TSTP Solution File: DAT276^1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : DAT276^1 : TPTP v8.1.2. Released v7.0.0.
% 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 : Wed Aug 30 22:12:41 EDT 2023
% Result : Theorem 7.36s 7.60s
% Output : Proof 7.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT276^1 : TPTP v8.1.2. Released v7.0.0.
% 0.15/0.13 % Command : duper %s
% 0.15/0.34 % Computer : n004.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu Aug 24 14:24:38 EDT 2023
% 0.15/0.35 % CPUTime :
% 7.36/7.60 SZS status Theorem for theBenchmark.p
% 7.36/7.60 SZS output start Proof for theBenchmark.p
% 7.36/7.60 Clause #0 (by assumption #[]): Eq (∀ (A : Type) (A0 : A) (A1 : «type/ind_types/list» A), Eq («const/lists/TL» A («const/ind_types/CONS» A A0 A1)) A1)
% 7.36/7.60 True
% 7.36/7.60 Clause #1 (by assumption #[]): Eq (∀ (A : Type) (A0 : «type/ind_types/list» A) (A1 : A), Eq («const/lists/HD» A («const/ind_types/CONS» A A1 A0)) A1)
% 7.36/7.60 True
% 7.36/7.60 Clause #2 (by assumption #[]): Eq
% 7.36/7.60 (∀ (A A0 A1 : Type) (A2 : A0) (A3 : A0 → A1 → A) (A4 : «type/ind_types/list» A0) (A5 : «type/ind_types/list» A1),
% 7.36/7.60 Eq («const/lists/MAP2» A0 A1 A A3 («const/ind_types/CONS» A0 A2 A4) A5)
% 7.36/7.60 («const/ind_types/CONS» A (A3 A2 («const/lists/HD» A1 A5))
% 7.36/7.60 («const/lists/MAP2» A0 A1 A A3 A4 («const/lists/TL» A1 A5))))
% 7.36/7.60 True
% 7.36/7.60 Clause #3 (by assumption #[]): Eq
% 7.36/7.60 (Not
% 7.36/7.60 (∀ (A A0 A1 : Type) (A2 : A0) (A3 : A1) (A4 : A0 → A1 → A) (A5 : «type/ind_types/list» A0)
% 7.36/7.60 (A6 : «type/ind_types/list» A1),
% 7.36/7.60 Eq («const/lists/MAP2» A0 A1 A A4 («const/ind_types/CONS» A0 A2 A5) («const/ind_types/CONS» A1 A3 A6))
% 7.36/7.60 («const/ind_types/CONS» A (A4 A2 A3) («const/lists/MAP2» A0 A1 A A4 A5 A6))))
% 7.36/7.60 True
% 7.36/7.60 Clause #4 (by clausification #[1]): ∀ (a : Type),
% 7.36/7.60 Eq (∀ (A0 : «type/ind_types/list» a) (A1 : a), Eq («const/lists/HD» a («const/ind_types/CONS» a A1 A0)) A1) True
% 7.36/7.60 Clause #5 (by clausification #[4]): ∀ (a : Type) (a_1 : «type/ind_types/list» a),
% 7.36/7.60 Eq (∀ (A1 : a), Eq («const/lists/HD» a («const/ind_types/CONS» a A1 a_1)) A1) True
% 7.36/7.60 Clause #6 (by clausification #[5]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a),
% 7.36/7.60 Eq (Eq («const/lists/HD» a («const/ind_types/CONS» a a_1 a_2)) a_1) True
% 7.36/7.60 Clause #7 (by clausification #[6]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a), Eq («const/lists/HD» a («const/ind_types/CONS» a a_1 a_2)) a_1
% 7.36/7.60 Clause #8 (by clausification #[0]): ∀ (a : Type),
% 7.36/7.60 Eq (∀ (A0 : a) (A1 : «type/ind_types/list» a), Eq («const/lists/TL» a («const/ind_types/CONS» a A0 A1)) A1) True
% 7.36/7.60 Clause #9 (by clausification #[8]): ∀ (a : Type) (a_1 : a),
% 7.36/7.60 Eq (∀ (A1 : «type/ind_types/list» a), Eq («const/lists/TL» a («const/ind_types/CONS» a a_1 A1)) A1) True
% 7.36/7.60 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a),
% 7.36/7.60 Eq (Eq («const/lists/TL» a («const/ind_types/CONS» a a_1 a_2)) a_2) True
% 7.36/7.60 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a), Eq («const/lists/TL» a («const/ind_types/CONS» a a_1 a_2)) a_2
% 7.36/7.60 Clause #12 (by clausification #[2]): ∀ (a : Type),
% 7.36/7.60 Eq
% 7.36/7.60 (∀ (A0 A1 : Type) (A2 : A0) (A3 : A0 → A1 → a) (A4 : «type/ind_types/list» A0) (A5 : «type/ind_types/list» A1),
% 7.36/7.60 Eq («const/lists/MAP2» A0 A1 a A3 («const/ind_types/CONS» A0 A2 A4) A5)
% 7.36/7.60 («const/ind_types/CONS» a (A3 A2 («const/lists/HD» A1 A5))
