TSTP Solution File: SEU570^2 by Duper---1.0
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- Process Solution
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% File : Duper---1.0
% Problem : SEU570^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n024.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 16:42:46 EDT 2023
% Result : Theorem 6.27s 6.45s
% Output : Proof 6.27s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10 % Problem : SEU570^2 : TPTP v8.1.2. Released v3.7.0.
% 0.05/0.10 % Command : duper %s
% 0.10/0.30 % Computer : n024.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Wed Aug 23 15:33:39 EDT 2023
% 0.10/0.30 % CPUTime :
% 6.27/6.45 SZS status Theorem for theBenchmark.p
% 6.27/6.45 SZS output start Proof for theBenchmark.p
% 6.27/6.45 Clause #0 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True
% 6.27/6.45 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True
% 6.27/6.45 Clause #2 (by assumption #[]): Eq (Not (subsetI2 → subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C)) True
% 6.27/6.45 Clause #3 (by clausification #[0]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)
% 6.27/6.45 Clause #5 (by clausify Prop equality #[3]): Or (Eq subsetI2 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True)
% 6.27/6.45 Clause #7 (by clausification #[5]): ∀ (a : Iota), Or (Eq subsetI2 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True)
% 6.27/6.45 Clause #8 (by clausification #[7]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True)
% 6.27/6.45 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI2 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True))
% 6.27/6.45 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.45 Or (Eq subsetI2 False)
% 6.27/6.45 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True))
% 6.27/6.45 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.45 Or (Eq subsetI2 False)
% 6.27/6.45 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False))
% 6.27/6.45 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True))
% 6.27/6.45 Clause #13 (by clausification #[11]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI2 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False))
% 6.27/6.45 Clause #22 (by clausification #[2]): Eq (subsetI2 → subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C) False
% 6.27/6.45 Clause #23 (by clausification #[22]): Eq subsetI2 True
% 6.27/6.45 Clause #24 (by clausification #[22]): Eq (subsetE → ∀ (A B C : Iota), subset A B → subset B C → subset A C) False
% 6.27/6.45 Clause #26 (by backward demodulation #[23, 12]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True))
% 6.27/6.45 Clause #28 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 6.27/6.45 Clause #39 (by clausification #[24]): Eq subsetE True
% 6.27/6.45 Clause #40 (by clausification #[24]): Eq (∀ (A B C : Iota), subset A B → subset B C → subset A C) False
% 6.27/6.45 Clause #41 (by backward demodulation #[39, 28]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 6.27/6.45 Clause #42 (by clausification #[41]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True
% 6.27/6.45 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True
% 6.27/6.45 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True
% 6.27/6.45 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True)
% 6.27/6.45 Clause #46 (by clausification #[45]): ∀ (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))
% 6.27/6.45 Clause #47 (by clausification #[40]): ∀ (a : Iota), Eq (Not (∀ (B C : Iota), subset (skS.0 4 a) B → subset B C → subset (skS.0 4 a) C)) True
% 6.27/6.45 Clause #48 (by clausification #[47]): ∀ (a : Iota), Eq (∀ (B C : Iota), subset (skS.0 4 a) B → subset B C → subset (skS.0 4 a) C) False
% 6.27/6.45 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota),
% 6.27/6.45 Eq (Not (∀ (C : Iota), subset (skS.0 4 a) (skS.0 5 a a_1) → subset (skS.0 5 a a_1) C → subset (skS.0 4 a) C)) True
% 6.27/6.45 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 6.27/6.45 Eq (∀ (C : Iota), subset (skS.0 4 a) (skS.0 5 a a_1) → subset (skS.0 5 a a_1) C → subset (skS.0 4 a) C) False
% 6.27/6.45 Clause #51 (by clausification #[50]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.45 Eq
% 6.27/6.45 (Not
% 6.27/6.45 (subset (skS.0 4 a) (skS.0 5 a a_1) →
% 6.27/6.49 subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2)))
% 6.27/6.49 True
% 6.27/6.49 Clause #52 (by clausification #[51]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.49 Eq
% 6.27/6.49 (subset (skS.0 4 a) (skS.0 5 a a_1) →
% 6.27/6.49 subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2))
% 6.27/6.49 False
% 6.27/6.49 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (subset (skS.0 4 a) (skS.0 5 a a_1)) True
% 6.27/6.49 Clause #54 (by clausification #[52]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2) → subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) False
% 6.27/6.49 Clause #55 (by superposition #[53, 46]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2)) True))
% 6.27/6.49 Clause #62 (by forward demodulation #[13, 23]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False))
% 6.27/6.49 Clause #63 (by clausification #[62]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)
% 6.27/6.49 Clause #79 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)
% 6.27/6.49 Clause #81 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 6 a a_1 a_2)) True
% 6.27/6.49 Clause #82 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) False
% 6.27/6.49 Clause #83 (by superposition #[81, 46]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.27/6.49 Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1 a_2 a_3)) True))
% 6.27/6.49 Clause #84 (by clausification #[55]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2)) True)
% 6.27/6.49 Clause #86 (by superposition #[84, 79]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.27/6.49 Or (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 5 a a_3)) True)
% 6.27/6.49 (Or (Eq (subset (skS.0 4 a) a_1) True) (Eq False True))
% 6.27/6.49 Clause #91 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 6 a_1 a_2 a_3)) True)
% 6.27/6.49 Clause #94 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.27/6.49 Or (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 5 a a_3)) True) (Eq (subset (skS.0 4 a) a_1) True)
% 6.27/6.49 Clause #95 (by superposition #[94, 91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.27/6.49 Or (Eq (subset (skS.0 4 a) a_1) True)
% 6.27/6.49 (Or (Eq True False) (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 6 a a_3 a_4)) True))
% 6.27/6.49 Clause #100 (by clausification #[95]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.27/6.49 Or (Eq (subset (skS.0 4 a) a_1) True) (Eq (in (skS.0 0 (skS.0 4 a) a_1 a_2) (skS.0 6 a a_3 a_4)) True)
% 6.27/6.49 Clause #101 (by superposition #[100, 63]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.49 Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True)
% 6.27/6.49 (Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) (Eq True False))
% 6.27/6.49 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota),
% 6.27/6.49 Or (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True) (Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True)
% 6.27/6.49 Clause #103 (by eliminate duplicate literals #[102]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 4 a) (skS.0 6 a a_1 a_2)) True
% 6.27/6.49 Clause #104 (by superposition #[103, 82]): Eq True False
% 6.27/6.49 Clause #106 (by clausification #[104]): False
% 6.27/6.49 SZS output end Proof for theBenchmark.p
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