TSTP Solution File: SEU752^2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU752^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n015.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 16:43:43 EDT 2023
% Result : Theorem 6.94s 7.17s
% Output : Proof 6.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU752^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.15 % Command : duper %s
% 0.15/0.35 % Computer : n015.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Wed Aug 23 15:09:20 EDT 2023
% 0.15/0.36 % CPUTime :
% 6.94/7.17 SZS status Theorem for theBenchmark.p
% 6.94/7.17 SZS output start Proof for theBenchmark.p
% 6.94/7.17 Clause #0 (by assumption #[]): Eq (Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))) True
% 6.94/7.17 Clause #1 (by assumption #[]): Eq (Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))) True
% 6.94/7.17 Clause #2 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True
% 6.94/7.17 Clause #3 (by assumption #[]): Eq
% 6.94/7.17 (Eq binintersectTELcontra
% 6.94/7.17 (∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))))
% 6.94/7.17 True
% 6.94/7.17 Clause #4 (by assumption #[]): Eq
% 6.94/7.17 (Eq binintersectTERcontra
% 6.94/7.17 (∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y))))
% 6.94/7.17 True
% 6.94/7.17 Clause #5 (by assumption #[]): Eq
% 6.94/7.17 (Not
% 6.94/7.17 (binunionE →
% 6.94/7.17 setminusI →
% 6.94/7.17 setminusER →
% 6.94/7.17 binintersectTELcontra →
% 6.94/7.17 binintersectTERcontra →
% 6.94/7.17 ∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota),
% 6.94/7.17 in Y (powerset A) →
% 6.94/7.17 ∀ (Xx : Iota),
% 6.94/7.17 in Xx A →
% 6.94/7.17 in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y))))
% 6.94/7.17 True
% 6.94/7.17 Clause #6 (by clausification #[2]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 6.94/7.17 Clause #23 (by clausification #[1]): Eq setminusI (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))
% 6.94/7.17 Clause #27 (by clausification #[0]): Eq binunionE (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))
% 6.94/7.17 Clause #58 (by clausification #[3]): Eq binintersectTELcontra
% 6.94/7.17 (∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 6.94/7.17 Clause #78 (by clausification #[4]): Eq binintersectTERcontra
% 6.94/7.17 (∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y)))
% 6.94/7.17 Clause #92 (by clausification #[5]): Eq
% 6.94/7.17 (binunionE →
% 6.94/7.17 setminusI →
% 6.94/7.17 setminusER →
% 6.94/7.17 binintersectTELcontra →
% 6.94/7.17 binintersectTERcontra →
% 6.94/7.17 ∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota),
% 6.94/7.17 in Y (powerset A) →
% 6.94/7.17 ∀ (Xx : Iota),
% 6.94/7.17 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.17 False
% 6.94/7.17 Clause #93 (by clausification #[92]): Eq binunionE True
% 6.94/7.17 Clause #94 (by clausification #[92]): Eq
% 6.94/7.17 (setminusI →
% 6.94/7.17 setminusER →
% 6.94/7.17 binintersectTELcontra →
% 6.94/7.17 binintersectTERcontra →
% 6.94/7.17 ∀ (A X : Iota),
% 6.94/7.17 in X (powerset A) →
% 6.94/7.17 ∀ (Y : Iota),
% 6.94/7.17 in Y (powerset A) →
% 6.94/7.17 ∀ (Xx : Iota),
% 6.94/7.17 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.17 False
% 6.94/7.17 Clause #95 (by backward demodulation #[93, 27]): Eq True (∀ (A B Xx : Iota), in Xx (binunion A B) → Or (in Xx A) (in Xx B))
% 6.94/7.17 Clause #98 (by clausification #[95]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binunion a B) → Or (in Xx a) (in Xx B)) True
% 6.94/7.17 Clause #99 (by clausification #[98]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binunion a a_1) → Or (in Xx a) (in Xx a_1)) True
% 6.94/7.17 Clause #100 (by clausification #[99]): ∀ (a a_1 a_2 : Iota), Eq (in a (binunion a_1 a_2) → Or (in a a_1) (in a a_2)) True
% 6.94/7.17 Clause #101 (by clausification #[100]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Eq (Or (in a a_1) (in a a_2)) True)
% 6.94/7.17 Clause #102 (by clausification #[101]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binunion a_1 a_2)) False) (Or (Eq (in a a_1) True) (Eq (in a a_2) True))
% 6.94/7.17 Clause #110 (by clausification #[94]): Eq setminusI True
% 6.94/7.20 Clause #111 (by clausification #[94]): Eq
% 6.94/7.20 (setminusER →
% 6.94/7.20 binintersectTELcontra →
% 6.94/7.20 binintersectTERcontra →
% 6.94/7.20 ∀ (A X : Iota),
% 6.94/7.20 in X (powerset A) →
% 6.94/7.20 ∀ (Y : Iota),
% 6.94/7.20 in Y (powerset A) →
% 6.94/7.20 ∀ (Xx : Iota),