% 7.36/7.60 («const/lists/MAP2» A0 A1 a A3 A4 («const/lists/TL» A1 A5))))
% 7.36/7.60 True
% 7.36/7.60 Clause #13 (by clausification #[12]): ∀ (a a_1 : Type),
% 7.36/7.60 Eq
% 7.36/7.60 (∀ (A1 : Type) (A2 : a) (A3 : a → A1 → a_1) (A4 : «type/ind_types/list» a) (A5 : «type/ind_types/list» A1),
% 7.36/7.60 Eq («const/lists/MAP2» a A1 a_1 A3 («const/ind_types/CONS» a A2 A4) A5)
% 7.36/7.60 («const/ind_types/CONS» a_1 (A3 A2 («const/lists/HD» A1 A5))
% 7.36/7.60 («const/lists/MAP2» a A1 a_1 A3 A4 («const/lists/TL» A1 A5))))
% 7.36/7.60 True
% 7.36/7.60 Clause #14 (by clausification #[13]): ∀ (a a_1 a_2 : Type),
% 7.36/7.60 Eq
% 7.36/7.60 (∀ (A2 : a) (A3 : a → a_1 → a_2) (A4 : «type/ind_types/list» a) (A5 : «type/ind_types/list» a_1),
% 7.36/7.60 Eq («const/lists/MAP2» a a_1 a_2 A3 («const/ind_types/CONS» a A2 A4) A5)
% 7.36/7.60 («const/ind_types/CONS» a_2 (A3 A2 («const/lists/HD» a_1 A5))
% 7.36/7.60 («const/lists/MAP2» a a_1 a_2 A3 A4 («const/lists/TL» a_1 A5))))
% 7.36/7.60 True
% 7.36/7.60 Clause #15 (by clausification #[14]): ∀ (a a_1 a_2 : Type) (a_3 : a),
% 7.36/7.60 Eq
% 7.36/7.60 (∀ (A3 : a → a_1 → a_2) (A4 : «type/ind_types/list» a) (A5 : «type/ind_types/list» a_1),
% 7.36/7.60 Eq («const/lists/MAP2» a a_1 a_2 A3 («const/ind_types/CONS» a a_3 A4) A5)
% 7.36/7.62 («const/ind_types/CONS» a_2 (A3 a_3 («const/lists/HD» a_1 A5))
% 7.36/7.62 («const/lists/MAP2» a a_1 a_2 A3 A4 («const/lists/TL» a_1 A5))))
% 7.36/7.62 True
% 7.36/7.62 Clause #16 (by clausification #[15]): ∀ (a a_1 a_2 : Type) (a_3 : a → a_1 → a_2) (a_4 : a),
% 7.36/7.62 Eq
% 7.36/7.62 (∀ (A4 : «type/ind_types/list» a) (A5 : «type/ind_types/list» a_1),
% 7.36/7.62 Eq («const/lists/MAP2» a a_1 a_2 a_3 («const/ind_types/CONS» a a_4 A4) A5)
% 7.36/7.62 («const/ind_types/CONS» a_2 (a_3 a_4 («const/lists/HD» a_1 A5))
% 7.36/7.62 («const/lists/MAP2» a a_1 a_2 a_3 A4 («const/lists/TL» a_1 A5))))
% 7.36/7.62 True
% 7.36/7.62 Clause #17 (by clausification #[16]): ∀ (a a_1 a_2 : Type) (a_3 : a_2 → a → a_1) (a_4 : a_2) (a_5 : «type/ind_types/list» a_2),
% 7.36/7.62 Eq
% 7.36/7.62 (∀ (A5 : «type/ind_types/list» a),
% 7.36/7.62 Eq («const/lists/MAP2» a_2 a a_1 a_3 («const/ind_types/CONS» a_2 a_4 a_5) A5)
% 7.36/7.62 («const/ind_types/CONS» a_1 (a_3 a_4 («const/lists/HD» a A5))
% 7.36/7.62 («const/lists/MAP2» a_2 a a_1 a_3 a_5 («const/lists/TL» a A5))))
% 7.36/7.62 True
% 7.36/7.62 Clause #18 (by clausification #[17]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a) (a_4 : a_1) (a_5 : «type/ind_types/list» a_1)
% 7.36/7.62 (a_6 : «type/ind_types/list» a_2),
% 7.36/7.62 Eq
% 7.36/7.62 (Eq («const/lists/MAP2» a_1 a_2 a a_3 («const/ind_types/CONS» a_1 a_4 a_5) a_6)
% 7.36/7.62 («const/ind_types/CONS» a (a_3 a_4 («const/lists/HD» a_2 a_6))
% 7.36/7.62 («const/lists/MAP2» a_1 a_2 a a_3 a_5 («const/lists/TL» a_2 a_6))))
% 7.36/7.62 True
% 7.36/7.62 Clause #19 (by clausification #[18]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a) (a_4 : a_1) (a_5 : «type/ind_types/list» a_1)
% 7.36/7.62 (a_6 : «type/ind_types/list» a_2),
% 7.36/7.62 Eq («const/lists/MAP2» a_1 a_2 a a_3 («const/ind_types/CONS» a_1 a_4 a_5) a_6)
% 7.36/7.62 («const/ind_types/CONS» a (a_3 a_4 («const/lists/HD» a_2 a_6))
% 7.36/7.62 («const/lists/MAP2» a_1 a_2 a a_3 a_5 («const/lists/TL» a_2 a_6)))
% 7.36/7.62 Clause #25 (by superposition #[19, 11]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a) (a_4 : a_1) (a_5 : «type/ind_types/list» a_1) (a_6 : a_2)
% 7.36/7.62 (a_7 : «type/ind_types/list» a_2),
