TSTP Solution File: SEU716^2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU716^2 : TPTP v8.1.2. Released v3.7.0.
% 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 : Thu Aug 31 16:43:31 EDT 2023
% Result : Theorem 4.70s 4.85s
% Output : Proof 4.70s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU716^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : duper %s
% 0.16/0.37 % Computer : n019.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Wed Aug 23 19:40:13 EDT 2023
% 0.16/0.37 % CPUTime :
% 4.70/4.85 SZS status Theorem for theBenchmark.p
% 4.70/4.85 SZS output start Proof for theBenchmark.p
% 4.70/4.85 Clause #0 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True
% 4.70/4.85 Clause #1 (by assumption #[]): Eq (Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True
% 4.70/4.85 Clause #2 (by assumption #[]): Eq
% 4.70/4.85 (Not
% 4.70/4.85 (powersetE →
% 4.70/4.85 subsetI2 →
% 4.70/4.85 ∀ (A X : Iota),
% 4.70/4.85 in X (powerset A) →
% 4.70/4.85 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y))
% 4.70/4.85 True
% 4.70/4.85 Clause #3 (by clausification #[1]): Eq subsetI2 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)
% 4.70/4.85 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)
% 4.70/4.85 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)
% 4.70/4.85 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)
% 4.70/4.85 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))
% 4.70/4.85 Clause #10 (by clausification #[9]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.85 Or (Eq subsetI2 False)
% 4.70/4.85 (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))
% 4.70/4.85 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.85 Or (Eq subsetI2 False)
% 4.70/4.85 (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))
% 4.70/4.85 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))
% 4.70/4.85 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))
% 4.70/4.85 Clause #22 (by clausification #[0]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)
% 4.70/4.85 Clause #26 (by clausification #[2]): Eq
% 4.70/4.85 (powersetE →
% 4.70/4.85 subsetI2 →
% 4.70/4.85 ∀ (A X : Iota),
% 4.70/4.85 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)
% 4.70/4.85 False
% 4.70/4.85 Clause #27 (by clausification #[26]): Eq powersetE True
% 4.70/4.85 Clause #28 (by clausification #[26]): Eq
% 4.70/4.85 (subsetI2 →
% 4.70/4.85 ∀ (A X : Iota),
% 4.70/4.85 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)
% 4.70/4.85 False
% 4.70/4.85 Clause #29 (by backward demodulation #[27, 22]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)
% 4.70/4.85 Clause #30 (by clausification #[29]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True
% 4.70/4.85 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True
% 4.70/4.85 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True
% 4.70/4.85 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True)
% 4.70/4.85 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 4.70/4.85 Clause #35 (by clausification #[28]): Eq subsetI2 True
% 4.70/4.85 Clause #36 (by clausification #[28]): Eq
% 4.70/4.85 (∀ (A X : Iota),
% 4.70/4.85 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)
% 4.70/4.85 False
% 4.70/4.85 Clause #38 (by backward demodulation #[35, 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))
% 4.70/4.85 Clause #48 (by clausification #[36]): ∀ (a : Iota),
% 4.70/4.85 Eq
% 4.70/4.85 (Not
% 4.70/4.85 (∀ (X : Iota),
% 4.70/4.85 in X (powerset (skS.0 4 a)) →
% 4.70/4.85 ∀ (Y : Iota),
% 4.70/4.85 in Y (powerset (skS.0 4 a)) → (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx X → in Xx Y) → subset X Y))
% 4.70/4.88 True
% 4.70/4.88 Clause #49 (by clausification #[48]): ∀ (a : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (∀ (X : Iota),
% 4.70/4.88 in X (powerset (skS.0 4 a)) →
% 4.70/4.88 ∀ (Y : Iota), in Y (powerset (skS.0 4 a)) → (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx X → in Xx Y) → subset X Y)
% 4.70/4.88 False
% 4.70/4.88 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (Not
% 4.70/4.88 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) →
% 4.70/4.88 ∀ (Y : Iota),
% 4.70/4.88 in Y (powerset (skS.0 4 a)) →
% 4.70/4.88 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y))
% 4.70/4.88 True
% 4.70/4.88 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) →
% 4.70/4.88 ∀ (Y : Iota),
% 4.70/4.88 in Y (powerset (skS.0 4 a)) →
% 4.70/4.88 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y)
% 4.70/4.88 False
% 4.70/4.88 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True
% 4.70/4.88 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (∀ (Y : Iota),
% 4.70/4.88 in Y (powerset (skS.0 4 a)) →
% 4.70/4.88 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx Y) → subset (skS.0 5 a a_1) Y)
