TSTP Solution File: LCL813_5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL813_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 07:11:22 EDT 2023
% Result : Theorem 27.62s 27.79s
% Output : Proof 27.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL813_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri Aug 25 02:31:12 EDT 2023
% 0.14/0.34 % CPUTime :
% 27.62/27.79 SZS status Theorem for theBenchmark.p
% 27.62/27.79 SZS output start Proof for theBenchmark.p
% 27.62/27.79 Clause #1 (by assumption #[]): Eq
% 27.62/27.79 (∀ (Ta1 : type) (X1 : nat) (Env : fun1 nat type),
% 27.62/27.79 Eq (aa nat type Env X1) Ta1 → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var X1)) Ta1))
% 27.62/27.79 True
% 27.62/27.79 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
% 27.62/27.79 Clause #104 (by assumption #[]): Eq
% 27.62/27.79 (∀ (A C B : Type) (R : A) (Q : B) (P : fun1 A (fun1 B C)),
% 27.62/27.79 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun1 B C) P R) Q))
% 27.62/27.79 True
% 27.62/27.79 Clause #111 (by assumption #[]): Eq
% 27.62/27.79 (Not
% 27.62/27.79 (pp
% 27.62/27.79 (aa type bool
% 27.62/27.79 (aa dB (fun1 type bool) (typing (shift type e (zero_zero nat) (foldr type type fun ts t)))
% 27.62/27.79 (var (zero_zero nat)))
% 27.62/27.79 (foldr type type fun ts t))))
% 27.62/27.79 True
% 27.62/27.79 Clause #123 (by clausification #[1]): ∀ (a : type),
% 27.62/27.79 Eq
% 27.62/27.79 (∀ (X1 : nat) (Env : fun1 nat type),
% 27.62/27.79 Eq (aa nat type Env X1) a → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var X1)) a))
% 27.62/27.79 True
% 27.62/27.79 Clause #124 (by clausification #[123]): ∀ (a : nat) (a_1 : type),
% 27.62/27.79 Eq
% 27.62/27.79 (∀ (Env : fun1 nat type),
% 27.62/27.79 Eq (aa nat type Env a) a_1 → pp (aa type bool (aa dB (fun1 type bool) (typing Env) (var a)) a_1))
% 27.62/27.79 True
% 27.62/27.79 Clause #125 (by clausification #[124]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type),
% 27.62/27.79 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
% 27.62/27.79 Clause #126 (by clausification #[125]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type),
% 27.62/27.79 Or (Eq (Eq (aa nat type a a_1) a_2) False)
% 27.62/27.79 (Eq (pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) a_2)) True)
% 27.62/27.79 Clause #127 (by clausification #[126]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type),
% 27.62/27.79 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)
% 27.62/27.79 Clause #128 (by destructive equality resolution #[127]): ∀ (a : fun1 nat type) (a_1 : nat),
% 27.62/27.79 Eq (pp (aa type bool (aa dB (fun1 type bool) (typing a) (var a_1)) (aa nat type a a_1))) True
% 27.62/27.79 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
% 27.62/27.79 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
% 27.62/27.79 Clause #424 (by clausification #[423]): ∀ (a : Type) (a_1 : fun1 nat a) (a_2 : a),
% 27.62/27.79 Eq (∀ (J1 Ib : nat), Eq Ib J1 → Eq (aa nat a (shift a a_1 Ib a_2) J1) a_2) True
% 27.62/27.79 Clause #425 (by clausification #[424]): ∀ (a : nat) (a_1 : Type) (a_2 : fun1 nat a_1) (a_3 : a_1),
% 27.62/27.79 Eq (∀ (Ib : nat), Eq Ib a → Eq (aa nat a_1 (shift a_1 a_2 Ib a_3) a) a_3) True
% 27.62/27.79 Clause #426 (by clausification #[425]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2),
% 27.62/27.79 Eq (Eq a a_1 → Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4) True
