TSTP Solution File: ANA109^1 by Duper---1.0
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% File : Duper---1.0
% Problem : ANA109^1 : TPTP v8.1.2. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n006.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 17:15:52 EDT 2023
% Result : Theorem 5.86s 6.11s
% Output : Proof 5.86s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : ANA109^1 : TPTP v8.1.2. Released v7.0.0.
% 0.00/0.11 % Command : duper %s
% 0.10/0.31 % Computer : n006.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri Aug 25 18:11:52 EDT 2023
% 0.10/0.31 % CPUTime :
% 5.86/6.11 SZS status Theorem for theBenchmark.p
% 5.86/6.11 SZS output start Proof for theBenchmark.p
% 5.86/6.11 Clause #0 (by assumption #[]): Eq
% 5.86/6.11 (∀ (A : Type) (A0 : A → «type/realax/real») (A1 : A),
% 5.86/6.11 Eq («const/iterate/sum» A («const/sets/INSERT» A A1 («const/sets/EMPTY» A)) A0) (A0 A1))
% 5.86/6.11 True
% 5.86/6.11 Clause #1 (by assumption #[]): Eq
% 5.86/6.11 (∀ (A : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/..» A A) («const/sets/INSERT» «type/nums/num» A («const/sets/EMPTY» «type/nums/num»)))
% 5.86/6.11 True
% 5.86/6.11 Clause #2 (by assumption #[]): Eq
% 5.86/6.11 (Not
% 5.86/6.11 (∀ (A : «type/nums/num» → «type/realax/real») (A0 : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) A) (A A0)))
% 5.86/6.11 True
% 5.86/6.11 Clause #3 (by clausification #[1]): ∀ (a : «type/nums/num»),
% 5.86/6.11 Eq (Eq («const/iterate/..» a a) («const/sets/INSERT» «type/nums/num» a («const/sets/EMPTY» «type/nums/num»))) True
% 5.86/6.11 Clause #4 (by clausification #[3]): ∀ (a : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/..» a a) («const/sets/INSERT» «type/nums/num» a («const/sets/EMPTY» «type/nums/num»))
% 5.86/6.11 Clause #10 (by clausification #[0]): ∀ (a : Type),
% 5.86/6.11 Eq
% 5.86/6.11 (∀ (A0 : a → «type/realax/real») (A1 : a),
% 5.86/6.11 Eq («const/iterate/sum» a («const/sets/INSERT» a A1 («const/sets/EMPTY» a)) A0) (A0 A1))
% 5.86/6.11 True
% 5.86/6.11 Clause #11 (by clausification #[10]): ∀ (a : Type) (a_1 : a → «type/realax/real»),
% 5.86/6.11 Eq (∀ (A1 : a), Eq («const/iterate/sum» a («const/sets/INSERT» a A1 («const/sets/EMPTY» a)) a_1) (a_1 A1)) True
% 5.86/6.11 Clause #12 (by clausification #[11]): ∀ (a : Type) (a_1 : a) (a_2 : a → «type/realax/real»),
% 5.86/6.11 Eq (Eq («const/iterate/sum» a («const/sets/INSERT» a a_1 («const/sets/EMPTY» a)) a_2) (a_2 a_1)) True
% 5.86/6.11 Clause #13 (by clausification #[12]): ∀ (a : Type) (a_1 : a) (a_2 : a → «type/realax/real»),
% 5.86/6.11 Eq («const/iterate/sum» a («const/sets/INSERT» a a_1 («const/sets/EMPTY» a)) a_2) (a_2 a_1)
% 5.86/6.11 Clause #14 (by superposition #[13, 4]): ∀ (a : «type/nums/num») (a_1 : «type/nums/num» → «type/realax/real»),
% 5.86/6.11 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» a a) a_1) (a_1 a)
% 5.86/6.11 Clause #81 (by clausification #[2]): Eq
% 5.86/6.11 (∀ (A : «type/nums/num» → «type/realax/real») (A0 : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) A) (A A0))
% 5.86/6.11 False
% 5.86/6.11 Clause #82 (by clausification #[81]): ∀ (a : «type/nums/num» → «type/realax/real»),
% 5.86/6.11 Eq
% 5.86/6.11 (Not
% 5.86/6.11 (∀ (A0 : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) (skS.0 0 a)) (skS.0 0 a A0)))
% 5.86/6.11 True
% 5.86/6.11 Clause #83 (by clausification #[82]): ∀ (a : «type/nums/num» → «type/realax/real»),
% 5.86/6.11 Eq
% 5.86/6.11 (∀ (A0 : «type/nums/num»),
% 5.86/6.11 Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» A0 A0) (skS.0 0 a)) (skS.0 0 a A0))
% 5.86/6.11 False
% 5.86/6.11 Clause #84 (by clausification #[83]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»),
% 5.86/6.11 Eq
% 5.86/6.11 (Not
% 5.86/6.11 (Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a))
% 5.86/6.11 (skS.0 0 a (skS.0 1 a a_1))))
% 5.86/6.11 True
% 5.86/6.11 Clause #85 (by clausification #[84]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»),
% 5.86/6.11 Eq
% 5.86/6.11 (Eq («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a))
% 5.86/6.11 (skS.0 0 a (skS.0 1 a a_1)))
% 5.86/6.11 False
% 5.86/6.11 Clause #86 (by clausification #[85]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»),
% 5.86/6.11 Ne («const/iterate/sum» «type/nums/num» («const/iterate/..» (skS.0 1 a a_1) (skS.0 1 a a_1)) (skS.0 0 a))
% 5.86/6.11 (skS.0 0 a (skS.0 1 a a_1))
% 5.86/6.11 Clause #87 (by forward demodulation #[86, 14]): ∀ (a : «type/nums/num» → «type/realax/real») (a_1 : «type/nums/num»),
% 5.86/6.11 Ne (skS.0 0 a (skS.0 1 a a_1)) (skS.0 0 a (skS.0 1 a a_1))
% 5.86/6.11 Clause #88 (by eliminate resolved literals #[87]): False
% 5.86/6.11 SZS output end Proof for theBenchmark.p
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