%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL813_5 : TPTP v9.3.1. Released v6.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n019.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 11:36:43 AM UTC 2026 % Result : Theorem 73.06s 73.34s % Output : Proof 73.26s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL813_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.05 % Command : duper %s % 0.11/0.37 % Computer : n019.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 09:24:53 UTC 2026 % 0.11/0.38 % CPUTime : % 73.06/73.34 SZS status Theorem for theBenchmark.p % 73.06/73.34 SZS output start Proof for theBenchmark.p % 73.06/73.34 Clause #1 (by assumption #[]): Eq % 73.06/73.34 (∀ (Ta1 : type) (X1 : nat) (Env : fun1 nat type), % 73.06/73.34 Eq (aa nat type Env X1) Ta1 → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var X1)) Ta1)) % 73.06/73.34 True % 73.06/73.34 Clause #10 (by assumption #[]): Eq (∀ (A : Type) (Ta1 : A) (Eb : fun1 nat A) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat A (shift A Eb Ib Ta1) J1) Ta1) True % 73.06/73.34 Clause #104 (by assumption #[]): Eq % 73.06/73.34 (∀ (A C B : Type) (R : A) (Q : B) (P : fun1 A (fun1 B C)), % 73.06/73.34 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun1 B C) P R) Q)) % 73.06/73.34 True % 73.06/73.34 Clause #111 (by assumption #[]): Eq % 73.06/73.34 (Not % 73.06/73.34 (pp % 73.06/73.34 (aa type bool % 73.06/73.34 (aa dB (fun1 type bool) (typing (shift type e (zero_zero nat) (foldr type type fun ts t))) % 73.06/73.34 (var (zero_zero nat))) % 73.06/73.34 (foldr type type fun ts t)))) % 73.06/73.34 True % 73.06/73.34 Clause #123 (by clausification #[1]): ∀ (a : type), % 73.06/73.34 Eq % 73.06/73.34 (∀ (X1 : nat) (Env : fun1 nat type), % 73.06/73.34 Eq (aa nat type Env X1) a → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var X1)) a)) % 73.06/73.34 True % 73.06/73.34 Clause #124 (by clausification #[123]): ∀ (a : nat) (a_1 : type), % 73.06/73.34 Eq % 73.06/73.34 (∀ (Env : fun1 nat type), % 73.06/73.34 Eq (aa nat type Env a) a_1 → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var a)) a_1)) % 73.06/73.34 True % 73.06/73.34 Clause #125 (by clausification #[124]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type), % 73.06/73.34 Eq (Eq (aa nat type a a_1) a_2 → pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) a_2)) True % 73.06/73.34 Clause #126 (by clausification #[125]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type), % 73.06/73.34 Or (Eq (Eq (aa nat type a a_1) a_2) False) % 73.06/73.34 (Eq (pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) a_2)) True) % 73.06/73.34 Clause #127 (by clausification #[126]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type), % 73.06/73.34 Or (Eq (pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) a_2)) True) (Ne (aa nat type a a_1) a_2) % 73.06/73.34 Clause #128 (by destructive equality resolution #[127]): ∀ (a : fun1 nat type) (a_1 : nat), % 73.06/73.34 Eq (pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) (aa nat type a a_1))) True % 73.06/73.34 Clause #422 (by clausification #[10]): ∀ (a : Type), Eq (∀ (Ta1 : a) (Eb : fun1 nat a) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a Eb Ib Ta1) J1) Ta1) True % 73.06/73.34 Clause #423 (by clausification #[422]): ∀ (a : Type) (a_1 : a), Eq (∀ (Eb : fun1 nat a) (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a Eb Ib a_1) J1) a_1) True % 73.06/73.34 Clause #424 (by clausification #[423]): ∀ (a : Type) (a_1 : fun1 nat a) (a_2 : a), % 73.06/73.34 Eq (∀ (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a a_1 Ib a_2) J1) a_2) True % 73.06/73.34 Clause #425 (by clausification #[424]): ∀ (a : nat) (a_1 : Type) (a_2 : fun1 nat a_1) (a_3 : a_1), % 73.06/73.34 Eq (∀ (Ib : nat), Eq Ib a → Eq (aa nat a_1 (shift a_1 a_2 Ib a_3) a) a_3) True % 73.06/73.34 Clause #426 (by clausification #[425]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2), % 