%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : DAT324^1 : TPTP v9.2.0. Released v7.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n009.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 07:47:23 PM UTC 2025 % Result : Theorem 3.77s 3.93s % Output : Proof 3.77s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.11 % Problem : DAT324^1 : TPTP v9.2.0. Released v7.0.0. % 0.11/0.12 % Command : duper %s % 0.13/0.33 % Computer : n009.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Thu Oct 2 21:39:08 EDT 2025 % 0.13/0.33 % CPUTime : % 3.77/3.93 SZS status Theorem for theBenchmark.p % 3.77/3.93 SZS output start Proof for theBenchmark.p % 3.77/3.93 Clause #0 (by assumption #[]): Eq % 3.77/3.93 (∀ (A : Type) (A0 : A → Prop), % 3.77/3.93 «const/sets/FINITE» A A0 → % 3.77/3.93 And (Eq («const/sets/set_of_list» A («const/sets/list_of_set» A A0)) A0) % 3.77/3.93 (Eq («const/lists/LENGTH» A («const/sets/list_of_set» A A0)) («const/sets/CARD» A A0))) % 3.77/3.93 True % 3.77/3.93 Clause #1 (by assumption #[]): Eq % 3.77/3.93 (Not % 3.77/3.93 (∀ (A : Type) (A0 : A → Prop), % 3.77/3.93 «const/sets/FINITE» A A0 → Eq («const/lists/LENGTH» A («const/sets/list_of_set» A A0)) («const/sets/CARD» A A0))) % 3.77/3.93 True % 3.77/3.93 Clause #2 (by clausification #[1]): Eq % 3.77/3.93 (∀ (A : Type) (A0 : A → Prop), % 3.77/3.93 «const/sets/FINITE» A A0 → Eq («const/lists/LENGTH» A («const/sets/list_of_set» A A0)) («const/sets/CARD» A A0)) % 3.77/3.93 False % 3.77/3.93 Clause #3 (by clausification #[2]): ∀ (a : Type), % 3.77/3.93 Eq % 3.77/3.93 (Not % 3.77/3.93 (∀ (A0 : skS.0 0 a → Prop), % 3.77/3.93 «const/sets/FINITE» (skS.0 0 a) A0 → % 3.77/3.93 Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) A0)) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) A0))) % 3.77/3.93 True % 3.77/3.93 Clause #4 (by clausification #[3]): ∀ (a : Type), % 3.77/3.93 Eq % 3.77/3.93 (∀ (A0 : skS.0 0 a → Prop), % 3.77/3.93 «const/sets/FINITE» (skS.0 0 a) A0 → % 3.77/3.93 Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) A0)) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) A0)) % 3.77/3.93 False % 3.77/3.93 Clause #5 (by clausification #[4]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.93 Eq % 3.77/3.93 (Not % 3.77/3.93 («const/sets/FINITE» (skS.0 0 a) (skS.0 1 a a_1) → % 3.77/3.93 Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1)))) % 3.77/3.93 True % 3.77/3.93 Clause #6 (by clausification #[5]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.93 Eq % 3.77/3.93 («const/sets/FINITE» (skS.0 0 a) (skS.0 1 a a_1) → % 3.77/3.93 Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.93 False % 3.77/3.93 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), Eq («const/sets/FINITE» (skS.0 0 a) (skS.0 1 a a_1)) True % 3.77/3.93 Clause #8 (by clausification #[6]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.93 Eq % 3.77/3.93 (Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.93 False % 3.77/3.93 Clause #9 (by clausification #[0]): ∀ (a : Type), % 3.77/3.93 Eq % 3.77/3.93 (∀ (A0 : a → Prop), % 3.77/3.93 «const/sets/FINITE» a A0 → % 3.77/3.93 And (Eq («const/sets/set_of_list» a («const/sets/list_of_set» a A0)) A0) % 3.77/3.93 (Eq («const/lists/LENGTH» a («const/sets/list_of_set» a A0)) («const/sets/CARD» a A0))) % 3.77/3.93 True % 3.77/3.93 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 : a → Prop), % 3.77/3.93 Eq % 3.77/3.93 («const/sets/FINITE» a a_1 → % 3.77/3.93 And (Eq («const/sets/set_of_list» a («const/sets/list_of_set» a a_1)) a_1) % 3.77/3.93 (Eq («const/lists/LENGTH» a («const/sets/list_of_set» a a_1)) («const/sets/CARD» a a_1))) % 3.77/3.93 True % 3.77/3.93 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : a → Prop), % 3.77/3.93 Or (Eq («const/sets/FINITE» a a_1) False) % 3.77/3.93 (Eq % 3.77/3.93 (And (Eq («const/sets/set_of_list» a («const/sets/list_of_set» a a_1)) a_1) % 3.77/3.93 (Eq («const/lists/LENGTH» a («const/sets/list_of_set» a a_1)) («const/sets/CARD» a a_1))) % 3.77/3.93 True) % 3.77/3.93 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : a → Prop), % 3.77/3.93 Or (Eq («const/sets/FINITE» a a_1) False) % 3.77/3.93 (Eq (Eq («const/lists/LENGTH» a («const/sets/list_of_set» a a_1)) («const/sets/CARD» a a_1)) True) % 3.77/3.93 Clause #14 (by clausification #[12]): ∀ (a : Type) (a_1 : a → Prop), % 3.77/3.93 Or (Eq («const/sets/FINITE» a a_1) False) % 3.77/3.93 (Eq («const/lists/LENGTH» a («const/sets/list_of_set» a a_1)) («const/sets/CARD» a a_1)) % 3.77/3.93 Clause #15 (by superposition #[14, 7]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.93 Or % 3.77/3.93 (Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) fun x => skS.0 1 a a_1 x)) % 3.77/3.93 («const/sets/CARD» (skS.0 0 a) fun x => skS.0 1 a a_1 x)) % 3.77/3.94 (Eq False True) % 3.77/3.94 Clause #23 (by clausification #[8]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.94 Ne («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.94 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1)) % 3.77/3.94 Clause #26 (by betaEtaReduce #[15]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.94 Or % 3.77/3.94 (Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.94 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.94 (Eq False True) % 3.77/3.94 Clause #27 (by clausification #[26]): ∀ (a : Type) (a_1 : skS.0 0 a → Prop), % 3.77/3.94 Eq («const/lists/LENGTH» (skS.0 0 a) («const/sets/list_of_set» (skS.0 0 a) (skS.0 1 a a_1))) % 3.77/3.94 («const/sets/CARD» (skS.0 0 a) (skS.0 1 a a_1)) % 3.77/3.94 Clause #28 (by forward contextual literal cutting #[27, 23]): False % 3.77/3.94 SZS output end Proof for theBenchmark.p 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