TSTP Solution File: DAT319^1 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : DAT319^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n019.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 22:12:47 EDT 2023
% Result : Theorem 3.64s 3.81s
% Output : Proof 3.64s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT319^1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.14 % Command : duper %s
% 0.18/0.35 % Computer : n019.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Thu Aug 24 14:50:59 EDT 2023
% 0.18/0.35 % CPUTime :
% 3.64/3.81 SZS status Theorem for theBenchmark.p
% 3.64/3.81 SZS output start Proof for theBenchmark.p
% 3.64/3.81 Clause #0 (by assumption #[]): Eq (∀ (A : Type) (A0 : «type/ind_types/list» A), Eq («const/lists/APPEND» A («const/ind_types/NIL» A) A0) A0) True
% 3.64/3.81 Clause #1 (by assumption #[]): Eq
% 3.64/3.81 (∀ (A : Type) (A0 : A) (A1 A2 : «type/ind_types/list» A),
% 3.64/3.81 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 A1) A2)
% 3.64/3.81 («const/ind_types/CONS» A A0 («const/lists/APPEND» A A1 A2)))
% 3.64/3.81 True
% 3.64/3.81 Clause #2 (by assumption #[]): Eq
% 3.64/3.81 (Not
% 3.64/3.81 (∀ (A : Type) (A0 : A) (A1 : «type/ind_types/list» A),
% 3.64/3.81 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 («const/ind_types/NIL» A)) A1)
% 3.64/3.81 («const/ind_types/CONS» A A0 A1)))
% 3.64/3.81 True
% 3.64/3.81 Clause #3 (by clausification #[0]): ∀ (a : Type), Eq (∀ (A0 : «type/ind_types/list» a), Eq («const/lists/APPEND» a («const/ind_types/NIL» a) A0) A0) True
% 3.64/3.81 Clause #4 (by clausification #[3]): ∀ (a : Type) (a_1 : «type/ind_types/list» a), Eq (Eq («const/lists/APPEND» a («const/ind_types/NIL» a) a_1) a_1) True
% 3.64/3.81 Clause #5 (by clausification #[4]): ∀ (a : Type) (a_1 : «type/ind_types/list» a), Eq («const/lists/APPEND» a («const/ind_types/NIL» a) a_1) a_1
% 3.64/3.81 Clause #6 (by clausification #[2]): Eq
% 3.64/3.81 (∀ (A : Type) (A0 : A) (A1 : «type/ind_types/list» A),
% 3.64/3.81 Eq («const/lists/APPEND» A («const/ind_types/CONS» A A0 («const/ind_types/NIL» A)) A1)
% 3.64/3.81 («const/ind_types/CONS» A A0 A1))
% 3.64/3.81 False
% 3.64/3.81 Clause #7 (by clausification #[6]): ∀ (a : Type),
% 3.64/3.81 Eq
% 3.64/3.81 (Not
% 3.64/3.81 (∀ (A0 : skS.0 0 a) (A1 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/CONS» (skS.0 0 a) A0 («const/ind_types/NIL» (skS.0 0 a)))
% 3.64/3.81 A1)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) A0 A1)))
% 3.64/3.81 True
% 3.64/3.81 Clause #8 (by clausification #[7]): ∀ (a : Type),
% 3.64/3.81 Eq
% 3.64/3.81 (∀ (A0 : skS.0 0 a) (A1 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/CONS» (skS.0 0 a) A0 («const/ind_types/NIL» (skS.0 0 a)))
% 3.64/3.81 A1)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) A0 A1))
% 3.64/3.81 False
% 3.64/3.81 Clause #9 (by clausification #[8]): ∀ (a : Type) (a_1 : skS.0 0 a),
% 3.64/3.81 Eq
% 3.64/3.81 (Not
% 3.64/3.81 (∀ (A1 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) A1)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) A1)))
% 3.64/3.81 True
% 3.64/3.81 Clause #10 (by clausification #[9]): ∀ (a : Type) (a_1 : skS.0 0 a),
% 3.64/3.81 Eq
% 3.64/3.81 (∀ (A1 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) A1)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) A1))
% 3.64/3.81 False
% 3.64/3.81 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 (Not
% 3.64/3.81 (Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2))
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))))
% 3.64/3.81 True
% 3.64/3.81 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Eq
% 3.64/3.81 (Eq
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2))
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2)))
% 3.64/3.81 False
% 3.64/3.81 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.81 Ne
% 3.64/3.81 («const/lists/APPEND» (skS.0 0 a)
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) («const/ind_types/NIL» (skS.0 0 a))) (skS.0 2 a a_1 a_2))
% 3.64/3.81 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 3.64/3.81 Clause #14 (by clausification #[1]): ∀ (a : Type),
% 3.64/3.82 Eq
% 3.64/3.82 (∀ (A0 : a) (A1 A2 : «type/ind_types/list» a),
% 3.64/3.82 Eq («const/lists/APPEND» a («const/ind_types/CONS» a A0 A1) A2)
% 3.64/3.82 («const/ind_types/CONS» a A0 («const/lists/APPEND» a A1 A2)))
% 3.64/3.82 True
% 3.64/3.82 Clause #15 (by clausification #[14]): ∀ (a : Type) (a_1 : a),
% 3.64/3.82 Eq
% 3.64/3.82 (∀ (A1 A2 : «type/ind_types/list» a),
% 3.64/3.82 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 A1) A2)
% 3.64/3.82 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a A1 A2)))
% 3.64/3.82 True
% 3.64/3.82 Clause #16 (by clausification #[15]): ∀ (a : Type) (a_1 : a) (a_2 : «type/ind_types/list» a),
% 3.64/3.82 Eq
% 3.64/3.82 (∀ (A2 : «type/ind_types/list» a),
% 3.64/3.82 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) A2)
% 3.64/3.82 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 A2)))
% 3.64/3.82 True
% 3.64/3.82 Clause #17 (by clausification #[16]): ∀ (a : Type) (a_1 : a) (a_2 a_3 : «type/ind_types/list» a),
% 3.64/3.82 Eq
% 3.64/3.82 (Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) a_3)
% 3.64/3.82 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 a_3)))
% 3.64/3.82 True
% 3.64/3.82 Clause #18 (by clausification #[17]): ∀ (a : Type) (a_1 : a) (a_2 a_3 : «type/ind_types/list» a),
% 3.64/3.82 Eq («const/lists/APPEND» a («const/ind_types/CONS» a a_1 a_2) a_3)
% 3.64/3.82 («const/ind_types/CONS» a a_1 («const/lists/APPEND» a a_2 a_3))
% 3.64/3.82 Clause #19 (by backward demodulation #[18, 13]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.82 Ne
% 3.64/3.82 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1)
% 3.64/3.82 («const/lists/APPEND» (skS.0 0 a) («const/ind_types/NIL» (skS.0 0 a)) (skS.0 2 a a_1 a_2)))
% 3.64/3.82 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 3.64/3.82 Clause #20 (by forward demodulation #[19, 5]): ∀ (a : Type) (a_1 : skS.0 0 a) (a_2 : «type/ind_types/list» (skS.0 0 a)),
% 3.64/3.82 Ne («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 3.64/3.82 («const/ind_types/CONS» (skS.0 0 a) (skS.0 1 a a_1) (skS.0 2 a a_1 a_2))
% 3.64/3.82 Clause #21 (by eliminate resolved literals #[20]): False
% 3.64/3.82 SZS output end Proof for theBenchmark.p
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