%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL796_5 : TPTP v9.3.1. Released v6.0.0. % 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 : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 11:36:40 AM UTC 2026 % Result : Theorem 35.15s 35.46s % Output : Proof 35.15s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL796_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.04 % Command : duper %s % 0.09/0.36 % Computer : n009.cluster.edu % 0.09/0.36 % Model : x86_64 x86_64 % 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.09/0.36 % Memory : 8046.5625MB % 0.09/0.36 % OS : Linux 6.8.0-71-generic % 0.09/0.36 % CPULimit : 300 % 0.09/0.36 % WCLimit : 300 % 0.09/0.36 % DateTime : Sat Sep 5 21:04:52 UTC 2026 % 0.09/0.36 % CPUTime : % 35.15/35.46 SZS status Theorem for theBenchmark.p % 35.15/35.46 SZS output start Proof for theBenchmark.p % 35.15/35.46 Clause #1 (by assumption #[]): Eq % 35.15/35.46 (∀ (Ta1 : type) (X2 : nat) (Env : fun nat type), % 35.15/35.46 Eq (aa nat type Env X2) Ta1 → pp (aa type bool (typing Env (var X2)) Ta1)) % 35.15/35.46 True % 35.15/35.46 Clause #7 (by assumption #[]): Eq (∀ (A : Type) (Ta1 : A) (Eb : fun nat A) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat A (shift A Eb Ib Ta1) J1) Ta1) True % 35.15/35.46 Clause #109 (by assumption #[]): Eq (Not (pp (aa type bool (typing (shift type e (zero_zero nat) t) (var (zero_zero nat))) t))) True % 35.15/35.46 Clause #117 (by clausification #[1]): ∀ (a : type), % 35.15/35.46 Eq (∀ (X2 : nat) (Env : fun nat type), Eq (aa nat type Env X2) a → pp (aa type bool (typing Env (var X2)) a)) True % 35.15/35.46 Clause #118 (by clausification #[117]): ∀ (a : nat) (a_1 : type), % 35.15/35.46 Eq (∀ (Env : fun nat type), Eq (aa nat type Env a) a_1 → pp (aa type bool (typing Env (var a)) a_1)) True % 35.15/35.46 Clause #119 (by clausification #[118]): ∀ (a : fun nat type) (a_1 : nat) (a_2 : type), % 35.15/35.46 Eq (Eq (aa nat type a a_1) a_2 → pp (aa type bool (typing a (var a_1)) a_2)) True % 35.15/35.46 Clause #120 (by clausification #[119]): ∀ (a : fun nat type) (a_1 : nat) (a_2 : type), % 35.15/35.46 Or (Eq (Eq (aa nat type a a_1) a_2) False) (Eq (pp (aa type bool (typing a (var a_1)) a_2)) True) % 35.15/35.46 Clause #121 (by clausification #[120]): ∀ (a : fun nat type) (a_1 : nat) (a_2 : type), % 35.15/35.46 Or (Eq (pp (aa type bool (typing a (var a_1)) a_2)) True) (Ne (aa nat type a a_1) a_2) % 35.15/35.46 Clause #122 (by destructive equality resolution #[121]): ∀ (a : fun nat type) (a_1 : nat), Eq (pp (aa type bool (typing a (var a_1)) (aa nat type a a_1))) True % 35.15/35.46 Clause #173 (by clausification #[7]): ∀ (a : Type), Eq (∀ (Ta1 : a) (Eb : fun nat a) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a Eb Ib Ta1) J1) Ta1) True % 35.15/35.46 Clause #174 (by clausification #[173]): ∀ (a : Type) (a_1 : a), Eq (∀ (Eb : fun nat a) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a Eb Ib a_1) J1) a_1) True % 35.15/35.46 Clause #175 (by clausification #[174]): ∀ (a : Type) (a_1 : fun nat a) (a_2 : a), % 35.15/35.46 Eq (∀ (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a a_1 Ib a_2) J1) a_2) True % 35.15/35.46 Clause #176 (by clausification #[175]): ∀ (a : nat) (a_1 : Type) (a_2 : fun nat a_1) (a_3 : a_1), % 35.15/35.46 Eq (∀ (Ib : nat), Eq Ib a → Eq (aa nat a_1 (shift a_1 a_2 Ib a_3) a) a_3) True % 35.15/35.46 Clause #177 (by clausification #[176]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun nat a_2) (a_4 : a_2), % 35.15/35.46 Eq (Eq a a_1 → Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) True % 35.15/35.46 Clause #178 (by clausification #[177]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun nat a_2) (a_4 : a_2), % 35.15/35.46 Or (Eq (Eq a a_1) False) (Eq (Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) True) % 35.15/35.46 Clause #179 (by clausification #[178]): ∀ (a : Type) (a_1 : fun nat a) (a_2 : nat) (a_3 : a) (a_4 : nat), % 35.15/35.46 Or (Eq (Eq (aa nat a (shift a a_1 a_2 a_3) a_4) a_3) True) (Ne a_2 a_4) % 35.15/35.46 Clause #180 (by clausification #[179]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun nat a_2) (a_4 : a_2), % 35.15/35.46 Or (Ne a a_1) (Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) % 35.15/35.46 Clause #181 (by destructive equality resolution #[180]): ∀ (a : Type) (a_1 : fun nat a) (a_2 : nat) (a_3 : a), Eq (aa nat a (shift a a_1 a_2 a_3) a_2) a_3 % 35.15/35.46 Clause #182 (by superposition #[181, 122]): ∀ (a : fun nat type) (a_1 : nat) (a_2 : type), Eq (pp (aa type bool (typing (shift type a a_1 a_2) (var a_1)) a_2)) True % 35.15/35.46 Clause #5432 (by clausification #[109]): Eq (pp (aa type bool (typing (shift type e (zero_zero nat) t) (var (zero_zero nat))) t)) False % 35.15/35.46 Clause #7165 (by superposition #[182, 5432]): Eq False True % 35.15/35.46 Clause #7224 (by clausification #[7165]): False % 35.15/35.46 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------