TSTP Solution File: SEU755^2 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU755^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n032.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 16:43:44 EDT 2023
% Result : Theorem 11.99s 12.21s
% Output : Proof 12.13s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU755^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.09 % Command : duper %s
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 300
% 0.10/0.29 % DateTime : Wed Aug 23 14:57:41 EDT 2023
% 0.10/0.29 % CPUTime :
% 11.99/12.21 SZS status Theorem for theBenchmark.p
% 11.99/12.21 SZS output start Proof for theBenchmark.p
% 11.99/12.21 Clause #0 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True
% 11.99/12.21 Clause #1 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True
% 11.99/12.21 Clause #2 (by assumption #[]): Eq
% 11.99/12.21 (Eq binunionTEcontra
% 11.99/12.21 (∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y))))
% 11.99/12.21 True
% 11.99/12.21 Clause #3 (by assumption #[]): Eq
% 11.99/12.21 (Not
% 11.99/12.21 (setminusI →
% 11.99/12.21 setminusER →
% 11.99/12.21 binunionTEcontra →
% 11.99/12.21 ∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) →
% 11.99/12.21 ∀ (Xx : Iota),
% 11.99/12.21 in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y))))
% 11.99/12.21 True
% 11.99/12.21 Clause #4 (by clausification #[1]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 11.99/12.21 Clause #21 (by clausification #[0]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))
% 11.99/12.21 Clause #25 (by clausification #[2]): Eq binunionTEcontra
% 11.99/12.21 (∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 11.99/12.21 Clause #61 (by clausification #[3]): Eq
% 11.99/12.21 (setminusI →
% 11.99/12.21 setminusER →
% 11.99/12.21 binunionTEcontra →
% 11.99/12.21 ∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) →
% 11.99/12.21 ∀ (Xx : Iota),
% 11.99/12.21 in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y)))
% 11.99/12.21 False
% 11.99/12.21 Clause #62 (by clausification #[61]): Eq setminusI True
% 11.99/12.21 Clause #63 (by clausification #[61]): Eq
% 11.99/12.21 (setminusER →
% 11.99/12.21 binunionTEcontra →
% 11.99/12.21 ∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) →
% 11.99/12.21 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y)))
% 11.99/12.21 False
% 11.99/12.21 Clause #64 (by backward demodulation #[62, 21]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))
% 11.99/12.21 Clause #67 (by clausification #[64]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True
% 11.99/12.21 Clause #68 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True
% 11.99/12.21 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True
% 11.99/12.21 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (Not (in a a_2) → in a (setminus a_1 a_2)) True)
% 11.99/12.21 Clause #71 (by clausification #[70]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (Not (in a a_2)) False) (Eq (in a (setminus a_1 a_2)) True))
% 11.99/12.21 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Or (Eq (in a (setminus a_1 a_2)) True) (Eq (in a a_2) True))
% 11.99/12.21 Clause #75 (by clausification #[63]): Eq setminusER True
% 11.99/12.21 Clause #76 (by clausification #[63]): Eq
% 11.99/12.21 (binunionTEcontra →
% 11.99/12.21 ∀ (A X : Iota),
% 11.99/12.21 in X (powerset A) →
% 11.99/12.21 ∀ (Y : Iota),
% 11.99/12.21 in Y (powerset A) →
% 11.99/12.21 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y)))
% 11.99/12.21 False
% 11.99/12.21 Clause #77 (by backward demodulation #[75, 4]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 11.99/12.21 Clause #80 (by clausification #[77]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True
% 11.99/12.21 Clause #81 (by clausification #[80]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True
% 11.99/12.21 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True
% 11.99/12.21 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True)
% 12.04/12.27 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False)
% 12.04/12.27 Clause #87 (by clausification #[76]): Eq binunionTEcontra True