% 6.94/7.20 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.20 False
% 6.94/7.20 Clause #112 (by backward demodulation #[110, 23]): Eq True (∀ (A B Xx : Iota), in Xx A → Not (in Xx B) → in Xx (setminus A B))
% 6.94/7.20 Clause #115 (by clausification #[112]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → Not (in Xx B) → in Xx (setminus a B)) True
% 6.94/7.20 Clause #116 (by clausification #[115]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → Not (in Xx a_1) → in Xx (setminus a a_1)) True
% 6.94/7.20 Clause #117 (by clausification #[116]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → Not (in a a_2) → in a (setminus a_1 a_2)) True
% 6.94/7.20 Clause #118 (by clausification #[117]): ∀ (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)
% 6.94/7.20 Clause #119 (by clausification #[118]): ∀ (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))
% 6.94/7.20 Clause #120 (by clausification #[119]): ∀ (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))
% 6.94/7.20 Clause #125 (by clausification #[111]): Eq setminusER True
% 6.94/7.20 Clause #126 (by clausification #[111]): Eq
% 6.94/7.20 (binintersectTELcontra →
% 6.94/7.20 binintersectTERcontra →
% 6.94/7.20 ∀ (A X : Iota),
% 6.94/7.20 in X (powerset A) →
% 6.94/7.20 ∀ (Y : Iota),
% 6.94/7.20 in Y (powerset A) →
% 6.94/7.20 ∀ (Xx : Iota),
% 6.94/7.20 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.20 False
% 6.94/7.20 Clause #127 (by backward demodulation #[125, 6]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 6.94/7.20 Clause #131 (by clausification #[127]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True
% 6.94/7.20 Clause #132 (by clausification #[131]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True
% 6.94/7.20 Clause #133 (by clausification #[132]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True
% 6.94/7.20 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True)
% 6.94/7.20 Clause #135 (by clausification #[134]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False)
% 6.94/7.20 Clause #140 (by clausification #[126]): Eq binintersectTELcontra True
% 6.94/7.20 Clause #141 (by clausification #[126]): Eq
% 6.94/7.20 (binintersectTERcontra →
% 6.94/7.20 ∀ (A X : Iota),
% 6.94/7.20 in X (powerset A) →
% 6.94/7.20 ∀ (Y : Iota),
% 6.94/7.20 in Y (powerset A) →
% 6.94/7.20 ∀ (Xx : Iota),
% 6.94/7.20 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.20 False
% 6.94/7.20 Clause #142 (by backward demodulation #[140, 58]): Eq True
% 6.94/7.20 (∀ (A X : Iota),
% 6.94/7.20 in X (powerset A) →
% 6.94/7.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 6.94/7.20 Clause #145 (by clausification #[142]): ∀ (a : Iota),
% 6.94/7.20 Eq
% 6.94/7.20 (∀ (X : Iota),
% 6.94/7.20 in X (powerset a) →
% 6.94/7.20 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 6.94/7.20 True
% 6.94/7.20 Clause #146 (by clausification #[145]): ∀ (a a_1 : Iota),
% 6.94/7.20 Eq
% 6.94/7.20 (in a (powerset a_1) →
% 6.94/7.20 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y)))
% 6.94/7.20 True
% 6.94/7.20 Clause #147 (by clausification #[146]): ∀ (a a_1 : Iota),
% 6.94/7.20 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.20 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y)))
% 6.94/7.20 True)
% 6.94/7.20 Clause #148 (by clausification #[147]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.20 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.20 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a a_2))) True)
% 6.94/7.23 Clause #149 (by clausification #[148]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a a_2))) True))
% 6.94/7.23 Clause #150 (by clausification #[149]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 a) → Not (in a_3 (binintersect a a_2))) True))
% 6.94/7.23 Clause #151 (by clausification #[150]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 a) → Not (in a_3 (binintersect a a_2))) True)))
% 6.94/7.23 Clause #152 (by clausification #[151]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a)) False) (Eq (Not (in a_3 (binintersect a a_2))) True))))
% 6.94/7.23 Clause #153 (by clausification #[152]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binintersect a a_2))) True) (Eq (in a_3 a) True))))
% 6.94/7.23 Clause #154 (by clausification #[153]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 a) True) (Eq (in a_3 (binintersect a a_2)) False))))
% 6.94/7.23 Clause #156 (by clausification #[141]): Eq binintersectTERcontra True
% 6.94/7.23 Clause #157 (by clausification #[141]): Eq
