TSTP Solution File: SEU717^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU717^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 16:43:32 EDT 2023
% Result : Theorem 8.55s 8.78s
% Output : Proof 8.70s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU717^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n028.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 21:13:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 8.55/8.78 SZS status Theorem for theBenchmark.p
% 8.55/8.78 SZS output start Proof for theBenchmark.p
% 8.55/8.78 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True
% 8.55/8.78 Clause #1 (by assumption #[]): Eq
% 8.55/8.78 (Eq subsetTI
% 8.55/8.78 (∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y))
% 8.55/8.78 True
% 8.55/8.78 Clause #2 (by assumption #[]): Eq
% 8.55/8.78 (Not
% 8.55/8.78 (powersetI1 →
% 8.55/8.78 subsetTI →
% 8.55/8.78 ∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) →
% 8.55/8.78 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y)))
% 8.55/8.78 True
% 8.55/8.78 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))
% 8.55/8.78 Clause #16 (by clausification #[1]): Eq subsetTI
% 8.55/8.78 (∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)
% 8.55/8.78 Clause #18 (by clausify Prop equality #[16]): Or (Eq subsetTI False)
% 8.55/8.78 (Eq
% 8.55/8.78 (∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → subset X Y)
% 8.55/8.78 True)
% 8.55/8.78 Clause #20 (by clausification #[2]): Eq
% 8.55/8.78 (powersetI1 →
% 8.55/8.78 subsetTI →
% 8.55/8.78 ∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) →
% 8.55/8.78 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y))
% 8.55/8.78 False
% 8.55/8.78 Clause #21 (by clausification #[20]): Eq powersetI1 True
% 8.55/8.78 Clause #22 (by clausification #[20]): Eq
% 8.55/8.78 (subsetTI →
% 8.55/8.78 ∀ (A X : Iota),
% 8.55/8.78 in X (powerset A) →
% 8.55/8.78 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y))
% 8.55/8.78 False
% 8.55/8.78 Clause #23 (by backward demodulation #[21, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A))
% 8.55/8.78 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True
% 8.55/8.78 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True
% 8.55/8.78 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True)
% 8.55/8.78 Clause #35 (by clausification #[18]): ∀ (a : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Eq
% 8.55/8.78 (∀ (X : Iota),
% 8.55/8.78 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → (∀ (Xx : Iota), in Xx a → in Xx X → in Xx Y) → subset X Y)
% 8.55/8.78 True)
% 8.55/8.78 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Eq
% 8.55/8.78 (in a (powerset a_1) →
% 8.55/8.78 ∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y)
% 8.55/8.78 True)
% 8.55/8.78 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.78 (Eq (∀ (Y : Iota), in Y (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx Y) → subset a Y) True))
% 8.55/8.78 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.78 (Eq (in a_2 (powerset a_1) → (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True))
% 8.55/8.78 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.78 (Or (Eq (in a_2 (powerset a_1)) False)
% 8.55/8.78 (Eq ((∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) → subset a a_2) True)))
% 8.55/8.78 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.78 (Or (Eq (in a_2 (powerset a_1)) False)
% 8.55/8.78 (Or (Eq (∀ (Xx : Iota), in Xx a_1 → in Xx a → in Xx a_2) False) (Eq (subset a a_2) True))))
% 8.55/8.78 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.78 Or (Eq subsetTI False)
% 8.55/8.78 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.78 (Or (Eq (in a_2 (powerset a_1)) False)
% 8.55/8.78 (Or (Eq (subset a a_2) True)
% 8.55/8.78 (Eq (Not (in (skS.0 4 a_1 a a_2 a_3) a_1 → in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2))
% 8.55/8.81 True))))
% 8.55/8.81 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.81 Or (Eq subsetTI False)
% 8.55/8.81 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (in a_2 (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (subset a a_2) True)
% 8.55/8.81 (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1 → in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2) False))))
% 8.55/8.81 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.81 Or (Eq subsetTI False)
% 8.55/8.81 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True))))
% 8.55/8.81 Clause #44 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.81 Or (Eq subsetTI False)
% 8.55/8.81 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (in a_2 (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a → in (skS.0 4 a_1 a a_2 a_3) a_2) False))))
% 8.55/8.81 Clause #45 (by clausification #[22]): Eq subsetTI True
