TSTP Solution File: LCL834_5 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : LCL834_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 07:11:29 EDT 2023
% Result : Theorem 15.85s 16.03s
% Output : Proof 15.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL834_5 : TPTP v8.1.2. Released v6.0.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n004.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 00:15:53 EDT 2023
% 0.14/0.34 % CPUTime :
% 15.85/16.03 SZS status Theorem for theBenchmark.p
% 15.85/16.03 SZS output start Proof for theBenchmark.p
% 15.85/16.03 Clause #3 (by assumption #[]): Eq
% 15.85/16.03 (∀ (T S2 : dB),
% 15.85/16.03 pp
% 15.85/16.03 (aa dB bool (aa dB (fun dB bool) beta (aa dB dB (aa dB (fun dB dB) app (abs S2)) T))
% 15.85/16.03 (subst S2 T (zero_zero nat))))
% 15.85/16.03 True
% 15.85/16.03 Clause #10 (by assumption #[]): Eq
% 15.85/16.03 (∀ (Ss1 : list dB) (S Ra : dB),
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta Ra) S) →
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app Ra Ss1)) (foldl dB dB app S Ss1)))
% 15.85/16.03 True
% 15.85/16.03 Clause #57 (by assumption #[]): Eq
% 15.85/16.03 (∀ (A B : Type) (Xs : list B) (X : B) (Aa : A) (F : fun A (fun B A)),
% 15.85/16.03 Eq (foldl A B F Aa (cons B X Xs)) (foldl A B F (aa B A (aa A (fun B A) F Aa) X) Xs))
% 15.85/16.03 True
% 15.85/16.03 Clause #103 (by assumption #[]): Eq
% 15.85/16.03 (∀ (A C B : Type) (R : A) (Q : B) (P : fun A (fun B C)),
% 15.85/16.03 Eq (aa A C (combc A B C P Q) R) (aa B C (aa A (fun B C) P R) Q))
% 15.85/16.03 True
% 15.85/16.03 Clause #108 (by assumption #[]): Eq
% 15.85/16.03 (Not
% 15.85/16.03 (pp
% 15.85/16.03 (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs r)) a) as))
% 15.85/16.03 (foldl dB dB app (subst r a (zero_zero nat)) as))))
% 15.85/16.03 True
% 15.85/16.03 Clause #133 (by clausification #[3]): ∀ (a : dB),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (S2 : dB),
% 15.85/16.03 pp
% 15.85/16.03 (aa dB bool (aa dB (fun dB bool) beta (aa dB dB (aa dB (fun dB dB) app (abs S2)) a))
% 15.85/16.03 (subst S2 a (zero_zero nat))))
% 15.85/16.03 True
% 15.85/16.03 Clause #134 (by clausification #[133]): ∀ (a a_1 : dB),
% 15.85/16.03 Eq
% 15.85/16.03 (pp
% 15.85/16.03 (aa dB bool (aa dB (fun dB bool) beta (aa dB dB (aa dB (fun dB dB) app (abs a)) a_1))
% 15.85/16.03 (subst a a_1 (zero_zero nat))))
% 15.85/16.03 True
% 15.85/16.03 Clause #255 (by clausification #[10]): ∀ (a : list dB),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (S Ra : dB),
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta Ra) S) →
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app Ra a)) (foldl dB dB app S a)))
% 15.85/16.03 True
% 15.85/16.03 Clause #256 (by clausification #[255]): ∀ (a : dB) (a_1 : list dB),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (Ra : dB),
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta Ra) a) →
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app Ra a_1)) (foldl dB dB app a a_1)))
% 15.85/16.03 True
% 15.85/16.03 Clause #257 (by clausification #[256]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.85/16.03 Eq
% 15.85/16.03 (pp (aa dB bool (aa dB (fun dB bool) beta a) a_1) →