% 6.94/7.23 (∀ (A X : Iota),
% 6.94/7.23 in X (powerset A) →
% 6.94/7.23 ∀ (Y : Iota),
% 6.94/7.23 in Y (powerset A) →
% 6.94/7.23 ∀ (Xx : Iota),
% 6.94/7.23 in Xx A → in Xx (binunion (setminus A X) (setminus A Y)) → in Xx (setminus A (binintersect X Y)))
% 6.94/7.23 False
% 6.94/7.23 Clause #158 (by backward demodulation #[156, 78]): Eq True
% 6.94/7.23 (∀ (A X : Iota),
% 6.94/7.23 in X (powerset A) →
% 6.94/7.23 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx Y) → Not (in Xx (binintersect X Y)))
% 6.94/7.23 Clause #161 (by clausification #[158]): ∀ (a : Iota),
% 6.94/7.23 Eq
% 6.94/7.23 (∀ (X : Iota),
% 6.94/7.23 in X (powerset a) →
% 6.94/7.23 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx Y) → Not (in Xx (binintersect X Y)))
% 6.94/7.23 True
% 6.94/7.23 Clause #162 (by clausification #[161]): ∀ (a a_1 : Iota),
% 6.94/7.23 Eq
% 6.94/7.23 (in a (powerset a_1) →
% 6.94/7.23 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx Y) → Not (in Xx (binintersect a Y)))
% 6.94/7.23 True
% 6.94/7.23 Clause #163 (by clausification #[162]): ∀ (a a_1 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx Y) → Not (in Xx (binintersect a Y)))
% 6.94/7.23 True)
% 6.94/7.23 Clause #164 (by clausification #[163]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a_2) → Not (in Xx (binintersect a a_2))) True)
% 6.94/7.23 Clause #165 (by clausification #[164]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx a_2) → Not (in Xx (binintersect a a_2))) True))
% 6.94/7.23 Clause #166 (by clausification #[165]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Eq (in a_3 a_1 → Not (in a_3 a_2) → Not (in a_3 (binintersect a a_2))) True))
% 6.94/7.23 Clause #167 (by clausification #[166]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 a_2) → Not (in a_3 (binintersect a a_2))) True)))
% 6.94/7.23 Clause #168 (by clausification #[167]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.23 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a_2)) False) (Eq (Not (in a_3 (binintersect a a_2))) True))))
% 6.94/7.26 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.26 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.26 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.26 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binintersect a a_2))) True) (Eq (in a_3 a_2) True))))
% 6.94/7.26 Clause #170 (by clausification #[169]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.26 Or (Eq (in a (powerset a_1)) False)
% 6.94/7.26 (Or (Eq (in a_2 (powerset a_1)) False)
% 6.94/7.26 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 a_2) True) (Eq (in a_3 (binintersect a a_2)) False))))
% 6.94/7.26 Clause #174 (by clausification #[157]): ∀ (a : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (Not
% 6.94/7.26 (∀ (X : Iota),
% 6.94/7.26 in X (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Y : Iota),
% 6.94/7.26 in Y (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) X) (setminus (skS.0 13 a) Y)) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect X Y))))
% 6.94/7.26 True
% 6.94/7.26 Clause #175 (by clausification #[174]): ∀ (a : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (∀ (X : Iota),
% 6.94/7.26 in X (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Y : Iota),
% 6.94/7.26 in Y (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) X) (setminus (skS.0 13 a) Y)) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect X Y)))
% 6.94/7.26 False
% 6.94/7.26 Clause #176 (by clausification #[175]): ∀ (a a_1 : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (Not
% 6.94/7.26 (in (skS.0 14 a a_1) (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Y : Iota),
% 6.94/7.26 in Y (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) Y)) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) Y))))
% 6.94/7.26 True
% 6.94/7.26 Clause #177 (by clausification #[176]): ∀ (a a_1 : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (in (skS.0 14 a a_1) (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Y : Iota),
% 6.94/7.26 in Y (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) Y)) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) Y)))
% 6.94/7.26 False
% 6.94/7.26 Clause #178 (by clausification #[177]): ∀ (a a_1 : Iota), Eq (in (skS.0 14 a a_1) (powerset (skS.0 13 a))) True
% 6.94/7.26 Clause #179 (by clausification #[177]): ∀ (a a_1 : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (∀ (Y : Iota),
