%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU217+1 : TPTP v9.2.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n014.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 08:01:08 PM UTC 2025 % Result : Theorem 3.98s 4.14s % Output : Proof 3.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU217+1 : TPTP v9.2.0. Released v3.3.0. % 0.10/0.13 % Command : duper %s % 0.13/0.35 % Computer : n014.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 05:36:38 EDT 2025 % 0.13/0.35 % CPUTime : % 3.98/4.14 SZS status Theorem for theBenchmark.p % 3.98/4.14 SZS output start Proof for theBenchmark.p % 3.98/4.14 Clause #18 (by assumption #[]): Eq (∀ (A : Iota), relation (identity_relation A)) True % 3.98/4.14 Clause #20 (by assumption #[]): Eq (∀ (A : Iota), And (relation (identity_relation A)) (function (identity_relation A))) True % 3.98/4.14 Clause #23 (by assumption #[]): Eq (Not (∀ (A B : Iota), in B A → Eq (apply (identity_relation A) B) B)) True % 3.98/4.14 Clause #24 (by assumption #[]): Eq % 3.98/4.14 (∀ (A B : Iota), % 3.98/4.14 And (relation B) (function B) → % 3.98/4.14 Iff (Eq B (identity_relation A)) (And (Eq (relation_dom B) A) (∀ (C : Iota), in C A → Eq (apply B C) C))) % 3.98/4.14 True % 3.98/4.14 Clause #36 (by clausification #[18]): ∀ (a : Iota), Eq (relation (identity_relation a)) True % 3.98/4.14 Clause #74 (by clausification #[20]): ∀ (a : Iota), Eq (And (relation (identity_relation a)) (function (identity_relation a))) True % 3.98/4.14 Clause #75 (by clausification #[74]): ∀ (a : Iota), Eq (function (identity_relation a)) True % 3.98/4.14 Clause #128 (by clausification #[23]): Eq (∀ (A B : Iota), in B A → Eq (apply (identity_relation A) B) B) False % 3.98/4.14 Clause #129 (by clausification #[128]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in B (skS.0 7 a) → Eq (apply (identity_relation (skS.0 7 a)) B) B)) True % 3.98/4.14 Clause #130 (by clausification #[129]): ∀ (a : Iota), Eq (∀ (B : Iota), in B (skS.0 7 a) → Eq (apply (identity_relation (skS.0 7 a)) B) B) False % 3.98/4.14 Clause #131 (by clausification #[130]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq (Not (in (skS.0 8 a a_1) (skS.0 7 a) → Eq (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1))) % 3.98/4.14 True % 3.98/4.14 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq (in (skS.0 8 a a_1) (skS.0 7 a) → Eq (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1)) False % 3.98/4.14 Clause #133 (by clausification #[132]): ∀ (a a_1 : Iota), Eq (in (skS.0 8 a a_1) (skS.0 7 a)) True % 3.98/4.14 Clause #134 (by clausification #[132]): ∀ (a a_1 : Iota), Eq (Eq (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1)) False % 3.98/4.14 Clause #146 (by clausification #[24]): ∀ (a : Iota), % 3.98/4.14 Eq % 3.98/4.14 (∀ (B : Iota), % 3.98/4.14 And (relation B) (function B) → % 3.98/4.14 Iff (Eq B (identity_relation a)) (And (Eq (relation_dom B) a) (∀ (C : Iota), in C a → Eq (apply B C) C))) % 3.98/4.14 True % 3.98/4.14 Clause #147 (by clausification #[146]): ∀ (a a_1 : Iota), % 3.98/4.14 Eq % 3.98/4.14 (And (relation a) (function a) → % 3.98/4.14 Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C))) % 3.98/4.14 True % 3.98/4.14 Clause #148 (by clausification #[147]): ∀ (a a_1 : Iota), % 3.98/4.14 Or (Eq (And (relation a) (function a)) False) % 3.98/4.14 (Eq (Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C))) % 3.98/4.14 True) % 3.98/4.14 Clause #149 (by clausification #[148]): ∀ (a a_1 : Iota), % 3.98/4.14 Or % 3.98/4.14 (Eq (Iff (Eq a (identity_relation a_1)) (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C))) % 3.98/4.14 True) % 3.98/4.14 (Or (Eq (relation a) False) (Eq (function a) False)) % 3.98/4.14 Clause #151 (by clausification #[149]): ∀ (a a_1 : Iota), % 3.98/4.14 Or (Eq (relation a) False) % 3.98/4.14 (Or (Eq (function a) False) % 3.98/4.14 (Or (Eq (Eq a (identity_relation a_1)) False) % 3.98/4.14 (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True))) % 3.98/4.14 Clause #193 (by clausification #[134]): ∀ (a a_1 : Iota), Ne (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1) % 3.98/4.14 Clause #198 (by clausification #[151]): ∀ (a a_1 : Iota), % 3.98/4.14 Or (Eq (relation a) False) % 3.98/4.14 (Or (Eq (function a) False) % 3.98/4.14 (Or (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True) % 3.98/4.14 (Ne a (identity_relation a_1)))) % 3.98/4.14 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), % 3.98/4.14 Or (Eq (relation a) False) % 3.98/4.14 (Or (Eq (function a) False) % 3.98/4.14 (Or (Ne a (identity_relation a_1)) (Eq (∀ (C : Iota), in C a_1 → Eq (apply a C) C) True))) % 3.98/4.14 Clause #201 (by clausification #[199]): ∀ (a a_1 a_2 : Iota), % 3.98/4.14 Or (Eq (relation a) False) % 3.98/4.14 (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Eq (in a_2 a_1 → Eq (apply a a_2) a_2) True))) % 3.98/4.14 Clause #202 (by clausification #[201]): ∀ (a a_1 a_2 : Iota), % 3.98/4.15 Or (Eq (relation a) False) % 3.98/4.15 (Or (Eq (function a) False) % 3.98/4.15 (Or (Ne a (identity_relation a_1)) (Or (Eq (in a_2 a_1) False) (Eq (Eq (apply a a_2) a_2) True)))) % 3.98/4.15 Clause #203 (by clausification #[202]): ∀ (a a_1 a_2 : Iota), % 3.98/4.15 Or (Eq (relation a) False) % 3.98/4.15 (Or (Eq (function a) False) (Or (Ne a (identity_relation a_1)) (Or (Eq (in a_2 a_1) False) (Eq (apply a a_2) a_2)))) % 3.98/4.15 Clause #204 (by destructive equality resolution #[203]): ∀ (a a_1 : Iota), % 3.98/4.15 Or (Eq (relation (identity_relation a)) False) % 3.98/4.15 (Or (Eq (function (identity_relation a)) False) % 3.98/4.15 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1))) % 3.98/4.15 Clause #205 (by forward demodulation #[204, 36]): ∀ (a a_1 : Iota), % 3.98/4.15 Or (Eq True False) % 3.98/4.15 (Or (Eq (function (identity_relation a)) False) % 3.98/4.15 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1))) % 3.98/4.15 Clause #206 (by clausification #[205]): ∀ (a a_1 : Iota), % 3.98/4.15 Or (Eq (function (identity_relation a)) False) (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1)) % 3.98/4.15 Clause #207 (by superposition #[206, 75]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Or (Eq (apply (identity_relation a_1) a) a) (Eq False True)) % 3.98/4.15 Clause #212 (by clausification #[207]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (apply (identity_relation a_1) a) a) % 3.98/4.15 Clause #213 (by superposition #[212, 133]): ∀ (a a_1 : Iota), Or (Eq (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1)) (Eq False True) % 3.98/4.15 Clause #239 (by clausification #[213]): ∀ (a a_1 : Iota), Eq (apply (identity_relation (skS.0 7 a)) (skS.0 8 a a_1)) (skS.0 8 a a_1) % 3.98/4.15 Clause #240 (by forward contextual literal cutting #[239, 193]): False % 3.98/4.15 SZS output end Proof for theBenchmark.p 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