73.06/73.34 Eq (Eq a a_1 → Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) True % 73.06/73.34 Clause #427 (by clausification #[426]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2), % 73.06/73.34 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) % 73.06/73.34 Clause #428 (by clausification #[427]): ∀ (a : Type) (a_1 : fun1 nat a) (a_2 : nat) (a_3 : a) (a_4 : nat), % 73.06/73.34 Or (Eq (Eq (aa nat a (shift a a_1 a_2 a_3) a_4) a_3) True) (Ne a_2 a_4) % 73.06/73.34 Clause #429 (by clausification #[428]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2), % 73.06/73.34 Or (Ne a a_1) (Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) % 73.06/73.34 Clause #430 (by destructive equality resolution #[429]): ∀ (a : Type) (a_1 : fun1 nat a) (a_2 : nat) (a_3 : a), Eq (aa nat a (shift a a_1 a_2 a_3) a_2) a_3 % 73.06/73.34 Clause #431 (by superposition #[430, 128]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type), % 73.06/73.34 Eq (pp (aa type bool (aa dB (fun1 type bool) (typing (shift type a a_1 a_2)) (var a_1)) a_2)) True % 73.06/73.34 Clause #5929 (by clausification #[104]): ∀ (a : Type), % 73.06/73.34 Eq % 73.06/73.34 (∀ (C B : Type) (R : a) (Q : B) (P : fun1 a (fun1 B C)), % 73.06/73.34 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun1 B C) P R) Q)) % 73.06/73.34 True % 73.06/73.34 Clause #5930 (by clausification #[5929]): ∀ (a a_1 : Type), % 73.26/73.50 Eq % 73.26/73.50 (∀ (B : Type) (R : a) (Q : B) (P : fun1 a (fun1 B a_1)), % 73.26/73.50 Eq (aa a a_1 (combc a B a_1 P Q) R) (aa B a_1 (aa a (fun1 B a_1) P R) Q)) % 73.26/73.50 True % 73.26/73.50 Clause #5931 (by clausification #[5930]): ∀ (a a_1 a_2 : Type), % 73.26/73.50 Eq % 73.26/73.50 (∀ (R : a) (Q : a_1) (P : fun1 a (fun1 a_1 a_2)), % 73.26/73.50 Eq (aa a a_2 (combc a a_1 a_2 P Q) R) (aa a_1 a_2 (aa a (fun1 a_1 a_2) P R) Q)) % 73.26/73.50 True % 73.26/73.50 Clause #5932 (by clausification #[5931]): ∀ (a a_1 a_2 : Type) (a_3 : a_1), % 73.26/73.50 Eq % 73.26/73.50 (∀ (Q : a) (P : fun1 a_1 (fun1 a a_2)), % 73.26/73.50 Eq (aa a_1 a_2 (combc a_1 a a_2 P Q) a_3) (aa a a_2 (aa a_1 (fun1 a a_2) P a_3) Q)) % 73.26/73.50 True % 73.26/73.50 Clause #5933 (by clausification #[5932]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a), % 73.26/73.50 Eq % 73.26/73.50 (∀ (P : fun1 a (fun1 a_1 a_2)), % 73.26/73.50 Eq (aa a a_2 (combc a a_1 a_2 P a_3) a_4) (aa a_1 a_2 (aa a (fun1 a_1 a_2) P a_4) a_3)) % 73.26/73.50 True % 73.26/73.50 Clause #5934 (by clausification #[5933]): ∀ (a a_1 a_2 : Type) (a_3 : fun1 a_1 (fun1 a_2 a)) (a_4 : a_2) (a_5 : a_1), % 73.26/73.50 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 (fun1 a_2 a) a_3 a_5) a_4)) True % 73.26/73.50 Clause #5935 (by clausification #[5934]): ∀ (a a_1 a_2 : Type) (a_3 : fun1 a_1 (fun1 a_2 a)) (a_4 : a_2) (a_5 : a_1), % 73.26/73.50 Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun1 a_2 a) a_3 a_5) a_4) % 73.26/73.50 Clause #6370 (by clausification #[111]): Eq % 73.26/73.50 (pp % 73.26/73.50 (aa type bool % 73.26/73.50 (aa dB (fun1 type bool) (typing (shift type e (zero_zero nat) (foldr type type fun ts t))) (var (zero_zero nat))) % 73.26/73.50 (foldr type type fun ts t))) % 73.26/73.50 False % 73.26/73.50 Clause #6371 (by forward demodulation #[6370, 5935]): Eq % 73.26/73.50 (pp % 73.26/73.50 (aa dB bool % 73.26/73.50 (combc dB type bool (typing (shift type e (zero_zero nat) (foldr type type fun ts t))) (foldr type type fun ts t)) % 73.26/73.50 (var (zero_zero nat)))) % 73.26/73.50 False % 73.26/73.50 Clause #13026 (by forward demodulation #[431, 5935]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type), % 73.26/73.50 Eq (pp (aa dB bool (combc dB type bool (typing (shift type a a_1 a_2)) a_2) (var a_1))) True % 73.26/73.50 Clause #13028 (by superposition #[13026, 6371]): Eq True False % 73.26/73.50 Clause #13125 (by clausification #[13028]): False % 73.26/73.50 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------