% 6.94/7.26 in Y (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) Y)) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) Y)))
% 6.94/7.26 False
% 6.94/7.26 Clause #180 (by superposition #[178, 154]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.26 Or (Eq True False)
% 6.94/7.26 (Or (Eq (in a (powerset (skS.0 13 a_1))) False)
% 6.94/7.26 (Or (Eq (in a_2 (skS.0 13 a_1)) False)
% 6.94/7.26 (Or (Eq (in a_2 (skS.0 14 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 14 a_1 a_3) a)) False))))
% 6.94/7.26 Clause #181 (by superposition #[178, 170]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.26 Or (Eq True False)
% 6.94/7.26 (Or (Eq (in a (powerset (skS.0 13 a_1))) False)
% 6.94/7.26 (Or (Eq (in a_2 (skS.0 13 a_1)) False)
% 6.94/7.26 (Or (Eq (in a_2 a) True) (Eq (in a_2 (binintersect (skS.0 14 a_1 a_3) a)) False))))
% 6.94/7.26 Clause #194 (by clausification #[179]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (Not
% 6.94/7.26 (in (skS.0 17 a a_1 a_2) (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2)))))
% 6.94/7.26 True
% 6.94/7.26 Clause #195 (by clausification #[194]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.26 Eq
% 6.94/7.26 (in (skS.0 17 a a_1 a_2) (powerset (skS.0 13 a)) →
% 6.94/7.26 ∀ (Xx : Iota),
% 6.94/7.26 in Xx (skS.0 13 a) →
% 6.94/7.26 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.26 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))))
% 6.94/7.29 False
% 6.94/7.29 Clause #196 (by clausification #[195]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 17 a a_1 a_2) (powerset (skS.0 13 a))) True
% 6.94/7.29 Clause #197 (by clausification #[195]): ∀ (a a_1 a_2 : Iota),
% 6.94/7.29 Eq
% 6.94/7.29 (∀ (Xx : Iota),
% 6.94/7.29 in Xx (skS.0 13 a) →
% 6.94/7.29 in Xx (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.29 in Xx (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))))
% 6.94/7.29 False
% 6.94/7.29 Clause #218 (by clausification #[197]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Eq
% 6.94/7.29 (Not
% 6.94/7.29 (in (skS.0 20 a a_1 a_2 a_3) (skS.0 13 a) →
% 6.94/7.29 in (skS.0 20 a a_1 a_2 a_3)
% 6.94/7.29 (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.29 in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2)))))
% 6.94/7.29 True
% 6.94/7.29 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Eq
% 6.94/7.29 (in (skS.0 20 a a_1 a_2 a_3) (skS.0 13 a) →
% 6.94/7.29 in (skS.0 20 a a_1 a_2 a_3)
% 6.94/7.29 (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.29 in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))))
% 6.94/7.29 False
% 6.94/7.29 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 13 a)) True
% 6.94/7.29 Clause #221 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Eq
% 6.94/7.29 (in (skS.0 20 a a_1 a_2 a_3)
% 6.94/7.29 (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) →
% 6.94/7.29 in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))))
% 6.94/7.29 False
% 6.94/7.29 Clause #222 (by superposition #[220, 120]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.29 Or (Eq True False)
% 6.94/7.29 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) a_4)) True) (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True))
% 6.94/7.29 Clause #247 (by clausification #[181]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Or (Eq (in a (powerset (skS.0 13 a_1))) False)
% 6.94/7.29 (Or (Eq (in a_2 (skS.0 13 a_1)) False)
% 6.94/7.29 (Or (Eq (in a_2 a) True) (Eq (in a_2 (binintersect (skS.0 14 a_1 a_3) a)) False)))
% 6.94/7.29 Clause #249 (by superposition #[247, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.29 Or (Eq (in a (skS.0 13 a_1)) False)
% 6.94/7.29 (Or (Eq (in a (skS.0 17 a_1 a_2 a_3)) True)
% 6.94/7.29 (Or (Eq (in a (binintersect (skS.0 14 a_1 a_4) (skS.0 17 a_1 a_2 a_3))) False) (Eq False True)))
% 6.94/7.29 Clause #250 (by clausification #[222]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.29 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) a_4)) True) (Eq (in (skS.0 20 a a_1 a_2 a_3) a_4) True)
% 6.94/7.29 Clause #257 (by clausification #[221]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Eq
% 6.94/7.29 (in (skS.0 20 a a_1 a_2 a_3)
% 6.94/7.29 (binunion (setminus (skS.0 13 a) (skS.0 14 a a_1)) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))))
% 6.94/7.29 True
% 6.94/7.29 Clause #258 (by clausification #[221]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2)))) False
% 6.94/7.29 Clause #259 (by superposition #[257, 102]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Or (Eq True False)
