%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL762_5 : TPTP v9.3.1. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n015.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 3.79s 4.11s % Output : Proof 3.79s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL762_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.04 % Command : duper %s % 0.10/0.36 % Computer : n015.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Sat Sep 5 15:00:42 UTC 2026 % 0.10/0.37 % CPUTime : % 3.79/4.11 SZS status Theorem for theBenchmark.p % 3.79/4.11 SZS output start Proof for theBenchmark.p % 3.79/4.11 Clause #0 (by assumption #[]): Eq % 3.79/4.11 (∀ (Ss1 : list dB) (S : dB) (M : nat), % 3.79/4.11 Iff (Eq (var M) (foldl dB dB app S Ss1)) (And (Eq (var M) S) (Eq Ss1 (nil dB)))) % 3.79/4.11 True % 3.79/4.11 Clause #104 (by assumption #[]): Eq (pp (aa dB bool it (foldl dB dB app (var n) (nil dB)))) True % 3.79/4.11 Clause #105 (by assumption #[]): Eq (Not (pp (aa dB bool it (var n)))) True % 3.79/4.11 Clause #112 (by clausification #[0]): ∀ (a : list dB), % 3.79/4.11 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 % 3.79/4.11 Clause #113 (by clausification #[112]): ∀ (a : dB) (a_1 : list dB), % 3.79/4.11 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 % 3.79/4.11 Clause #114 (by clausification #[113]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 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 % 3.79/4.11 Clause #115 (by clausification #[114]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 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) % 3.79/4.11 Clause #117 (by clausification #[115]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 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)) % 3.79/4.11 Clause #118 (by clausification #[117]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 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)) % 3.79/4.11 Clause #119 (by clausification #[118]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 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)) % 3.79/4.11 Clause #120 (by clausification #[119]): ∀ (a : nat) (a_1 : dB) (a_2 : list dB), % 3.79/4.11 Or (Eq (var a) (foldl dB dB app a_1 a_2)) (Or (Ne (var a) a_1) (Ne a_2 (nil dB))) % 3.79/4.11 Clause #121 (by destructive equality resolution #[120]): ∀ (a : nat) (a_1 : list dB), Or (Eq (var a) (foldl dB dB app (var a) a_1)) (Ne a_1 (nil dB)) % 3.79/4.11 Clause #122 (by destructive equality resolution #[121]): ∀ (a : nat), Eq (var a) (foldl dB dB app (var a) (nil dB)) % 3.79/4.11 Clause #123 (by clausification #[105]): Eq (pp (aa dB bool it (var n))) False % 3.79/4.11 Clause #249 (by forward demodulation #[104, 122]): Eq (pp (aa dB bool it (var n))) True % 3.79/4.11 Clause #250 (by superposition #[249, 123]): Eq True False % 3.79/4.11 Clause #252 (by clausification #[250]): False % 3.79/4.11 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------