% 27.62/27.79 Clause #427 (by clausification #[426]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2),
% 27.62/27.79 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)
% 27.62/27.79 Clause #428 (by clausification #[427]): ∀ (a : Type) (a_1 : fun1 nat a) (a_2 : nat) (a_3 : a) (a_4 : nat),
% 27.62/27.79 Or (Eq (Eq (aa nat a (shift a a_1 a_2 a_3) a_4) a_3) True) (Ne a_2 a_4)
% 27.62/27.79 Clause #429 (by clausification #[428]): ∀ (a a_1 : nat) (a_2 : Type) (a_3 : fun1 nat a_2) (a_4 : a_2),
% 27.62/27.79 Or (Ne a a_1) (Eq (aa nat a_2 (shift a_2 a_3 a a_4) a_1) a_4)
% 27.62/27.79 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
% 27.62/27.79 Clause #431 (by superposition #[430, 128]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type),
% 27.62/27.79 Eq (pp (aa type bool (aa dB (fun1 type bool) (typing (shift type a a_1 a_2)) (var a_1)) a_2)) True
% 27.62/27.79 Clause #5929 (by clausification #[104]): ∀ (a : Type),
% 27.62/27.79 Eq
% 27.62/27.79 (∀ (C B : Type) (R : a) (Q : B) (P : fun1 a (fun1 B C)),
% 27.62/27.79 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun1 B C) P R) Q))
% 27.62/27.79 True
% 27.62/27.79 Clause #5930 (by clausification #[5929]): ∀ (a a_1 : Type),
% 27.68/27.88 Eq
% 27.68/27.88 (∀ (B : Type) (R : a) (Q : B) (P : fun1 a (fun1 B a_1)),
% 27.68/27.88 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))
% 27.68/27.88 True
% 27.68/27.88 Clause #5931 (by clausification #[5930]): ∀ (a a_1 a_2 : Type),
% 27.68/27.88 Eq
% 27.68/27.88 (∀ (R : a) (Q : a_1) (P : fun1 a (fun1 a_1 a_2)),
% 27.68/27.88 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))
% 27.68/27.88 True
% 27.68/27.88 Clause #5932 (by clausification #[5931]): ∀ (a a_1 a_2 : Type) (a_3 : a_1),
% 27.68/27.88 Eq
% 27.68/27.88 (∀ (Q : a) (P : fun1 a_1 (fun1 a a_2)),
% 27.68/27.88 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))
% 27.68/27.88 True
% 27.68/27.88 Clause #5933 (by clausification #[5932]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a),
% 27.68/27.88 Eq
% 27.68/27.88 (∀ (P : fun1 a (fun1 a_1 a_2)),
% 27.68/27.88 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))
% 27.68/27.88 True
% 27.68/27.88 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),
% 27.68/27.88 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
% 27.68/27.88 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),
% 27.68/27.88 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)
% 27.68/27.88 Clause #6370 (by clausification #[111]): Eq
% 27.68/27.88 (pp
% 27.68/27.88 (aa type bool
% 27.68/27.88 (aa dB (fun1 type bool) (typing (shift type e (zero_zero nat) (foldr type type fun ts t))) (var (zero_zero nat)))
% 27.68/27.88 (foldr type type fun ts t)))
% 27.68/27.88 False
% 27.68/27.88 Clause #6371 (by forward demodulation #[6370, 5935]): Eq
% 27.68/27.88 (pp
% 27.68/27.88 (aa dB bool
% 27.68/27.88 (combc dB type bool (typing (shift type e (zero_zero nat) (foldr type type fun ts t))) (foldr type type fun ts t))
% 27.68/27.88 (var (zero_zero nat))))
% 27.68/27.88 False
% 27.68/27.88 Clause #13026 (by forward demodulation #[431, 5935]): ∀ (a : fun1 nat type) (a_1 : nat) (a_2 : type),
% 27.68/27.88 Eq (pp (aa dB bool (combc dB type bool (typing (shift type a a_1 a_2)) a_2) (var a_1))) True
% 27.68/27.88 Clause #13028 (by superposition #[13026, 6371]): Eq True False
% 27.68/27.88 Clause #13125 (by clausification #[13028]): False
% 27.68/27.88 SZS output end Proof for theBenchmark.p
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