TSTP Solution File: SEU814^2 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SEU814^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n029.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 16:44:01 EDT 2023
% Result : Theorem 3.68s 3.91s
% Output : Proof 3.68s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU814^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Wed Aug 23 15:42:53 EDT 2023
% 0.16/0.34 % CPUTime :
% 3.68/3.91 SZS status Theorem for theBenchmark.p
% 3.68/3.91 SZS output start Proof for theBenchmark.p
% 3.68/3.91 Clause #0 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True
% 3.68/3.91 Clause #1 (by assumption #[]): Eq (Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A) True
% 3.68/3.91 Clause #3 (by assumption #[]): Eq (Not (subsetE → transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X)) True
% 3.68/3.91 Clause #16 (by clausification #[1]): Eq transitiveset fun A => ∀ (X : Iota), in X A → subset X A
% 3.68/3.91 Clause #17 (by argument congruence #[16]): ∀ (a : Iota), Eq (transitiveset a) ((fun A => ∀ (X : Iota), in X A → subset X A) a)
% 3.68/3.91 Clause #18 (by clausification #[0]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 3.68/3.91 Clause #22 (by betaEtaReduce #[17]): ∀ (a : Iota), Eq (transitiveset a) (∀ (X : Iota), in X a → subset X a)
% 3.68/3.91 Clause #24 (by clausify Prop equality #[22]): ∀ (a : Iota), Or (Eq (transitiveset a) False) (Eq (∀ (X : Iota), in X a → subset X a) True)
% 3.68/3.91 Clause #26 (by clausification #[24]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Eq (in a_1 a → subset a_1 a) True)
% 3.68/3.91 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq (transitiveset a) False) (Or (Eq (in a_1 a) False) (Eq (subset a_1 a) True))
% 3.68/3.91 Clause #38 (by clausification #[3]): Eq (subsetE → transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False
% 3.68/3.91 Clause #39 (by clausification #[38]): Eq subsetE True
% 3.68/3.91 Clause #40 (by clausification #[38]): Eq (transitivesetOp1 → ∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False
% 3.68/3.91 Clause #41 (by backward demodulation #[39, 18]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 3.68/3.91 Clause #43 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True
% 3.68/3.91 Clause #44 (by clausification #[43]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True
% 3.68/3.91 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True
% 3.68/3.91 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True)
% 3.68/3.91 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 3.68/3.91 Clause #49 (by clausification #[40]): Eq (∀ (X : Iota), transitiveset X → ∀ (A Xx : Iota), in A X → in Xx A → in Xx X) False
% 3.68/3.91 Clause #53 (by clausification #[49]): ∀ (a : Iota),
% 3.68/3.91 Eq (Not (transitiveset (skS.0 2 a) → ∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a))) True
% 3.68/3.91 Clause #54 (by clausification #[53]): ∀ (a : Iota), Eq (transitiveset (skS.0 2 a) → ∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a)) False
% 3.68/3.91 Clause #55 (by clausification #[54]): ∀ (a : Iota), Eq (transitiveset (skS.0 2 a)) True
% 3.68/3.91 Clause #56 (by clausification #[54]): ∀ (a : Iota), Eq (∀ (A Xx : Iota), in A (skS.0 2 a) → in Xx A → in Xx (skS.0 2 a)) False
% 3.68/3.91 Clause #57 (by superposition #[55, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 2 a_1)) False) (Eq (subset a (skS.0 2 a_1)) True))
% 3.68/3.91 Clause #72 (by clausification #[56]): ∀ (a a_1 : Iota),
% 3.68/3.91 Eq (Not (∀ (Xx : Iota), in (skS.0 7 a a_1) (skS.0 2 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 2 a))) True
% 3.68/3.91 Clause #73 (by clausification #[72]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in (skS.0 7 a a_1) (skS.0 2 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 2 a)) False
% 3.68/3.91 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.91 Eq
% 3.68/3.91 (Not (in (skS.0 7 a a_1) (skS.0 2 a) → in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a)))
% 3.68/3.91 True
% 3.68/3.91 Clause #75 (by clausification #[74]): ∀ (a a_1 a_2 : Iota),
% 3.68/3.91 Eq (in (skS.0 7 a a_1) (skS.0 2 a) → in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a))
% 3.68/3.91 False
% 3.68/3.91 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (skS.0 2 a)) True
% 3.68/3.91 Clause #77 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) → in (skS.0 8 a a_1 a_2) (skS.0 2 a)) False
% 3.68/3.91 Clause #81 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True
% 3.68/3.91 Clause #82 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) False
% 3.68/3.91 Clause #83 (by clausification #[57]): ∀ (a a_1 : Iota), Or (Eq (in a (skS.0 2 a_1)) False) (Eq (subset a (skS.0 2 a_1)) True)
% 3.68/3.91 Clause #84 (by superposition #[83, 76]): ∀ (a a_1 : Iota), Or (Eq (subset (skS.0 7 a a_1) (skS.0 2 a)) True) (Eq False True)
% 3.68/3.91 Clause #86 (by clausification #[84]): ∀ (a a_1 : Iota), Eq (subset (skS.0 7 a a_1) (skS.0 2 a)) True
% 3.68/3.91 Clause #87 (by superposition #[86, 47]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 2 a_1)) True))
% 3.68/3.91 Clause #91 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 2 a_1)) True)
% 3.68/3.91 Clause #92 (by superposition #[91, 81]): ∀ (a a_1 a_2 : Iota), Or (Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) True) (Eq False True)
% 3.68/3.91 Clause #94 (by clausification #[92]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 2 a)) True
% 3.68/3.91 Clause #95 (by superposition #[94, 82]): Eq True False
% 3.68/3.91 Clause #97 (by clausification #[95]): False
% 3.68/3.91 SZS output end Proof for theBenchmark.p
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