21]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (Eq (relation_image a (relation_dom a)) (relation_rng a)) True) % 4.01/4.24 Clause #23 (by clausification #[22]): ∀ (a : Iota), Or (Eq (relation a) False) (Eq (relation_image a (relation_dom a)) (relation_rng a)) % 4.01/4.24 Clause #24 (by superposition #[23, 17]): ∀ (a : Iota), Or (Eq (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a))) (relation_rng (skS.0 0 a))) (Eq False True) % 4.01/4.24 Clause #31 (by clausification #[15]): ∀ (a : Iota), Eq (finite (relation_dom (skS.0 0 a))) True % 4.01/4.24 Clause #32 (by clausification #[15]): ∀ (a : Iota), Eq (finite (relation_rng (skS.0 0 a))) False % 4.01/4.24 Clause #33 (by superposition #[31, 10]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image a (relation_dom (skS.0 0 a_1)))) True) % 4.01/4.24 (Or (Eq True False) (Or (Eq (relation a) False) (Eq (function a) False))) % 4.01/4.24 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image a (relation_dom (skS.0 0 a_1)))) True) % 4.01/4.24 (Or (Eq (relation a) False) (Eq (function a) False)) % 4.01/4.24 Clause #35 (by superposition #[34, 17]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a_1)))) True) % 4.01/4.24 (Or (Eq (function (skS.0 0 a)) False) (Eq False True)) % 4.01/4.24 Clause #37 (by clausification #[24]): ∀ (a : Iota), Eq (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a))) (relation_rng (skS.0 0 a)) % 4.01/4.24 Clause #39 (by clausification #[35]): ∀ (a a_1 : Iota), % 4.01/4.24 Or (Eq (finite (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a_1)))) True) (Eq (function (skS.0 0 a)) False) % 4.01/4.24 Clause #40 (by forward demodulation #[39, 16]): ∀ (a a_1 : Iota), Or (Eq (finite (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a_1)))) True) (Eq True False) % 4.01/4.25 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Eq (finite (relation_image (skS.0 0 a) (relation_dom (skS.0 0 a_1)))) True % 4.01/4.25 Clause #43 (by superposition #[41, 37]): ∀ (a : Iota), Eq (finite (relation_rng (skS.0 0 a))) True % 4.01/4.25 Clause #44 (by superposition #[43, 32]): Eq True False % 4.01/4.25 Clause #46 (by clausification #[44]): False % 4.01/4.25 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------