% 8.55/8.81 Clause #46 (by clausification #[22]): Eq
% 8.55/8.81 (∀ (A X : Iota),
% 8.55/8.81 in X (powerset A) →
% 8.55/8.81 ∀ (Y : Iota), in Y (powerset A) → (∀ (Xx : Iota), in Xx A → in Xx X → in Xx Y) → in X (powerset Y))
% 8.55/8.81 False
% 8.55/8.81 Clause #49 (by backward demodulation #[45, 43]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.81 Or (Eq True False)
% 8.55/8.81 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.81 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True))))
% 8.55/8.81 Clause #61 (by clausification #[46]): ∀ (a : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (Not
% 8.55/8.81 (∀ (X : Iota),
% 8.55/8.81 in X (powerset (skS.0 6 a)) →
% 8.55/8.81 ∀ (Y : Iota),
% 8.55/8.81 in Y (powerset (skS.0 6 a)) → (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx Y) → in X (powerset Y)))
% 8.55/8.81 True
% 8.55/8.81 Clause #62 (by clausification #[61]): ∀ (a : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (∀ (X : Iota),
% 8.55/8.81 in X (powerset (skS.0 6 a)) →
% 8.55/8.81 ∀ (Y : Iota),
% 8.55/8.81 in Y (powerset (skS.0 6 a)) → (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx X → in Xx Y) → in X (powerset Y))
% 8.55/8.81 False
% 8.55/8.81 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (Not
% 8.55/8.81 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) →
% 8.55/8.81 ∀ (Y : Iota),
% 8.55/8.81 in Y (powerset (skS.0 6 a)) →
% 8.55/8.81 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y)))
% 8.55/8.81 True
% 8.55/8.81 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) →
% 8.55/8.81 ∀ (Y : Iota),
% 8.55/8.81 in Y (powerset (skS.0 6 a)) →
% 8.55/8.81 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y))
% 8.55/8.81 False
% 8.55/8.81 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 6 a))) True
% 8.55/8.81 Clause #66 (by clausification #[64]): ∀ (a a_1 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (∀ (Y : Iota),
% 8.55/8.81 in Y (powerset (skS.0 6 a)) →
% 8.55/8.81 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx Y) → in (skS.0 7 a a_1) (powerset Y))
% 8.55/8.81 False
% 8.55/8.81 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (Not
% 8.55/8.81 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) →
% 8.55/8.81 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) →
% 8.55/8.81 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))))
% 8.55/8.81 True
% 8.55/8.81 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) →
% 8.55/8.81 (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) →
% 8.55/8.81 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2)))
% 8.55/8.81 False
% 8.55/8.81 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a))) True
% 8.55/8.81 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 : Iota),
% 8.55/8.81 Eq
% 8.55/8.81 ((∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) →
% 8.55/8.81 in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2)))
% 8.55/8.81 False
% 8.55/8.81 Clause #78 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (skS.0 7 a a_1) → in Xx (skS.0 8 a a_1 a_2)) True
% 8.55/8.84 Clause #79 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) False
% 8.55/8.84 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in a (skS.0 6 a_1) → in a (skS.0 7 a_1 a_2) → in a (skS.0 8 a_1 a_2 a_3)) True
% 8.55/8.84 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (skS.0 6 a_1)) False) (Eq (in a (skS.0 7 a_1 a_2) → in a (skS.0 8 a_1 a_2 a_3)) True)
% 8.55/8.84 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (skS.0 6 a_1)) False) (Or (Eq (in a (skS.0 7 a_1 a_2)) False) (Eq (in a (skS.0 8 a_1 a_2 a_3)) True))
% 8.55/8.84 Clause #90 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq subsetTI False)
% 8.55/8.84 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True))))
% 8.55/8.84 Clause #91 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq subsetTI False)
% 8.55/8.84 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False))))
% 8.55/8.84 Clause #92 (by forward demodulation #[90, 45]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq True False)
% 8.55/8.84 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True))))
% 8.55/8.84 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a) True)))
% 8.55/8.84 Clause #94 (by superposition #[93, 65]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.55/8.84 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True)
% 8.55/8.84 (Or (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 7 a_1 a_2)) True) (Eq False True)))
% 8.55/8.84 Clause #102 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_1) True)))
% 8.55/8.84 Clause #103 (by superposition #[102, 65]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.55/8.84 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True)
