%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL763_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 11:36:35 AM UTC 2026 % Result : Theorem 4.05s 4.30s % Output : Proof 4.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL763_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.05 % Command : duper %s % 0.11/0.39 % Computer : n011.cluster.edu % 0.11/0.39 % Model : x86_64 x86_64 % 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.39 % Memory : 8046.5625MB % 0.11/0.39 % OS : Linux 6.8.0-71-generic % 0.11/0.39 % CPULimit : 300 % 0.11/0.39 % WCLimit : 300 % 0.11/0.39 % DateTime : Sat Sep 5 14:52:59 UTC 2026 % 0.11/0.39 % CPUTime : % 4.05/4.30 SZS status Theorem for theBenchmark.p % 4.05/4.30 SZS output start Proof for theBenchmark.p % 4.05/4.30 Clause #0 (by assumption #[]): Eq % 4.05/4.30 (∀ (Ss1 : list dB) (S : dB) (M : nat), % 4.05/4.30 Iff (Eq (var M) (foldl dB dB app S Ss1)) (And (Eq (var M) S) (Eq Ss1 (nil dB)))) % 4.05/4.30 True % 4.05/4.30 Clause #7 (by assumption #[]): Eq (∀ (B A : Type) (A5 : A) (F : fun A (fun B A)), Eq (foldl A B F A5 (nil B)) A5) True % 4.05/4.30 Clause #8 (by assumption #[]): Eq (∀ (Na : nat) (Rs : list dB), listsp dB it Rs → pp (aa dB bool it (foldl dB dB app (var Na) Rs))) True % 4.05/4.30 Clause #13 (by assumption #[]): Eq (∀ (A : Type) (A1 : fun A bool), listsp A A1 (nil A)) True % 4.05/4.30 Clause #104 (by assumption #[]): Eq (Not (pp (aa dB bool it (foldl dB dB app (var n) (nil dB))))) True % 4.05/4.30 Clause #106 (by clausification #[13]): ∀ (a : Type), Eq (∀ (A1 : fun a bool), listsp a A1 (nil a)) True % 4.05/4.30 Clause #107 (by clausification #[106]): ∀ (a : Type) (a_1 : fun a bool), Eq (listsp a a_1 (nil a)) True % 4.05/4.30 Clause #111 (by clausification #[0]): ∀ (a : list dB), % 4.05/4.30 Eq (∀ (S : dB) (M : nat), Iff (Eq (var M) (foldl dB dB app S a)) (And (Eq (var M) S) (Eq a (nil dB)))) True % 4.05/4.30 Clause #112 (by clausification #[111]): ∀ (a : dB) (a_1 : list dB), % 4.05/4.30 Eq (∀ (M : nat), Iff (Eq (var M) (foldl dB dB app a a_1)) (And (Eq (var M) a) (Eq a_1 (nil dB)))) True % 4.05/4.30 Clause #113 (by clausification #[112]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Eq (Iff (Eq (var a) (foldl dB dB app a_1 a_2)) (And (Eq (var a) a_1) (Eq a_2 (nil dB)))) True % 4.05/4.30 Clause #114 (by clausification #[113]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Or (Eq (Eq (var a) (foldl dB dB app a_1 a_2)) True) (Eq (And (Eq (var a) a_1) (Eq a_2 (nil dB))) False) % 4.05/4.30 Clause #116 (by clausification #[114]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Or (Eq (And (Eq (var a) a_1) (Eq a_2 (nil dB))) False) (Eq (var a) (foldl dB dB app a_1 a_2)) % 4.05/4.30 Clause #117 (by clausification #[116]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Or (Eq (var a) (foldl dB dB app a_1 a_2)) (Or (Eq (Eq (var a) a_1) False) (Eq (Eq a_2 (nil dB)) False)) % 4.05/4.30 Clause #118 (by clausification #[117]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Or (Eq (var a) (foldl dB dB app a_1 a_2)) (Or (Eq (Eq a_2 (nil dB)) False) (Ne (var a) a_1)) % 4.05/4.30 Clause #119 (by clausification #[118]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 4.05/4.30 Or (Eq (var a) (foldl dB dB app a_1 a_2)) (Or (Ne (var a) a_1) (Ne a_2 (nil dB))) % 4.05/4.30 Clause #120 (by destructive equality resolution #[119]): ∀ (a : nat) (a_1 : list dB), Or (Eq (var a) (foldl dB dB app (var a) a_1)) (Ne a_1 (nil dB)) % 4.05/4.30 Clause #121 (by destructive equality resolution #[120]): ∀ (a : nat), Eq (var a) (foldl dB dB app (var a) (nil dB)) % 4.05/4.30 Clause #323 (by clausification #[104]): Eq (pp (aa dB bool it (foldl dB dB app (var n) (nil dB)))) False % 4.05/4.30 Clause #324 (by forward demodulation #[323, 121]): Eq (pp (aa dB bool it (var n))) False % 4.05/4.30 Clause #325 (by clausification #[7]): ∀ (a : Type), Eq (∀ (A : Type) (A5 : A) (F : fun A (fun a A)), Eq (foldl A a F A5 (nil a)) A5) True % 4.05/4.30 Clause #326 (by clausification #[325]): ∀ (a a_1 : Type), Eq (∀ (A5 : a) (F : fun a (fun a_1 a)), Eq (foldl a a_1 F A5 (nil a_1)) A5) True % 4.05/4.30 Clause #327 (by clausification #[326]): ∀ (a a_1 : Type) (a_2 : a), Eq (∀ (F : fun a (fun a_1 a)), Eq (foldl a a_1 F a_2 (nil a_1)) a_2) True % 4.05/4.30 Clause #328 (by clausification #[327]): ∀ (a a_1 : Type) (a_2 : fun a (fun a_1 a)) (a_3 : a), Eq (Eq (foldl a a_1 a_2 a_3 (nil a_1)) a_3) True % 4.05/4.30 Clause #329 (by clausification #[328]): ∀ (a a_1 : Type) (a_2 : fun a (fun a_1 a)) (a_3 : a), Eq (foldl a a_1 a_2 a_3 (nil a_1)) a_3 % 4.05/4.30 Clause #334 (by clausification #[8]): ∀ (a : nat), Eq (∀ (Rs : list dB), listsp dB it Rs → pp (aa dB bool it (foldl dB dB app (var a) Rs))) True % 4.05/4.30 Clause #335 (by clausification #[334]): ∀ (a : list dB) (a_1 : nat), Eq (listsp dB it a → pp (aa dB bool it (foldl dB dB app (var a_1) a))) True % 4.05/4.30 Clause #336 (by clausification #[335]): ∀ (a : list dB) (a_1 : nat), Or (Eq (listsp dB it a) False) (Eq (pp (aa dB bool it (foldl dB dB app (var a_1) a))) True) % 4.05/4.30 Clause #337 (by superposition #[336, 107]): ∀ (a : nat), Or (Eq (pp (aa dB bool it (foldl dB dB app (var a) (nil dB)))) True) (Eq False True) % 4.05/4.31 Clause #338 (by clausification #[337]): ∀ (a : nat), Eq (pp (aa dB bool it (foldl dB dB app (var a) (nil dB)))) True % 4.05/4.31 Clause #339 (by forward demodulation #[338, 329]): ∀ (a : nat), Eq (pp (aa dB bool it (var a))) True % 4.05/4.31 Clause #344 (by superposition #[339, 324]): Eq True False % 4.05/4.31 Clause #346 (by clausification #[344]): False % 4.05/4.31 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------