TSTP Solution File: LCL769_5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL769_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n013.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 07:11:09 EDT 2023
% Result : Theorem 27.32s 27.52s
% Output : Proof 27.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL769_5 : TPTP v8.1.2. Released v6.0.0.
% 0.12/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n013.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 : Thu Aug 24 20:25:47 EDT 2023
% 0.14/0.34 % CPUTime :
% 27.32/27.52 SZS status Theorem for theBenchmark.p
% 27.32/27.52 SZS output start Proof for theBenchmark.p
% 27.32/27.52 Clause #0 (by assumption #[]): Eq (∀ (N2 : nat), pp (aa dB bool it (var N2))) True
% 27.32/27.52 Clause #1 (by assumption #[]): Eq (∀ (A : Type) (A1 : fun A bool), listsp A A1 (nil A)) True
% 27.32/27.52 Clause #10 (by assumption #[]): Eq
% 27.32/27.52 (∀ (A : Type) (A2 : list A) (A1 : fun A bool),
% 27.32/27.52 Iff (listsp A A1 A2)
% 27.32/27.52 (Or (Eq A2 (nil A))
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And (And (Eq A2 (aa (list A) (list A) (aa A (fun (list A) (list A)) (cons A) A4) L)) (pp (aa A bool A1 A4)))
% 27.32/27.52 (listsp A A1 L))))
% 27.32/27.52 True
% 27.32/27.52 Clause #21 (by assumption #[]): Eq
% 27.32/27.52 (∀ (A : Type) (X : A),
% 27.32/27.52 Eq (insert A X (nil A)) (aa (list A) (list A) (aa A (fun (list A) (list A)) (cons A) X) (nil A)))
% 27.32/27.52 True
% 27.32/27.52 Clause #115 (by assumption #[]): Eq (Not (listsp dB it (aa (list dB) (list dB) (aa dB (fun (list dB) (list dB)) (cons dB) (var i)) (nil dB)))) True
% 27.32/27.52 Clause #119 (by clausification #[1]): ∀ (a : Type), Eq (∀ (A1 : fun a bool), listsp a A1 (nil a)) True
% 27.32/27.52 Clause #120 (by clausification #[119]): ∀ (a : Type) (a_1 : fun a bool), Eq (listsp a a_1 (nil a)) True
% 27.32/27.52 Clause #121 (by clausification #[0]): ∀ (a : nat), Eq (pp (aa dB bool it (var a))) True
% 27.32/27.52 Clause #361 (by clausification #[10]): ∀ (a : Type),
% 27.32/27.52 Eq
% 27.32/27.52 (∀ (A2 : list a) (A1 : fun a bool),
% 27.32/27.52 Iff (listsp a A1 A2)
% 27.32/27.52 (Or (Eq A2 (nil a))
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And
% 27.32/27.52 (And (Eq A2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) A4) L)) (pp (aa a bool A1 A4)))
% 27.32/27.52 (listsp a A1 L))))
% 27.32/27.52 True
% 27.32/27.52 Clause #362 (by clausification #[361]): ∀ (a : Type) (a_1 : list a),
% 27.32/27.52 Eq
% 27.32/27.52 (∀ (A1 : fun a bool),
% 27.32/27.52 Iff (listsp a A1 a_1)
% 27.32/27.52 (Or (Eq a_1 (nil a))
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And
% 27.32/27.52 (And (Eq a_1 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) A4) L))
% 27.32/27.52 (pp (aa a bool A1 A4)))
% 27.32/27.52 (listsp a A1 L))))
% 27.32/27.52 True
% 27.32/27.52 Clause #363 (by clausification #[362]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a),
% 27.32/27.52 Eq
% 27.32/27.52 (Iff (listsp a a_1 a_2)
% 27.32/27.52 (Or (Eq a_2 (nil a))
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And
% 27.32/27.52 (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) A4) L)) (pp (aa a bool a_1 A4)))
% 27.32/27.52 (listsp a a_1 L))))
% 27.32/27.52 True
% 27.32/27.52 Clause #364 (by clausification #[363]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a),
% 27.32/27.52 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.52 (Eq
% 27.32/27.52 (Or (Eq a_2 (nil a))
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And
% 27.32/27.52 (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) A4) L)) (pp (aa a bool a_1 A4)))
% 27.32/27.52 (listsp a a_1 L)))
% 27.32/27.52 False)
% 27.32/27.52 Clause #366 (by clausification #[364]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a),
% 27.32/27.52 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.52 (Eq
% 27.32/27.52 (Exists fun A4 =>
% 27.32/27.52 Exists fun L =>
% 27.32/27.52 And (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) A4) L)) (pp (aa a bool a_1 A4)))
% 27.32/27.52 (listsp a a_1 L))
% 27.32/27.52 False)
% 27.32/27.52 Clause #368 (by clausification #[366]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a) (a_3 : a),