% 12.04/12.27 Clause #88 (by clausification #[76]): Eq
% 12.04/12.27 (∀ (A X : Iota),
% 12.04/12.27 in X (powerset A) →
% 12.04/12.27 ∀ (Y : Iota),
% 12.04/12.27 in Y (powerset A) →
% 12.04/12.27 ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → in Xx (setminus A Y) → in Xx (setminus A (binunion X Y)))
% 12.04/12.27 False
% 12.04/12.27 Clause #89 (by backward demodulation #[87, 25]): Eq True
% 12.04/12.27 (∀ (A X : Iota),
% 12.04/12.27 in X (powerset A) →
% 12.04/12.27 ∀ (Y : Iota),
% 12.04/12.27 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 12.04/12.27 Clause #92 (by clausification #[89]): ∀ (a : Iota),
% 12.04/12.27 Eq
% 12.04/12.27 (∀ (X : Iota),
% 12.04/12.27 in X (powerset a) →
% 12.04/12.27 ∀ (Y : Iota),
% 12.04/12.27 in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx X) → Not (in Xx Y) → Not (in Xx (binunion X Y)))
% 12.04/12.27 True
% 12.04/12.27 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota),
% 12.04/12.27 Eq
% 12.04/12.27 (in a (powerset a_1) →
% 12.04/12.27 ∀ (Y : Iota),
% 12.04/12.27 in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx Y) → Not (in Xx (binunion a Y)))
% 12.04/12.27 True
% 12.04/12.27 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Eq
% 12.04/12.27 (∀ (Y : Iota),
% 12.04/12.27 in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx Y) → Not (in Xx (binunion a Y)))
% 12.04/12.27 True)
% 12.04/12.27 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Eq
% 12.04/12.27 (in a_2 (powerset a_1) →
% 12.04/12.27 ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx a_2) → Not (in Xx (binunion a a_2)))
% 12.04/12.27 True)
% 12.04/12.27 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx a_2) → Not (in Xx (binunion a a_2))) True))
% 12.04/12.27 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Eq (in a_3 a_1 → Not (in a_3 a) → Not (in a_3 a_2) → Not (in a_3 (binunion a a_2))) True))
% 12.04/12.27 Clause #98 (by clausification #[97]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 a) → Not (in a_3 a_2) → Not (in a_3 (binunion a a_2))) True)))
% 12.04/12.27 Clause #99 (by clausification #[98]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False)
% 12.04/12.27 (Or (Eq (Not (in a_3 a)) False) (Eq (Not (in a_3 a_2) → Not (in a_3 (binunion a a_2))) True))))
% 12.04/12.27 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False)
% 12.04/12.27 (Or (Eq (Not (in a_3 a_2) → Not (in a_3 (binunion a a_2))) True) (Eq (in a_3 a) True))))
% 12.04/12.27 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False)
% 12.04/12.27 (Or (Eq (in a_3 a) True) (Or (Eq (Not (in a_3 a_2)) False) (Eq (Not (in a_3 (binunion a a_2))) True)))))
% 12.04/12.27 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False)
% 12.04/12.27 (Or (Eq (in a_3 a) True) (Or (Eq (Not (in a_3 (binunion a a_2))) True) (Eq (in a_3 a_2) True)))))
% 12.04/12.27 Clause #103 (by clausification #[102]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.27 Or (Eq (in a (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_2 (powerset a_1)) False)
% 12.04/12.27 (Or (Eq (in a_3 a_1) False)
% 12.04/12.27 (Or (Eq (in a_3 a) True) (Or (Eq (in a_3 a_2) True) (Eq (in a_3 (binunion a a_2)) False)))))
% 12.04/12.27 Clause #104 (by clausification #[88]): ∀ (a : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (Not
% 12.04/12.33 (∀ (X : Iota),
% 12.04/12.33 in X (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Y : Iota),
% 12.04/12.33 in Y (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) X) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) Y) → in Xx (setminus (skS.0 8 a) (binunion X Y))))
% 12.04/12.33 True
% 12.04/12.33 Clause #105 (by clausification #[104]): ∀ (a : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (∀ (X : Iota),
% 12.04/12.33 in X (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Y : Iota),
% 12.04/12.33 in Y (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) X) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) Y) → in Xx (setminus (skS.0 8 a) (binunion X Y)))
% 12.04/12.33 False
% 12.04/12.33 Clause #106 (by clausification #[105]): ∀ (a a_1 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (Not
