%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEU217+3 : TPTP v9.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n022.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 4.58s 4.76s % Output : Proof 4.58s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU217+3 : TPTP v9.2.0. Released v3.2.0. % 0.07/0.14 % Command : duper %s % 0.14/0.35 % Computer : n022.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 04:48:08 EDT 2025 % 0.14/0.35 % CPUTime : % 4.58/4.76 SZS status Theorem for theBenchmark.p % 4.58/4.76 SZS output start Proof for theBenchmark.p % 4.58/4.76 Clause #17 (by assumption #[]): Eq (∀ (A : Iota), relation (identity_relation A)) True % 4.58/4.76 Clause #18 (by assumption #[]): Eq (∀ (A : Iota), And (relation (identity_relation A)) (function (identity_relation A))) True % 4.58/4.76 Clause #29 (by assumption #[]): Eq (Not (∀ (A B : Iota), in B A → Eq (apply (identity_relation A) B) B)) True % 4.58/4.76 Clause #30 (by assumption #[]): Eq % 4.58/4.76 (∀ (A B : Iota), % 4.58/4.76 And (relation B) (function B) → % 4.58/4.76 Iff (Eq B (identity_relation A)) (And (Eq (relation_dom B) A) (∀ (C : Iota), in C A → Eq (apply B C) C))) % 4.58/4.76 True % 4.58/4.76 Clause #41 (by clausification #[17]): ∀ (a : Iota), Eq (relation (identity_relation a)) True % 4.58/4.76 Clause #139 (by clausification #[18]): ∀ (a : Iota), Eq (And (relation (identity_relation a)) (function (identity_relation a))) True % 4.58/4.76 Clause #140 (by clausification #[139]): ∀ (a : Iota), Eq (function (identity_relation a)) True % 4.58/4.76 Clause #194 (by clausification #[29]): Eq (∀ (A B : Iota), in B A → Eq (apply (identity_relation A) B) B) False % 4.58/4.76 Clause #195 (by clausification #[194]): ∀ (a : Iota), Eq (Not (∀ (B : Iota), in B (skS.0 9 a) → Eq (apply (identity_relation (skS.0 9 a)) B) B)) True % 4.58/4.76 Clause #196 (by clausification #[195]): ∀ (a : Iota), Eq (∀ (B : Iota), in B (skS.0 9 a) → Eq (apply (identity_relation (skS.0 9 a)) B) B) False % 4.58/4.76 Clause #197 (by clausification #[196]): ∀ (a a_1 : Iota), % 4.58/4.76 Eq % 4.58/4.76 (Not % 4.58/4.76 (in (skS.0 10 a a_1) (skS.0 9 a) → Eq (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1))) % 4.58/4.76 True % 4.58/4.76 Clause #198 (by clausification #[197]): ∀ (a a_1 : Iota), % 4.58/4.76 Eq (in (skS.0 10 a a_1) (skS.0 9 a) → Eq (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1)) % 4.58/4.76 False % 4.58/4.76 Clause #199 (by clausification #[198]): ∀ (a a_1 : Iota), Eq (in (skS.0 10 a a_1) (skS.0 9 a)) True % 4.58/4.76 Clause #200 (by clausification #[198]): ∀ (a a_1 : Iota), Eq (Eq (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1)) False % 4.58/4.76 Clause #214 (by clausification #[30]): ∀ (a : Iota), % 4.58/4.76 Eq % 4.58/4.76 (∀ (B : Iota), % 4.58/4.76 And (relation B) (function B) → % 4.58/4.76 Iff (Eq B (identity_relation a)) (And (Eq (relation_dom B) a) (∀ (C : Iota), in C a → Eq (apply B C) C))) % 4.58/4.76 True % 4.58/4.76 Clause #215 (by clausification #[214]): ∀ (a a_1 : Iota), % 4.58/4.76 Eq % 4.58/4.76 (And (relation a) (function a) → % 4.58/4.76 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))) % 4.58/4.76 True % 4.58/4.76 Clause #216 (by clausification #[215]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (And (relation a) (function a)) False) % 4.58/4.76 (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))) % 