% 6.94/7.29 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True)
% 6.94/7.29 (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) True))
% 6.94/7.29 Clause #261 (by clausification #[180]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Or (Eq (in a (powerset (skS.0 13 a_1))) False)
% 6.94/7.29 (Or (Eq (in a_2 (skS.0 13 a_1)) False)
% 6.94/7.29 (Or (Eq (in a_2 (skS.0 14 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 14 a_1 a_3) a)) False)))
% 6.94/7.29 Clause #263 (by superposition #[261, 196]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.29 Or (Eq (in a (skS.0 13 a_1)) False)
% 6.94/7.29 (Or (Eq (in a (skS.0 14 a_1 a_2)) True)
% 6.94/7.29 (Or (Eq (in a (binintersect (skS.0 14 a_1 a_2) (skS.0 17 a_1 a_3 a_4))) False) (Eq False True)))
% 6.94/7.29 Clause #264 (by superposition #[258, 250]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.29 Or (Eq False True) (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))) True)
% 6.94/7.32 Clause #265 (by clausification #[264]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_1) (skS.0 17 a a_1 a_2))) True
% 6.94/7.32 Clause #271 (by clausification #[263]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.32 Or (Eq (in a (skS.0 13 a_1)) False)
% 6.94/7.32 (Or (Eq (in a (skS.0 14 a_1 a_2)) True) (Eq (in a (binintersect (skS.0 14 a_1 a_2) (skS.0 17 a_1 a_3 a_4))) False))
% 6.94/7.32 Clause #272 (by superposition #[271, 220]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_4)) True)
% 6.94/7.32 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_4) (skS.0 17 a a_5 a_6))) False) (Eq False True))
% 6.94/7.32 Clause #284 (by clausification #[249]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 6.94/7.32 Or (Eq (in a (skS.0 13 a_1)) False)
% 6.94/7.32 (Or (Eq (in a (skS.0 17 a_1 a_2 a_3)) True)
% 6.94/7.32 (Eq (in a (binintersect (skS.0 14 a_1 a_4) (skS.0 17 a_1 a_2 a_3))) False))
% 6.94/7.32 Clause #285 (by superposition #[284, 220]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_4 a_5)) True)
% 6.94/7.32 (Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_6) (skS.0 17 a a_4 a_5))) False) (Eq False True))
% 6.94/7.32 Clause #303 (by clausification #[272]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_4)) True)
% 6.94/7.32 (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_4) (skS.0 17 a a_5 a_6))) False)
% 6.94/7.32 Clause #304 (by superposition #[303, 265]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_1)) True) (Eq False True)
% 6.94/7.32 Clause #305 (by clausification #[304]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_1)) True
% 6.94/7.32 Clause #307 (by clausification #[259]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True)
% 6.94/7.32 (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 17 a a_1 a_2))) True)
% 6.94/7.32 Clause #308 (by superposition #[307, 135]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True)
% 6.94/7.32 (Or (Eq True False) (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_1 a_2)) False))
% 6.94/7.32 Clause #312 (by clausification #[308]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True)
% 6.94/7.32 (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_1 a_2)) False)
% 6.94/7.32 Clause #321 (by clausification #[285]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_4 a_5)) True)
% 6.94/7.32 (Eq (in (skS.0 20 a a_1 a_2 a_3) (binintersect (skS.0 14 a a_6) (skS.0 17 a a_4 a_5))) False)
% 6.94/7.32 Clause #322 (by superposition #[321, 265]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_1 a_2)) True) (Eq False True)
% 6.94/7.32 Clause #323 (by clausification #[322]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 17 a a_1 a_2)) True
% 6.94/7.32 Clause #324 (by superposition #[323, 312]): ∀ (a a_1 a_2 a_3 : Iota),
% 6.94/7.32 Or (Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True) (Eq True False)
% 6.94/7.32 Clause #326 (by clausification #[324]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (setminus (skS.0 13 a) (skS.0 14 a a_1))) True
% 6.94/7.32 Clause #328 (by superposition #[326, 135]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_1)) False)
% 6.94/7.32 Clause #330 (by clausification #[328]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 20 a a_1 a_2 a_3) (skS.0 14 a a_1)) False
% 6.94/7.32 Clause #331 (by superposition #[330, 305]): Eq False True
% 6.94/7.32 Clause #332 (by clausification #[331]): False
% 6.94/7.32 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------