% 12.04/12.33 (in (skS.0 9 a a_1) (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Y : Iota),
% 12.04/12.33 in Y (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) Y) → in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y))))
% 12.04/12.33 True
% 12.04/12.33 Clause #107 (by clausification #[106]): ∀ (a a_1 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (in (skS.0 9 a a_1) (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Y : Iota),
% 12.04/12.33 in Y (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) Y) → in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y)))
% 12.04/12.33 False
% 12.04/12.33 Clause #108 (by clausification #[107]): ∀ (a a_1 : Iota), Eq (in (skS.0 9 a a_1) (powerset (skS.0 8 a))) True
% 12.04/12.33 Clause #109 (by clausification #[107]): ∀ (a a_1 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (∀ (Y : Iota),
% 12.04/12.33 in Y (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) Y) → in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) Y)))
% 12.04/12.33 False
% 12.04/12.33 Clause #110 (by superposition #[108, 103]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.33 Or (Eq True False)
% 12.04/12.33 (Or (Eq (in a (powerset (skS.0 8 a_1))) False)
% 12.04/12.33 (Or (Eq (in a_2 (skS.0 8 a_1)) False)
% 12.04/12.33 (Or (Eq (in a_2 (skS.0 9 a_1 a_3)) True)
% 12.04/12.33 (Or (Eq (in a_2 a) True) (Eq (in a_2 (binunion (skS.0 9 a_1 a_3) a)) False)))))
% 12.04/12.33 Clause #121 (by clausification #[109]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (Not
% 12.04/12.33 (in (skS.0 11 a a_1 a_2) (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2)))))
% 12.04/12.33 True
% 12.04/12.33 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (in (skS.0 11 a a_1 a_2) (powerset (skS.0 8 a)) →
% 12.04/12.33 ∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))))
% 12.04/12.33 False
% 12.04/12.33 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 11 a a_1 a_2) (powerset (skS.0 8 a))) True
% 12.04/12.33 Clause #124 (by clausification #[122]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (∀ (Xx : Iota),
% 12.04/12.33 in Xx (skS.0 8 a) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.04/12.33 in Xx (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))))
% 12.04/12.33 False
% 12.04/12.33 Clause #139 (by clausification #[124]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.33 Eq
% 12.04/12.33 (Not
% 12.04/12.33 (in (skS.0 13 a a_1 a_2 a_3) (skS.0 8 a) →
% 12.04/12.33 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.04/12.33 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.04/12.33 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2)))))
% 12.13/12.39 True
% 12.13/12.39 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Eq
% 12.13/12.39 (in (skS.0 13 a a_1 a_2 a_3) (skS.0 8 a) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))))
% 12.13/12.39 False
% 12.13/12.39 Clause #141 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 8 a)) True
% 12.13/12.39 Clause #142 (by clausification #[140]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Eq
% 12.13/12.39 (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1)) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))))
% 12.13/12.39 False
% 12.13/12.39 Clause #143 (by superposition #[141, 72]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.13/12.39 Or (Eq True False)
% 12.13/12.39 (Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) a_4)) True) (Eq (in (skS.0 13 a a_1 a_2 a_3) a_4) True))
% 12.13/12.39 Clause #160 (by clausification #[110]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Or (Eq (in a (powerset (skS.0 8 a_1))) False)
% 12.13/12.39 (Or (Eq (in a_2 (skS.0 8 a_1)) False)
% 12.13/12.39 (Or (Eq (in a_2 (skS.0 9 a_1 a_3)) True)
% 12.13/12.39 (Or (Eq (in a_2 a) True) (Eq (in a_2 (binunion (skS.0 9 a_1 a_3) a)) False))))
% 12.13/12.39 Clause #162 (by superposition #[160, 123]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.13/12.39 Or (Eq (in a (skS.0 8 a_1)) False)
% 12.13/12.39 (Or (Eq (in a (skS.0 9 a_1 a_2)) True)