% 15.85/16.03 pp (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app a a_2)) (foldl dB dB app a_1 a_2)))
% 15.85/16.03 True
% 15.85/16.03 Clause #258 (by clausification #[257]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.85/16.03 Or (Eq (pp (aa dB bool (aa dB (fun dB bool) beta a) a_1)) False)
% 15.85/16.03 (Eq (pp (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app a a_2)) (foldl dB dB app a_1 a_2))) True)
% 15.85/16.03 Clause #259 (by superposition #[258, 134]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.85/16.03 Or
% 15.85/16.03 (Eq
% 15.85/16.03 (pp
% 15.85/16.03 (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs a)) a_1) a_2))
% 15.85/16.03 (foldl dB dB app (subst a a_1 (zero_zero nat)) a_2)))
% 15.85/16.03 True)
% 15.85/16.03 (Eq False True)
% 15.85/16.03 Clause #2201 (by clausification #[57]): ∀ (a : Type),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (B : Type) (Xs : list B) (X : B) (Aa : a) (F : fun a (fun B a)),
% 15.85/16.03 Eq (foldl a B F Aa (cons B X Xs)) (foldl a B F (aa B a (aa a (fun B a) F Aa) X) Xs))
% 15.85/16.03 True
% 15.85/16.03 Clause #2202 (by clausification #[2201]): ∀ (a a_1 : Type),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (Xs : list a) (X : a) (Aa : a_1) (F : fun a_1 (fun a a_1)),
% 15.85/16.03 Eq (foldl a_1 a F Aa (cons a X Xs)) (foldl a_1 a F (aa a a_1 (aa a_1 (fun a a_1) F Aa) X) Xs))
% 15.85/16.03 True
% 15.85/16.03 Clause #2203 (by clausification #[2202]): ∀ (a a_1 : Type) (a_2 : list a),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (X : a) (Aa : a_1) (F : fun a_1 (fun a a_1)),
% 15.85/16.03 Eq (foldl a_1 a F Aa (cons a X a_2)) (foldl a_1 a F (aa a a_1 (aa a_1 (fun a a_1) F Aa) X) a_2))
% 15.85/16.03 True
% 15.85/16.03 Clause #2204 (by clausification #[2203]): ∀ (a a_1 : Type) (a_2 : a_1) (a_3 : list a_1),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (Aa : a) (F : fun a (fun a_1 a)),
% 15.85/16.03 Eq (foldl a a_1 F Aa (cons a_1 a_2 a_3)) (foldl a a_1 F (aa a_1 a (aa a (fun a_1 a) F Aa) a_2) a_3))
% 15.85/16.03 True
% 15.85/16.03 Clause #2205 (by clausification #[2204]): ∀ (a a_1 : Type) (a_2 : a) (a_3 : a_1) (a_4 : list a_1),
% 15.85/16.03 Eq
% 15.85/16.03 (∀ (F : fun a (fun a_1 a)),
% 15.85/16.03 Eq (foldl a a_1 F a_2 (cons a_1 a_3 a_4)) (foldl a a_1 F (aa a_1 a (aa a (fun a_1 a) F a_2) a_3) a_4))
% 15.92/16.09 True
% 15.92/16.09 Clause #2206 (by clausification #[2205]): ∀ (a a_1 : Type) (a_2 : fun a (fun a_1 a)) (a_3 : a) (a_4 : a_1) (a_5 : list a_1),
% 15.92/16.09 Eq (Eq (foldl a a_1 a_2 a_3 (cons a_1 a_4 a_5)) (foldl a a_1 a_2 (aa a_1 a (aa a (fun a_1 a) a_2 a_3) a_4) a_5)) True
% 15.92/16.09 Clause #2207 (by clausification #[2206]): ∀ (a a_1 : Type) (a_2 : fun a (fun a_1 a)) (a_3 : a) (a_4 : a_1) (a_5 : list a_1),
% 15.92/16.09 Eq (foldl a a_1 a_2 a_3 (cons a_1 a_4 a_5)) (foldl a a_1 a_2 (aa a_1 a (aa a (fun a_1 a) a_2 a_3) a_4) a_5)
% 15.92/16.09 Clause #5104 (by clausification #[103]): ∀ (a : Type),
% 15.92/16.09 Eq
% 15.92/16.09 (∀ (C B : Type) (R : a) (Q : B) (P : fun a (fun B C)),
% 15.92/16.09 Eq (aa a C (combc a B C P Q) R) (aa B C (aa a (fun B C) P R) Q))
% 15.92/16.09 True
% 15.92/16.09 Clause #5105 (by clausification #[5104]): ∀ (a a_1 : Type),
% 15.92/16.09 Eq