% 7.36/7.62 Eq («const/lists/MAP2» a_1 a_2 a a_3 («const/ind_types/CONS» a_1 a_4 a_5) («const/ind_types/CONS» a_2 a_6 a_7))
% 7.36/7.62 («const/ind_types/CONS» a (a_3 a_4 («const/lists/HD» a_2 («const/ind_types/CONS» a_2 a_6 a_7)))
% 7.36/7.62 («const/lists/MAP2» a_1 a_2 a a_3 a_5 a_7))
% 7.36/7.62 Clause #158 (by clausification #[3]): Eq
% 7.36/7.62 (∀ (A A0 A1 : Type) (A2 : A0) (A3 : A1) (A4 : A0 → A1 → A) (A5 : «type/ind_types/list» A0)
% 7.36/7.62 (A6 : «type/ind_types/list» A1),
% 7.36/7.62 Eq («const/lists/MAP2» A0 A1 A A4 («const/ind_types/CONS» A0 A2 A5) («const/ind_types/CONS» A1 A3 A6))
% 7.36/7.62 («const/ind_types/CONS» A (A4 A2 A3) («const/lists/MAP2» A0 A1 A A4 A5 A6)))
% 7.36/7.62 False
% 7.36/7.62 Clause #159 (by clausification #[158]): ∀ (a : Type),
% 7.36/7.62 Eq
% 7.36/7.62 (Not
% 7.36/7.62 (∀ (A0 A1 : Type) (A2 : A0) (A3 : A1) (A4 : A0 → A1 → skS.0 0 a) (A5 : «type/ind_types/list» A0)
% 7.36/7.62 (A6 : «type/ind_types/list» A1),
% 7.36/7.62 Eq («const/lists/MAP2» A0 A1 (skS.0 0 a) A4 («const/ind_types/CONS» A0 A2 A5) («const/ind_types/CONS» A1 A3 A6))
% 7.36/7.62 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3) («const/lists/MAP2» A0 A1 (skS.0 0 a) A4 A5 A6))))
% 7.36/7.62 True
% 7.36/7.62 Clause #160 (by clausification #[159]): ∀ (a : Type),
% 7.36/7.62 Eq
% 7.36/7.62 (∀ (A0 A1 : Type) (A2 : A0) (A3 : A1) (A4 : A0 → A1 → skS.0 0 a) (A5 : «type/ind_types/list» A0)
% 7.36/7.62 (A6 : «type/ind_types/list» A1),
% 7.36/7.62 Eq («const/lists/MAP2» A0 A1 (skS.0 0 a) A4 («const/ind_types/CONS» A0 A2 A5) («const/ind_types/CONS» A1 A3 A6))
% 7.36/7.62 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3) («const/lists/MAP2» A0 A1 (skS.0 0 a) A4 A5 A6)))
% 7.36/7.62 False
% 7.36/7.62 Clause #161 (by clausification #[160]): ∀ (a a_1 : Type),
% 7.36/7.62 Eq
% 7.36/7.62 (Not
% 7.36/7.62 (∀ (A1 : Type) (A2 : skS.0 1 a a_1) (A3 : A1) (A4 : skS.0 1 a a_1 → A1 → skS.0 0 a)
% 7.36/7.62 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» A1),
% 7.36/7.62 Eq
% 7.36/7.62 («const/lists/MAP2» (skS.0 1 a a_1) A1 (skS.0 0 a) A4 («const/ind_types/CONS» (skS.0 1 a a_1) A2 A5)
% 7.36/7.62 («const/ind_types/CONS» A1 A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3) («const/lists/MAP2» (skS.0 1 a a_1) A1 (skS.0 0 a) A4 A5 A6))))
% 7.49/7.64 True
% 7.49/7.64 Clause #162 (by clausification #[161]): ∀ (a a_1 : Type),
% 7.49/7.64 Eq
% 7.49/7.64 (∀ (A1 : Type) (A2 : skS.0 1 a a_1) (A3 : A1) (A4 : skS.0 1 a a_1 → A1 → skS.0 0 a)
% 7.49/7.64 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» A1),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) A1 (skS.0 0 a) A4 («const/ind_types/CONS» (skS.0 1 a a_1) A2 A5)
% 7.49/7.64 («const/ind_types/CONS» A1 A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3) («const/lists/MAP2» (skS.0 1 a a_1) A1 (skS.0 0 a) A4 A5 A6)))
% 7.49/7.64 False
% 7.49/7.64 Clause #163 (by clausification #[162]): ∀ (a a_1 a_2 : Type),
% 7.49/7.64 Eq
% 7.49/7.64 (Not
% 7.49/7.64 (∀ (A2 : skS.0 1 a a_1) (A3 : skS.0 2 a a_1 a_2) (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a)
% 7.49/7.64 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.64 («const/ind_types/CONS» (skS.0 1 a a_1) A2 A5) («const/ind_types/CONS» (skS.0 2 a a_1 a_2) A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3)
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6))))
% 7.49/7.64 True
% 7.49/7.64 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 : Type),
% 7.49/7.64 Eq
% 7.49/7.64 (∀ (A2 : skS.0 1 a a_1) (A3 : skS.0 2 a a_1 a_2) (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a)