4.58/4.76 True) % 4.58/4.76 Clause #217 (by clausification #[216]): ∀ (a a_1 : Iota), % 4.58/4.76 Or % 4.58/4.76 (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))) % 4.58/4.76 True) % 4.58/4.76 (Or (Eq (relation a) False) (Eq (function a) False)) % 4.58/4.76 Clause #219 (by clausification #[217]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (relation a) False) % 4.58/4.76 (Or (Eq (function a) False) % 4.58/4.76 (Or (Eq (Eq a (identity_relation a_1)) False) % 4.58/4.76 (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True))) % 4.58/4.76 Clause #303 (by clausification #[200]): ∀ (a a_1 : Iota), Ne (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1) % 4.58/4.76 Clause #326 (by clausification #[219]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (relation a) False) % 4.58/4.76 (Or (Eq (function a) False) % 4.58/4.76 (Or (Eq (And (Eq (relation_dom a) a_1) (∀ (C : Iota), in C a_1 → Eq (apply a C) C)) True) % 4.58/4.76 (Ne a (identity_relation a_1)))) % 4.58/4.76 Clause #327 (by clausification #[326]): ∀ (a a_1 : Iota), % 4.58/4.76 Or (Eq (relation a) False) % 4.58/4.76 (Or (Eq (function a) False) % 4.58/4.76 (Or (Ne a (identity_relation a_1)) (Eq (∀ (C : Iota), in C a_1 → Eq (apply a C) C) True))) % 4.58/4.76 Clause #329 (by clausification #[327]): ∀ (a a_1 a_2 : Iota), % 4.58/4.76 Or (Eq (relation a) False) % 4.58/4.76 (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))) % 4.58/4.77 Clause #330 (by clausification #[329]): ∀ (a a_1 a_2 : Iota), % 4.58/4.77 Or (Eq (relation a) False) % 4.58/4.77 (Or (Eq (function a) False) % 4.58/4.77 (Or (Ne a (identity_relation a_1)) (Or (Eq (in a_2 a_1) False) (Eq (Eq (apply a a_2) a_2) True)))) % 4.58/4.77 Clause #331 (by clausification #[330]): ∀ (a a_1 a_2 : Iota), % 4.58/4.77 Or (Eq (relation a) False) % 4.58/4.77 (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)))) % 4.58/4.77 Clause #332 (by destructive equality resolution #[331]): ∀ (a a_1 : Iota), % 4.58/4.77 Or (Eq (relation (identity_relation a)) False) % 4.58/4.77 (Or (Eq (function (identity_relation a)) False) % 4.58/4.77 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1))) % 4.58/4.77 Clause #333 (by forward demodulation #[332, 41]): ∀ (a a_1 : Iota), % 4.58/4.77 Or (Eq True False) % 4.58/4.77 (Or (Eq (function (identity_relation a)) False) % 4.58/4.77 (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1))) % 4.58/4.77 Clause #334 (by clausification #[333]): ∀ (a a_1 : Iota), % 4.58/4.77 Or (Eq (function (identity_relation a)) False) (Or (Eq (in a_1 a) False) (Eq (apply (identity_relation a) a_1) a_1)) % 4.58/4.77 Clause #335 (by superposition #[334, 140]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Or (Eq (apply (identity_relation a_1) a) a) (Eq False True)) % 4.58/4.77 Clause #336 (by clausification #[335]): ∀ (a a_1 : Iota), Or (Eq (in a a_1) False) (Eq (apply (identity_relation a_1) a) a) % 4.58/4.77 Clause #337 (by superposition #[336, 199]): ∀ (a a_1 : Iota), Or (Eq (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1)) (Eq False True) % 4.58/4.77 Clause #397 (by clausification #[337]): ∀ (a a_1 : Iota), Eq (apply (identity_relation (skS.0 9 a)) (skS.0 10 a a_1)) (skS.0 10 a a_1) % 4.58/4.77 Clause #398 (by forward contextual literal cutting #[397, 303]): False % 4.58/4.77 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------