% 12.13/12.39 (Or (Eq (in a (skS.0 11 a_1 a_3 a_4)) True)
% 12.13/12.39 (Or (Eq (in a (binunion (skS.0 9 a_1 a_2) (skS.0 11 a_1 a_3 a_4))) False) (Eq False True))))
% 12.13/12.39 Clause #163 (by clausification #[143]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.13/12.39 Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) a_4)) True) (Eq (in (skS.0 13 a a_1 a_2 a_3) a_4) True)
% 12.13/12.39 Clause #167 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 9 a a_1))) True
% 12.13/12.39 Clause #168 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Eq
% 12.13/12.39 (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2)) →
% 12.13/12.39 in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))))
% 12.13/12.39 False
% 12.13/12.39 Clause #169 (by superposition #[167, 84]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_1)) False)
% 12.13/12.39 Clause #171 (by clausification #[169]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_1)) False
% 12.13/12.39 Clause #172 (by clausification #[168]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (skS.0 11 a a_1 a_2))) True
% 12.13/12.39 Clause #173 (by clausification #[168]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Eq (in (skS.0 13 a a_1 a_2 a_3) (setminus (skS.0 8 a) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2)))) False
% 12.13/12.39 Clause #174 (by superposition #[172, 84]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) False)
% 12.13/12.39 Clause #179 (by clausification #[174]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) False
% 12.13/12.39 Clause #180 (by superposition #[173, 163]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.39 Or (Eq False True) (Eq (in (skS.0 13 a a_1 a_2 a_3) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))) True)
% 12.13/12.39 Clause #181 (by clausification #[180]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (binunion (skS.0 9 a a_1) (skS.0 11 a a_1 a_2))) True
% 12.13/12.39 Clause #199 (by clausification #[162]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.13/12.39 Or (Eq (in a (skS.0 8 a_1)) False)
% 12.13/12.39 (Or (Eq (in a (skS.0 9 a_1 a_2)) True)
% 12.13/12.39 (Or (Eq (in a (skS.0 11 a_1 a_3 a_4)) True)
% 12.13/12.39 (Eq (in a (binunion (skS.0 9 a_1 a_2) (skS.0 11 a_1 a_3 a_4))) False)))
% 12.13/12.39 Clause #200 (by superposition #[199, 141]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.13/12.39 Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_4)) True)
% 12.13/12.39 (Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_5 a_6)) True)
% 12.13/12.40 (Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (binunion (skS.0 9 a a_4) (skS.0 11 a a_5 a_6))) False) (Eq False True)))
% 12.13/12.40 Clause #232 (by clausification #[200]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 12.13/12.40 Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_4)) True)
% 12.13/12.40 (Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_5 a_6)) True)
% 12.13/12.40 (Eq (in (skS.0 13 a a_1 a_2 a_3) (binunion (skS.0 9 a a_4) (skS.0 11 a a_5 a_6))) False))
% 12.13/12.40 Clause #233 (by superposition #[232, 181]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.40 Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_1)) True)
% 12.13/12.40 (Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) True) (Eq False True))
% 12.13/12.40 Clause #235 (by clausification #[233]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.13/12.40 Or (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 9 a a_1)) True)
% 12.13/12.40 (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) True)
% 12.13/12.40 Clause #236 (by forward demodulation #[235, 171]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq False True) (Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) True)
% 12.13/12.40 Clause #237 (by clausification #[236]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 13 a a_1 a_2 a_3) (skS.0 11 a a_1 a_2)) True
% 12.13/12.40 Clause #238 (by superposition #[237, 179]): Eq True False
% 12.13/12.40 Clause #240 (by clausification #[238]): False
% 12.13/12.40 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------