% 7.49/7.64 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.64 («const/ind_types/CONS» (skS.0 1 a a_1) A2 A5) («const/ind_types/CONS» (skS.0 2 a a_1 a_2) A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 A2 A3)
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6)))
% 7.49/7.64 False
% 7.49/7.64 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1),
% 7.49/7.64 Eq
% 7.49/7.64 (Not
% 7.49/7.64 (∀ (A3 : skS.0 2 a a_1 a_2) (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a)
% 7.49/7.64 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.64 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.64 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 (skS.0 3 a a_1 a_2 a_3) A3)
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6))))
% 7.49/7.64 True
% 7.49/7.64 Clause #166 (by clausification #[165]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1),
% 7.49/7.64 Eq
% 7.49/7.64 (∀ (A3 : skS.0 2 a a_1 a_2) (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a)
% 7.49/7.64 (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.64 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.64 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) A3 A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 (skS.0 3 a a_1 a_2 a_3) A3)
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6)))
% 7.49/7.64 False
% 7.49/7.64 Clause #167 (by clausification #[166]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2),
% 7.49/7.64 Eq
% 7.49/7.64 (Not
% 7.49/7.64 (∀ (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (A5 : «type/ind_types/list» (skS.0 1 a a_1))
% 7.49/7.64 (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.64 Eq
% 7.49/7.64 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.64 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.64 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.49/7.64 («const/ind_types/CONS» (skS.0 0 a) (A4 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6))))
% 7.49/7.66 True
% 7.49/7.66 Clause #168 (by clausification #[167]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2),
% 7.49/7.66 Eq
% 7.49/7.66 (∀ (A4 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (A5 : «type/ind_types/list» (skS.0 1 a a_1))
% 7.49/7.66 (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.66 Eq
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4
% 7.49/7.66 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 0 a) (A4 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) A4 A5 A6)))
% 7.49/7.66 False
% 7.49/7.66 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.49/7.66 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a),
% 7.49/7.66 Eq
% 7.49/7.66 (Not
% 7.49/7.66 (∀ (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.66 Eq
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 0 a)
% 7.49/7.66 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5) A5
% 7.49/7.66 A6))))
% 7.49/7.66 True
% 7.49/7.66 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.49/7.66 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a),
% 7.49/7.66 Eq
% 7.49/7.66 (∀ (A5 : «type/ind_types/list» (skS.0 1 a a_1)) (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.66 Eq
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) A5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 0 a)
% 7.49/7.66 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5) A5 A6)))
% 7.49/7.66 False
% 7.49/7.66 Clause #171 (by clausification #[170]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.49/7.66 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (a_6 : «type/ind_types/list» (skS.0 1 a a_1)),