% 4.70/4.88 False
% 4.70/4.88 Clause #54 (by superposition #[52, 34]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True))
% 4.70/4.88 Clause #61 (by forward demodulation #[13, 35]): ∀ (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))
% 4.70/4.88 Clause #62 (by clausification #[61]): ∀ (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)
% 4.70/4.88 Clause #72 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (Not
% 4.70/4.88 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 4 a)) →
% 4.70/4.88 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) →
% 4.70/4.88 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)))
% 4.70/4.88 True
% 4.70/4.88 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 (in (skS.0 9 a a_1 a_2) (powerset (skS.0 4 a)) →
% 4.70/4.88 (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) →
% 4.70/4.88 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2))
% 4.70/4.88 False
% 4.70/4.88 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.88 Eq
% 4.70/4.88 ((∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) →
% 4.70/4.88 subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2))
% 4.70/4.88 False
% 4.70/4.88 Clause #81 (by clausification #[38]): ∀ (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)
% 4.70/4.88 Clause #88 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 4 a) → in Xx (skS.0 5 a a_1) → in Xx (skS.0 9 a a_1 a_2)) True
% 4.70/4.88 Clause #89 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) False
% 4.70/4.88 Clause #90 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in a (skS.0 4 a_1) → in a (skS.0 5 a_1 a_2) → in a (skS.0 9 a_1 a_2 a_3)) True
% 4.70/4.88 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.70/4.88 Or (Eq (in a (skS.0 4 a_1)) False) (Eq (in a (skS.0 5 a_1 a_2) → in a (skS.0 9 a_1 a_2 a_3)) True)
% 4.70/4.88 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.70/4.88 Or (Eq (in a (skS.0 4 a_1)) False) (Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 9 a_1 a_2 a_3)) True))
% 4.70/4.88 Clause #95 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 5 a_1 a_2)) False) (Eq (in a (skS.0 4 a_1)) True)
% 4.70/4.88 Clause #97 (by superposition #[95, 81]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.70/4.88 Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 4 a)) True)
% 4.70/4.88 (Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq False True))
% 4.70/4.88 Clause #108 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.70/4.88 Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 4 a)) True) (Eq (subset (skS.0 5 a a_1) a_2) True)
% 4.70/4.88 Clause #109 (by superposition #[108, 92]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.70/4.88 Or (Eq (subset (skS.0 5 a a_1) a_2) True)
% 4.70/4.88 (Or (Eq True False)
% 4.70/4.89 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 5 a a_4)) False)
% 4.70/4.89 (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_4 a_5)) True)))
% 4.70/4.89 Clause #185 (by clausification #[109]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) a_2) True)
% 4.70/4.89 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 5 a a_4)) False)
% 4.70/4.89 (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_4 a_5)) True))
% 4.70/4.89 Clause #186 (by superposition #[185, 81]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) a_2) True)
% 4.70/4.89 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True)
% 4.70/4.89 (Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq False True)))
% 4.70/4.89 Clause #187 (by clausification #[186]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) a_2) True)
% 4.70/4.89 (Or (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True) (Eq (subset (skS.0 5 a a_1) a_2) True))
% 4.70/4.89 Clause #188 (by eliminate duplicate literals #[187]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) a_2) True) (Eq (in (skS.0 0 (skS.0 5 a a_1) a_2 a_3) (skS.0 9 a a_1 a_4)) True)
% 4.70/4.89 Clause #190 (by superposition #[188, 62]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True)
% 4.70/4.89 (Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) (Eq True False))
% 4.70/4.89 Clause #192 (by clausification #[190]): ∀ (a a_1 a_2 : Iota),
% 4.70/4.89 Or (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True) (Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True)
% 4.70/4.89 Clause #193 (by eliminate duplicate literals #[192]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 5 a a_1) (skS.0 9 a a_1 a_2)) True
% 4.70/4.89 Clause #194 (by superposition #[193, 89]): Eq True False
% 4.70/4.89 Clause #195 (by clausification #[194]): False
% 4.70/4.89 SZS output end Proof for theBenchmark.p
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