% 8.55/8.84 (Or (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True) (Eq False True)))
% 8.55/8.84 Clause #105 (by forward demodulation #[91, 45]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq True False)
% 8.55/8.84 (Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False))))
% 8.55/8.84 Clause #106 (by clausification #[105]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset a_1)) False)
% 8.55/8.84 (Or (Eq (in a_2 (powerset a_1)) False) (Or (Eq (subset a a_2) True) (Eq (in (skS.0 4 a_1 a a_2 a_3) a_2) False)))
% 8.55/8.84 Clause #107 (by superposition #[106, 65]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.55/8.84 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True)
% 8.55/8.84 (Or (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False) (Eq False True)))
% 8.55/8.84 Clause #109 (by clausification #[107]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.55/8.84 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True) (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) a) False))
% 8.55/8.84 Clause #111 (by superposition #[109, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.55/8.84 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.55/8.84 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_2 a_3)) False)
% 8.55/8.84 (Eq False True))
% 8.55/8.84 Clause #124 (by clausification #[103]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.55/8.84 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.55/8.84 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True)
% 8.55/8.84 (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 6 a_1)) True))
% 8.55/8.84 Clause #126 (by superposition #[124, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.55/8.84 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.55/8.84 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 6 a)) True) (Eq False True))
% 8.70/8.87 Clause #127 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota),
% 8.70/8.87 Or (Eq (in a (powerset (skS.0 6 a_1))) False)
% 8.70/8.87 (Or (Eq (subset (skS.0 7 a_1 a_2) a) True)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a_1) (skS.0 7 a_1 a_2) a a_3) (skS.0 7 a_1 a_2)) True))
% 8.70/8.87 Clause #129 (by superposition #[127, 70]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_1)) True) (Eq False True))
% 8.70/8.87 Clause #171 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_2 a_3)) False)
% 8.70/8.87 Clause #184 (by clausification #[126]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 6 a)) True)
% 8.70/8.87 Clause #185 (by superposition #[184, 82]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Or (Eq True False)
% 8.70/8.87 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_5)) False)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_5 a_6)) True)))
% 8.70/8.87 Clause #189 (by clausification #[129]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_1)) True)
% 8.70/8.87 Clause #237 (by clausification #[185]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 7 a a_5)) False)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_5 a_6)) True))
% 8.70/8.87 Clause #238 (by superposition #[237, 189]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True)
% 8.70/8.87 (Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True) (Eq False True)))
% 8.70/8.87 Clause #239 (by clausification #[238]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Or (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True)
% 8.70/8.87 (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True))
% 8.70/8.87 Clause #240 (by eliminate duplicate literals #[239]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) True)
% 8.70/8.87 (Eq (in (skS.0 4 (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3) a_4) (skS.0 8 a a_1 a_5)) True)
% 8.70/8.87 Clause #241 (by superposition #[240, 171]): ∀ (a a_1 a_2 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True)
% 8.70/8.87 (Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) (Eq True False))
% 8.70/8.87 Clause #242 (by clausification #[241]): ∀ (a a_1 a_2 : Iota),
% 8.70/8.87 Or (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True) (Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True)
% 8.70/8.87 Clause #243 (by eliminate duplicate literals #[242]): ∀ (a a_1 a_2 : Iota), Eq (subset (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True
% 8.70/8.87 Clause #244 (by superposition #[243, 28]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) True)
% 8.70/8.87 Clause #245 (by clausification #[244]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (powerset (skS.0 8 a a_1 a_2))) True
% 8.70/8.87 Clause #246 (by superposition #[245, 79]): Eq True False
% 8.70/8.87 Clause #257 (by clausification #[246]): False
% 8.70/8.87 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------