% 7.49/7.66 Eq
% 7.49/7.66 (Not
% 7.49/7.66 (∀ (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.66 Eq
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 0 a)
% 7.49/7.66 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.49/7.66 (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6) A6))))
% 7.49/7.66 True
% 7.49/7.66 Clause #172 (by clausification #[171]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.49/7.66 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (a_6 : «type/ind_types/list» (skS.0 1 a a_1)),
% 7.49/7.66 Eq
% 7.49/7.66 (∀ (A6 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.49/7.66 Eq
% 7.49/7.66 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.49/7.66 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6))
% 7.49/7.66 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) A6))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 0 a)
% 7.56/7.71 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6) A6)))
% 7.56/7.71 False
% 7.56/7.71 Clause #173 (by clausification #[172]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.56/7.71 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (a_6 : «type/ind_types/list» (skS.0 1 a a_1))
% 7.56/7.71 (a_7 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.56/7.71 Eq
% 7.56/7.71 (Not
% 7.56/7.71 (Eq
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4)
% 7.56/7.71 (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 0 a)
% 7.56/7.71 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)))))
% 7.56/7.71 True
% 7.56/7.71 Clause #174 (by clausification #[173]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.56/7.71 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (a_6 : «type/ind_types/list» (skS.0 1 a a_1))
% 7.56/7.71 (a_7 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.56/7.71 Eq
% 7.56/7.71 (Eq
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4)
% 7.56/7.71 (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 0 a)
% 7.56/7.71 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7))))
% 7.56/7.71 False
% 7.56/7.71 Clause #175 (by clausification #[174]): ∀ (a a_1 a_2 : Type) (a_3 : skS.0 1 a a_1) (a_4 : skS.0 2 a a_1 a_2)
% 7.56/7.71 (a_5 : skS.0 1 a a_1 → skS.0 2 a a_1 a_2 → skS.0 0 a) (a_6 : «type/ind_types/list» (skS.0 1 a a_1))
% 7.56/7.71 (a_7 : «type/ind_types/list» (skS.0 2 a a_1 a_2)),
% 7.56/7.71 Ne
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 («const/ind_types/CONS» (skS.0 1 a a_1) (skS.0 3 a a_1 a_2 a_3) (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 2 a a_1 a_2) (skS.0 4 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)))
% 7.56/7.71 («const/ind_types/CONS» (skS.0 0 a)
% 7.56/7.71 (skS.0 5 a a_1 a_2 a_3 a_4 a_5 (skS.0 3 a a_1 a_2 a_3) (skS.0 4 a a_1 a_2 a_3 a_4))
% 7.56/7.71 («const/lists/MAP2» (skS.0 1 a a_1) (skS.0 2 a a_1 a_2) (skS.0 0 a) (skS.0 5 a a_1 a_2 a_3 a_4 a_5)
% 7.56/7.71 (skS.0 6 a a_1 a_2 a_3 a_4 a_5 a_6) (skS.0 7 a a_1 a_2 a_3 a_4 a_5 a_6 a_7)))
% 7.56/7.71 Clause #1674 (by forward demodulation #[25, 7]): ∀ (a a_1 a_2 : Type) (a_3 : a_1 → a_2 → a) (a_4 : a_1) (a_5 : «type/ind_types/list» a_1) (a_6 : a_2)
% 7.56/7.71 (a_7 : «type/ind_types/list» a_2),
% 7.56/7.71 Eq («const/lists/MAP2» a_1 a_2 a a_3 («const/ind_types/CONS» a_1 a_4 a_5) («const/ind_types/CONS» a_2 a_6 a_7))
% 7.56/7.71 («const/ind_types/CONS» a (a_3 a_4 a_6) («const/lists/MAP2» a_1 a_2 a a_3 a_5 a_7))
% 7.56/7.71 Clause #1675 (by backward contextual literal cutting #[1674, 175]): False
% 7.56/7.71 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------