% 15.92/16.09 (∀ (B : Type) (R : a) (Q : B) (P : fun a (fun B a_1)),
% 15.92/16.09 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))
% 15.92/16.09 True
% 15.92/16.09 Clause #5106 (by clausification #[5105]): ∀ (a a_1 a_2 : Type),
% 15.92/16.09 Eq
% 15.92/16.09 (∀ (R : a) (Q : a_1) (P : fun a (fun a_1 a_2)),
% 15.92/16.09 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))
% 15.92/16.09 True
% 15.92/16.09 Clause #5107 (by clausification #[5106]): ∀ (a a_1 a_2 : Type) (a_3 : a_1),
% 15.92/16.09 Eq
% 15.92/16.09 (∀ (Q : a) (P : fun a_1 (fun a a_2)),
% 15.92/16.09 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))
% 15.92/16.09 True
% 15.92/16.09 Clause #5108 (by clausification #[5107]): ∀ (a a_1 a_2 : Type) (a_3 : a_1) (a_4 : a),
% 15.92/16.09 Eq
% 15.92/16.09 (∀ (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))
% 15.92/16.09 True
% 15.92/16.09 Clause #5109 (by clausification #[5108]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1),
% 15.92/16.09 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
% 15.92/16.09 Clause #5110 (by clausification #[5109]): ∀ (a a_1 a_2 : Type) (a_3 : fun a_1 (fun a_2 a)) (a_4 : a_2) (a_5 : a_1),
% 15.92/16.09 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)
% 15.92/16.09 Clause #5326 (by clausification #[108]): Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs r)) a) as))
% 15.92/16.09 (foldl dB dB app (subst r a (zero_zero nat)) as)))
% 15.92/16.09 False
% 15.92/16.09 Clause #5327 (by forward demodulation #[5326, 5110]): Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (combc dB dB bool beta (foldl dB dB app (subst r a (zero_zero nat)) as))
% 15.92/16.09 (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs r)) a) as)))
% 15.92/16.09 False
% 15.92/16.09 Clause #5328 (by forward demodulation #[5327, 2207]): Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (combc dB dB bool beta (foldl dB dB app (subst r a (zero_zero nat)) as))
% 15.92/16.09 (foldl dB dB app (abs r) (cons dB a as))))
% 15.92/16.09 False
% 15.92/16.09 Clause #7059 (by clausification #[259]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.92/16.09 Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (aa dB (fun dB bool) beta (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs a)) a_1) a_2))
% 15.92/16.09 (foldl dB dB app (subst a a_1 (zero_zero nat)) a_2)))
% 15.92/16.09 True
% 15.92/16.09 Clause #7060 (by forward demodulation #[7059, 5110]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.92/16.09 Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (combc dB dB bool beta (foldl dB dB app (subst a a_1 (zero_zero nat)) a_2))
% 15.92/16.09 (foldl dB dB app (aa dB dB (aa dB (fun dB dB) app (abs a)) a_1) a_2)))
% 15.92/16.09 True
% 15.92/16.09 Clause #7061 (by forward demodulation #[7060, 2207]): ∀ (a a_1 : dB) (a_2 : list dB),
% 15.92/16.09 Eq
% 15.92/16.09 (pp
% 15.92/16.09 (aa dB bool (combc dB dB bool beta (foldl dB dB app (subst a a_1 (zero_zero nat)) a_2))
% 15.92/16.09 (foldl dB dB app (abs a) (cons dB a_1 a_2))))
% 15.92/16.09 True
% 15.92/16.09 Clause #7063 (by superposition #[7061, 5328]): Eq True False
% 15.92/16.09 Clause #7143 (by clausification #[7063]): False
% 15.92/16.09 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------