%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : LCL838_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 11:36:46 AM UTC 2026 % Result : Theorem 36.25s 36.59s % Output : Proof 36.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.02 % Problem : LCL838_5 : TPTP v9.3.1. Released v6.0.0. % 0.00/0.04 % Command : duper %s % 0.08/0.35 % Computer : n031.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Fri Sep 4 15:14:39 UTC 2026 % 0.08/0.35 % CPUTime : % 36.25/36.59 SZS status Theorem for theBenchmark.p % 36.25/36.59 SZS output start Proof for theBenchmark.p % 36.25/36.59 Clause #3 (by assumption #[]): Eq (typing (shift type e i t) (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs r)) a) as) t1) True % 36.25/36.59 Clause #71 (by assumption #[]): Eq % 36.25/36.59 (∀ (Ta : type) (Ts : list dB) (Ta1 : dB) (Eb : fun nat type), % 36.25/36.59 typing Eb (foldl dB dB app Ta1 Ts) Ta → % 36.25/36.59 Not (∀ (Ts1 : list type), typing Eb Ta1 (foldr type type fun1 Ts1 Ta) → Not (typings Eb Ts Ts1))) % 36.25/36.59 True % 36.25/36.59 Clause #98 (by assumption #[]): Eq % 36.25/36.59 (∀ (A C B : Type) (R : A) (Q : B) (P : fun A (fun B C)), % 36.25/36.59 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun B C) P R) Q)) % 36.25/36.59 True % 36.25/36.59 Clause #104 (by assumption #[]): Eq (∀ (U : type), typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) U → thesis) True % 36.25/36.59 Clause #105 (by assumption #[]): Eq (Not thesis) True % 36.25/36.59 Clause #106 (by clausification #[105]): Eq thesis False % 36.25/36.59 Clause #108 (by clausification #[104]): ∀ (a_1 : type), Eq (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) a_1 → thesis) True % 36.25/36.59 Clause #109 (by clausification #[108]): ∀ (a_1 : type), % 36.25/36.59 Or (Eq (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) a_1) False) (Eq thesis True) % 36.25/36.59 Clause #110 (by forward demodulation #[109, 106]): ∀ (a_1 : type), % 36.25/36.59 Or (Eq (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) a_1) False) (Eq False True) % 36.25/36.59 Clause #111 (by clausification #[110]): ∀ (a_1 : type), Eq (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) a_1) False % 36.25/36.59 Clause #396 (by clausification #[71]): ∀ (a : type), % 36.25/36.59 Eq % 36.25/36.59 (∀ (Ts : list dB) (Ta1 : dB) (Eb : fun nat type), % 36.25/36.59 typing Eb (foldl dB dB app Ta1 Ts) a → % 36.25/36.59 Not (∀ (Ts1 : list type), typing Eb Ta1 (foldr type type fun1 Ts1 a) → Not (typings Eb Ts Ts1))) % 36.25/36.59 True % 36.25/36.59 Clause #397 (by clausification #[396]): ∀ (a : list dB) (a_1 : type), % 36.25/36.59 Eq % 36.25/36.59 (∀ (Ta1 : dB) (Eb : fun nat type), % 36.25/36.59 typing Eb (foldl dB dB app Ta1 a) a_1 → % 36.25/36.59 Not (∀ (Ts1 : list type), typing Eb Ta1 (foldr type type fun1 Ts1 a_1) → Not (typings Eb a Ts1))) % 36.25/36.59 True % 36.25/36.59 Clause #398 (by clausification #[397]): ∀ (a : dB) (a_1 : list dB) (a_2 : type), % 36.25/36.59 Eq % 36.25/36.59 (∀ (Eb : fun nat type), % 36.25/36.59 typing Eb (foldl dB dB app a a_1) a_2 → % 36.25/36.59 Not (∀ (Ts1 : list type), typing Eb a (foldr type type fun1 Ts1 a_2) → Not (typings Eb a_1 Ts1))) % 36.25/36.59 True % 36.25/36.59 Clause #399 (by clausification #[398]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type), % 36.25/36.59 Eq % 36.25/36.59 (typing a (foldl dB dB app a_1 a_2) a_3 → % 36.25/36.59 Not (∀ (Ts1 : list type), typing a a_1 (foldr type type fun1 Ts1 a_3) → Not (typings a a_2 Ts1))) % 36.25/36.59 True % 36.25/36.59 Clause #400 (by clausification #[399]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type), % 36.25/36.59 Or (Eq (typing a (foldl dB dB app a_1 a_2) a_3) False) % 36.25/36.59 (Eq (Not (∀ (Ts1 : list type), typing a a_1 (foldr type type fun1 Ts1 a_3) → Not (typings a a_2 Ts1))) True) % 36.25/36.59 Clause #401 (by clausification #[400]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type), % 36.25/36.59 Or (Eq (typing a (foldl dB dB app a_1 a_2) a_3) False) % 36.25/36.59 (Eq (∀ (Ts1 : list type), typing a a_1 (foldr type type fun1 Ts1 a_3) → Not (typings a a_2 Ts1)) False) % 36.25/36.59 Clause #402 (by clausification #[401]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type) (a_4 : list type), % 36.25/36.59 Or (Eq (typing a (foldl dB dB app a_1 a_2) a_3) False) % 36.25/36.59 (Eq % 36.25/36.59 (Not % 36.25/36.59 (typing a a_1 (foldr type type fun1 (skS.0 7 a a_1 a_3 a_2 a_4) a_3) → % 36.25/36.59 Not (typings a a_2 (skS.0 7 a a_1 a_3 a_2 a_4)))) % 36.25/36.59 True) % 36.25/36.59 Clause #403 (by clausification #[402]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type) (a_4 : list type), % 36.25/36.59 Or (Eq (typing a (foldl dB dB app a_1 a_2) a_3) False) % 36.25/36.59 (Eq % 36.25/36.59 (typing a a_1 (foldr type type fun1 (skS.0 7 a a_1 a_3 a_2 a_4) a_3) → % 36.25/36.59 Not (typings a a_2 (skS.0 7 a a_1 a_3 a_2 a_4))) % 36.25/36.59 False) % 36.25/36.59 Clause #404 (by clausification #[403]): ∀ (a : fun nat type) (a_1 : dB) (a_2 : list dB) (a_3 : type) (a_4 : list type), % 36.25/36.59 Or (Eq (typing a (foldl dB dB app a_1 a_2) a_3) False) % 36.25/36.59 (Eq (typing a a_1 (foldr type type fun1 (skS.0 7 a a_1 a_3 a_2 a_4) a_3)) True) % 36.35/36.63 Clause #406 (by superposition #[404, 3]): ∀ (a_1 : list type), % 36.35/36.63 Or % 36.35/36.63 (Eq % 36.35/36.63 (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) % 36.35/36.63 (foldr type type fun1 (skS.0 7 (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) t1 as a_1) t1)) % 36.35/36.63 True) % 36.35/36.63 (Eq False True) % 36.35/36.63 Clause #2061 (by clausification #[98]): ∀ (a : Type), % 36.35/36.63 Eq % 36.35/36.63 (∀ (C B : Type) (R : a) (Q : B) (P : fun a (fun B C)), % 36.35/36.63 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun B C) P R) Q)) % 36.35/36.63 True % 36.35/36.63 Clause #2062 (by clausification #[2061]): ∀ (a a_1 : Type), % 36.35/36.63 Eq % 36.35/36.63 (∀ (B : Type) (R : a) (Q : B) (P : fun a (fun B a_1)), % 36.35/36.63 Eq (aa a a_1 (combc a B a_1 P Q) R) (aa B a_1 (aa a (fun B a_1) P R) Q)) % 36.35/36.63 True % 36.35/36.63 Clause #2063 (by clausification #[2062]): ∀ (a a_1 a_2 : Type), % 36.35/36.63 Eq % 36.35/36.63 (∀ (R : a) (Q : a_1) (P : fun a (fun a_1 a_2)), % 36.35/36.63 Eq (aa a a_2 (combc a a_1 a_2 P Q) R) (aa a_1 a_2 (aa a (fun a_1 a_2) P R) Q)) % 36.35/36.63 True % 36.35/36.63 Clause #2064 (by clausification #[2063]): ∀ (a a_1 a_2 : Type) (a_3 : a_1), % 36.35/36.63 Eq % 36.35/36.63 (∀ (Q : a) (P : fun a_1 (fun a a_2)), % 36.35/36.63 Eq (aa a_1 a_2 (combc a_1 a a_2 P Q) a_3) (aa a a_2 (aa a_1 (fun a a_2) P a_3) Q)) % 36.35/36.63 True % 36.35/36.63 Clause #2065 (by clausification #[2064]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a), % 36.35/36.63 Eq % 36.35/36.63 (∀ (P : fun a (fun a_1 a_2)), Eq (aa a a_2 (combc a a_1 a_2 P a_3) a_4) (aa a_1 a_2 (aa a (fun a_1 a_2) P a_4) a_3)) % 36.35/36.63 True % 36.35/36.63 Clause #2066 (by clausification #[2065]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1), % 36.35/36.63 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 (fun a_2 a) a_3 a_5) a_4)) True % 36.35/36.63 Clause #2067 (by clausification #[2066]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1), % 36.35/36.63 Eq (aa a_1 a (combc a_1 a_2 a a_3 a_4) a_5) (aa a_2 a (aa a_1 (fun a_2 a) a_3 a_5) a_4) % 36.35/36.63 Clause #2071 (by superposition #[2067, 111]): ∀ (a_1 : type), Eq (typing (shift type e i t) (aa dB dB (combc dB dB dB app a) (abs r)) a_1) False % 36.35/36.63 Clause #4205 (by clausification #[406]): ∀ (a_1 : list type), % 36.35/36.63 Eq % 36.35/36.63 (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) % 36.35/36.63 (foldr type type fun1 (skS.0 7 (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) t1 as a_1) t1)) % 36.35/36.63 True % 36.35/36.63 Clause #4206 (by forward demodulation #[4205, 2067]): ∀ (a_1 : list type), % 36.35/36.63 Eq % 36.35/36.63 (typing (shift type e i t) (aa dB dB (aa dB (fun dB dB) app (abs r)) a) % 36.35/36.63 (foldr type type fun1 (skS.0 7 (shift type e i t) (aa dB dB (combc dB dB dB app a) (abs r)) t1 as a_1) t1)) % 36.35/36.63 True % 36.35/36.63 Clause #4207 (by forward demodulation #[4206, 2067]): ∀ (a_1 : list type), % 36.35/36.63 Eq % 36.35/36.63 (typing (shift type e i t) (aa dB dB (combc dB dB dB app a) (abs r)) % 36.35/36.63 (foldr type type fun1 (skS.0 7 (shift type e i t) (aa dB dB (combc dB dB dB app a) (abs r)) t1 as a_1) t1)) % 36.35/36.63 True % 36.35/36.63 Clause #4209 (by superposition #[4207, 2071]): Eq True False % 36.35/36.63 Clause #4220 (by clausification #[4209]): False % 36.35/36.63 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------