%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n011.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:42 AM UTC 2026 % Result : Theorem 24.25s 24.53s % Output : Proof 24.25s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL809_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.05 % Command : duper %s % 0.11/0.38 % Computer : n011.cluster.edu % 0.11/0.38 % Model : x86_64 x86_64 % 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.38 % Memory : 8046.5625MB % 0.11/0.38 % OS : Linux 6.8.0-71-generic % 0.11/0.38 % CPULimit : 300 % 0.11/0.38 % WCLimit : 300 % 0.11/0.38 % DateTime : Sat Sep 5 14:12:29 UTC 2026 % 0.11/0.38 % CPUTime : % 24.25/24.53 SZS status Theorem for theBenchmark.p % 24.25/24.53 SZS output start Proof for theBenchmark.p % 24.25/24.53 Clause #3 (by assumption #[]): Eq (pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i))) True % 24.25/24.53 Clause #5 (by assumption #[]): Eq (∀ (I : nat) (T : dB), pp (aa dB bool it T) → pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) lift T) I))) True % 24.25/24.53 Clause #100 (by assumption #[]): Eq % 24.25/24.53 (∀ (A C B : Type) (R : A) (Q : B) (P : fun A (fun B C)), % 24.25/24.53 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun B C) P R) Q)) % 24.25/24.53 True % 24.25/24.53 Clause #108 (by assumption #[]): Eq % 24.25/24.53 (Not % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa nat dB (aa dB (fun nat dB) lift (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)) % 24.25/24.53 (zero_zero nat))))) % 24.25/24.53 True % 24.25/24.53 Clause #123 (by clausification #[5]): ∀ (a : nat), Eq (∀ (T : dB), pp (aa dB bool it T) → pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) lift T) a))) True % 24.25/24.53 Clause #124 (by clausification #[123]): ∀ (a : dB) (a_1 : nat), Eq (pp (aa dB bool it a) → pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) lift a) a_1))) True % 24.25/24.53 Clause #125 (by clausification #[124]): ∀ (a : dB) (a_1 : nat), % 24.25/24.53 Or (Eq (pp (aa dB bool it a)) False) (Eq (pp (aa dB bool it (aa nat dB (aa dB (fun nat dB) lift a) a_1))) True) % 24.25/24.53 Clause #129 (by superposition #[125, 3]): ∀ (a : nat), % 24.25/24.53 Or % 24.25/24.53 (Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa nat dB % 24.25/24.53 (aa dB (fun nat dB) lift (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)) a))) % 24.25/24.53 True) % 24.25/24.53 (Eq False True) % 24.25/24.53 Clause #2031 (by clausification #[100]): ∀ (a : Type), % 24.25/24.53 Eq % 24.25/24.53 (∀ (C B : Type) (R : a) (Q : B) (P : fun a (fun B C)), % 24.25/24.53 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun B C) P R) Q)) % 24.25/24.53 True % 24.25/24.53 Clause #2032 (by clausification #[2031]): ∀ (a a_1 : Type), % 24.25/24.53 Eq % 24.25/24.53 (∀ (B : Type) (R : a) (Q : B) (P : fun a (fun B a_1)), % 24.25/24.53 Eq (aa a a_1 (combc a B a_1 P Q) R) (aa B a_1 (aa a (fun B a_1) P R) Q)) % 24.25/24.53 True % 24.25/24.53 Clause #2033 (by clausification #[2032]): ∀ (a a_1 a_2 : Type), % 24.25/24.53 Eq % 24.25/24.53 (∀ (R : a) (Q : a_1) (P : fun a (fun a_1 a_2)), % 24.25/24.53 Eq (aa a a_2 (combc a a_1 a_2 P Q) R) (aa a_1 a_2 (aa a (fun a_1 a_2) P R) Q)) % 24.25/24.53 True % 24.25/24.53 Clause #2034 (by clausification #[2033]): ∀ (a a_1 a_2 : Type) (a_3 : a_1), % 24.25/24.53 Eq % 24.25/24.53 (∀ (Q : a) (P : fun a_1 (fun a a_2)), % 24.25/24.53 Eq (aa a_1 a_2 (combc a_1 a a_2 P Q) a_3) (aa a a_2 (aa a_1 (fun a a_2) P a_3) Q)) % 24.25/24.53 True % 24.25/24.53 Clause #2035 (by clausification #[2034]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a), % 24.25/24.53 Eq % 24.25/24.53 (∀ (P : fun a (fun a_1 a_2)), Eq (aa a a_2 (combc a a_1 a_2 P a_3) a_4) (aa a_1 a_2 (aa a (fun a_1 a_2) P a_4) a_3)) % 24.25/24.53 True % 24.25/24.53 Clause #2036 (by clausification #[2035]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1), % 24.25/24.53 Eq (Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun a_2 a) a_3 a_5) a_4)) True % 24.25/24.53 Clause #2037 (by clausification #[2036]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1), % 24.25/24.53 Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun a_2 a) a_3 a_5) a_4) % 24.25/24.53 Clause #2987 (by clausification #[108]): Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa nat dB (aa dB (fun nat dB) lift (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)) % 24.25/24.53 (zero_zero nat)))) % 24.25/24.53 False % 24.25/24.53 Clause #2988 (by forward demodulation #[2987, 2037]): Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa dB dB (combc dB nat dB lift (zero_zero nat)) % 24.25/24.53 (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)))) % 24.25/24.53 False % 24.25/24.53 Clause #2989 (by forward demodulation #[2988, 2037]): Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa dB dB (combc dB nat dB lift (zero_zero nat)) % 24.25/24.53 (aa dB dB (combc dB nat dB (aa dB (fun dB (fun nat dB)) subst b) i) u)))) % 24.25/24.53 False % 24.25/24.53 Clause #3192 (by clausification #[129]): ∀ (a : nat), % 24.25/24.53 Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa nat dB (aa dB (fun nat dB) lift (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)) % 24.25/24.53 a))) % 24.25/24.53 True % 24.25/24.53 Clause #3193 (by forward demodulation #[3192, 2037]): ∀ (a : nat), % 24.25/24.53 Eq % 24.25/24.53 (pp % 24.25/24.53 (aa dB bool it % 24.25/24.53 (aa dB dB (combc dB nat dB lift a) (aa nat dB (aa dB (fun nat dB) (aa dB (fun dB (fun nat dB)) subst b) u) i)))) % 24.25/24.55 True % 24.25/24.55 Clause #3194 (by forward demodulation #[3193, 2037]): ∀ (a : nat), % 24.25/24.55 Eq % 24.25/24.55 (pp % 24.25/24.55 (aa dB bool it % 24.25/24.55 (aa dB dB (combc dB nat dB lift a) (aa dB dB (combc dB nat dB (aa dB (fun dB (fun nat dB)) subst b) i) u)))) % 24.25/24.55 True % 24.25/24.55 Clause #3199 (by superposition #[3194, 2989]): Eq True False % 24.25/24.55 Clause #3245 (by clausification #[3199]): False % 24.25/24.55 SZS output end Proof for theBenchmark.p 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