%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n031.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 11:36:41 AM UTC 2026 % Result : Theorem 55.45s 55.78s % Output : Proof 55.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL800_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.05 % Command : duper %s % 0.10/0.37 % Computer : n031.cluster.edu % 0.10/0.37 % Model : x86_64 x86_64 % 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.37 % Memory : 8046.5625MB % 0.10/0.37 % OS : Linux 6.8.0-71-generic % 0.10/0.38 % CPULimit : 300 % 0.10/0.38 % WCLimit : 300 % 0.10/0.38 % DateTime : Fri Sep 4 23:13:24 UTC 2026 % 0.10/0.38 % CPUTime : % 55.45/55.78 SZS status Theorem for theBenchmark.p % 55.45/55.78 SZS output start Proof for theBenchmark.p % 55.45/55.78 Clause #4 (by assumption #[]): Eq (it (subst (app (lift u (zero_zero nat)) (var (zero_zero nat))) (subst a u i) (zero_zero nat))) True % 55.45/55.78 Clause #6 (by assumption #[]): Eq (∀ (K : nat) (S U T : dB), Eq (subst (app T U) S K) (app (subst T S K) (subst U S K))) True % 55.45/55.78 Clause #13 (by assumption #[]): Eq (∀ (S : dB) (K : nat) (T : dB), Eq (subst (lift T K) S K) T) True % 55.45/55.78 Clause #14 (by assumption #[]): Eq (∀ (U : dB) (K : nat), Eq (subst (var K) U K) U) True % 55.45/55.78 Clause #59 (by assumption #[]): Eq (∀ (M : nat), Ne (zero_zero nat) (suc M)) True % 55.45/55.78 Clause #60 (by assumption #[]): Eq (∀ (N : nat), Ne N (zero_zero nat) → Exists fun M2 => Eq N (suc M2)) True % 55.45/55.78 Clause #101 (by assumption #[]): Eq (Not (it (app u (subst a u i)))) True % 55.45/55.78 Clause #110 (by clausification #[59]): ∀ (a : nat), Eq (Ne (zero_zero nat) (suc a)) True % 55.45/55.78 Clause #111 (by clausification #[110]): ∀ (a : nat), Ne (zero_zero nat) (suc a) % 55.45/55.78 Clause #132 (by clausification #[6]): ∀ (a : nat), Eq (∀ (S U T : dB), Eq (subst (app T U) S a) (app (subst T S a) (subst U S a))) True % 55.45/55.78 Clause #133 (by clausification #[132]): ∀ (a : dB) (a_1 : nat), Eq (∀ (U T : dB), Eq (subst (app T U) a a_1) (app (subst T a a_1) (subst U a a_1))) True % 55.45/55.78 Clause #134 (by clausification #[133]): ∀ (a a_1 : dB) (a_2 : nat), Eq (∀ (T : dB), Eq (subst (app T a) a_1 a_2) (app (subst T a_1 a_2) (subst a a_1 a_2))) True % 55.45/55.78 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : dB) (a_3 : nat), Eq (Eq (subst (app a a_1) a_2 a_3) (app (subst a a_2 a_3) (subst a_1 a_2 a_3))) True % 55.45/55.78 Clause #136 (by clausification #[135]): ∀ (a a_1 a_2 : dB) (a_3 : nat), Eq (subst (app a a_1) a_2 a_3) (app (subst a a_2 a_3) (subst a_1 a_2 a_3)) % 55.45/55.78 Clause #233 (by clausification #[101]): Eq (it (app u (subst a u i))) False % 55.45/55.78 Clause #248 (by clausification #[13]): ∀ (a : dB), Eq (∀ (K : nat) (T : dB), Eq (subst (lift T K) a K) T) True % 55.45/55.78 Clause #249 (by clausification #[248]): ∀ (a : nat) (a_1 : dB), Eq (∀ (T : dB), Eq (subst (lift T a) a_1 a) T) True % 55.45/55.78 Clause #250 (by clausification #[249]): ∀ (a : dB) (a_1 : nat) (a_2 : dB), Eq (Eq (subst (lift a a_1) a_2 a_1) a) True % 55.45/55.78 Clause #251 (by clausification #[250]): ∀ (a : dB) (a_1 : nat) (a_2 : dB), Eq (subst (lift a a_1) a_2 a_1) a % 55.45/55.78 Clause #253 (by superposition #[251, 136]): ∀ (a : dB) (a_1 : nat) (a_2 a_3 : dB), Eq (subst (app (lift a a_1) a_2) a_3 a_1) (app a (subst a_2 a_3 a_1)) % 55.45/55.78 Clause #272 (by clausification #[14]): ∀ (a : dB), Eq (∀ (K : nat), Eq (subst (var K) a K) a) True % 55.45/55.78 Clause #273 (by clausification #[272]): ∀ (a : nat) (a_1 : dB), Eq (Eq (subst (var a) a_1 a) a_1) True % 55.45/55.78 Clause #274 (by clausification #[273]): ∀ (a : nat) (a_1 : dB), Eq (subst (var a) a_1 a) a_1 % 55.45/55.78 Clause #421 (by clausification #[60]): ∀ (a : nat), Eq (Ne a (zero_zero nat) → Exists fun M2 => Eq a (suc M2)) True % 55.45/55.78 Clause #422 (by clausification #[421]): ∀ (a : nat), Or (Eq (Ne a (zero_zero nat)) False) (Eq (Exists fun M2 => Eq a (suc M2)) True) % 55.45/55.78 Clause #423 (by clausification #[422]): ∀ (a : nat), Or (Eq (Exists fun M2 => Eq a (suc M2)) True) (Eq a (zero_zero nat)) % 55.45/55.79 Clause #424 (by clausification #[423]): ∀ (a a_1 : nat), Or (Eq a (zero_zero nat)) (Eq (Eq a (suc (skS.0 2 a a_1))) True) % 55.45/55.79 Clause #425 (by clausification #[424]): ∀ (a a_1 : nat), Or (Eq a (zero_zero nat)) (Eq a (suc (skS.0 2 a a_1))) % 55.45/55.79 Clause #426 (by superposition #[425, 4]): ∀ (a_1 a_2 : nat), % 55.45/55.79 Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (subst (app (lift u a_1) (var a_1)) (subst a u i) a_1)) True) % 55.45/55.79 Clause #4966 (by forward demodulation #[426, 253]): ∀ (a_1 a_2 : nat), Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (app u (subst (var a_1) (subst a u i) a_1))) True) % 55.45/55.79 Clause #4967 (by forward demodulation #[4966, 274]): ∀ (a_1 a_2 : nat), Or (Eq a_1 (suc (skS.0 2 a_1 a_2))) (Eq (it (app u (subst a u i))) True) % 55.45/55.79 Clause #4969 (by superposition #[4967, 111]): ∀ (a_1 : nat), Or (Eq (it (app u (subst a u i))) True) (Ne (zero_zero nat) a_1) % 55.45/55.79 Clause #8952 (by destructive equality resolution #[4969]): Eq (it (app u (subst a u i))) True % 55.45/55.79 Clause #8953 (by superposition #[8952, 233]): Eq True False % 55.55/55.86 Clause #8963 (by clausification #[8953]): False % 55.55/55.86 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------