% 27.32/27.52 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.52 (Eq
% 27.32/27.52 (Exists fun L =>
% 27.32/27.52 And (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_3) L)) (pp (aa a bool a_1 a_3)))
% 27.32/27.52 (listsp a a_1 L))
% 27.32/27.52 False)
% 27.32/27.52 Clause #369 (by clausification #[368]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a) (a_3 : a) (a_4 : list a),
% 27.32/27.52 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.52 (Eq
% 27.32/27.52 (And
% 27.32/27.52 (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_3) a_4)) (pp (aa a bool a_1 a_3)))
% 27.32/27.52 (listsp a a_1 a_4))
% 27.32/27.52 False)
% 27.32/27.52 Clause #370 (by clausification #[369]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : list a) (a_3 : a) (a_4 : list a),
% 27.32/27.52 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.52 (Or
% 27.32/27.52 (Eq (And (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_3) a_4)) (pp (aa a bool a_1 a_3)))
% 27.32/27.56 False)
% 27.32/27.56 (Eq (listsp a a_1 a_4) False))
% 27.32/27.56 Clause #371 (by clausification #[370]): ∀ (a : Type) (a_1 : fun a bool) (a_2 a_3 : list a) (a_4 : a),
% 27.32/27.56 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.56 (Or (Eq (listsp a a_1 a_3) False)
% 27.32/27.56 (Or (Eq (Eq a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_4) a_3)) False)
% 27.32/27.56 (Eq (pp (aa a bool a_1 a_4)) False)))
% 27.32/27.56 Clause #372 (by clausification #[371]): ∀ (a : Type) (a_1 : fun a bool) (a_2 a_3 : list a) (a_4 : a),
% 27.32/27.56 Or (Eq (listsp a a_1 a_2) True)
% 27.32/27.56 (Or (Eq (listsp a a_1 a_3) False)
% 27.32/27.56 (Or (Eq (pp (aa a bool a_1 a_4)) False)
% 27.32/27.56 (Ne a_2 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_4) a_3))))
% 27.32/27.56 Clause #373 (by destructive equality resolution #[372]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : a) (a_3 : list a),
% 27.32/27.56 Or (Eq (listsp a a_1 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_2) a_3)) True)
% 27.32/27.56 (Or (Eq (listsp a a_1 a_3) False) (Eq (pp (aa a bool a_1 a_2)) False))
% 27.32/27.56 Clause #374 (by superposition #[373, 120]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : a),
% 27.32/27.56 Or (Eq (listsp a a_1 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_2) (nil a))) True)
% 27.32/27.56 (Or (Eq (pp (aa a bool a_1 a_2)) False) (Eq False True))
% 27.32/27.56 Clause #642 (by clausification #[21]): ∀ (a : Type),
% 27.32/27.56 Eq (∀ (X : a), Eq (insert a X (nil a)) (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) X) (nil a))) True
% 27.32/27.56 Clause #643 (by clausification #[642]): ∀ (a : Type) (a_1 : a),
% 27.32/27.56 Eq (Eq (insert a a_1 (nil a)) (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_1) (nil a))) True
% 27.32/27.56 Clause #644 (by clausification #[643]): ∀ (a : Type) (a_1 : a),
% 27.32/27.56 Eq (insert a a_1 (nil a)) (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_1) (nil a))
% 27.32/27.56 Clause #2743 (by clausification #[115]): Eq (listsp dB it (aa (list dB) (list dB) (aa dB (fun (list dB) (list dB)) (cons dB) (var i)) (nil dB))) False
% 27.32/27.56 Clause #2744 (by forward demodulation #[2743, 644]): Eq (listsp dB it (insert dB (var i) (nil dB))) False
% 27.32/27.56 Clause #3445 (by clausification #[374]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : a),
% 27.32/27.56 Or (Eq (listsp a a_1 (aa (list a) (list a) (aa a (fun (list a) (list a)) (cons a) a_2) (nil a))) True)
% 27.32/27.56 (Eq (pp (aa a bool a_1 a_2)) False)
% 27.32/27.56 Clause #3446 (by forward demodulation #[3445, 644]): ∀ (a : Type) (a_1 : fun a bool) (a_2 : a),
% 27.32/27.56 Or (Eq (listsp a a_1 (insert a a_2 (nil a))) True) (Eq (pp (aa a bool a_1 a_2)) False)
% 27.32/27.56 Clause #3447 (by superposition #[3446, 121]): ∀ (a : nat), Or (Eq (listsp dB it (insert dB (var a) (nil dB))) True) (Eq False True)
% 27.32/27.56 Clause #3501 (by clausification #[3447]): ∀ (a : nat), Eq (listsp dB it (insert dB (var a) (nil dB))) True
% 27.32/27.56 Clause #3502 (by superposition #[3501, 2744]): Eq True False
% 27.32/27.56 Clause #3513 (by clausification #[3502]): False
% 27.32/27.56 SZS output end Proof for theBenchmark.p
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