TSTP Solution File: SEU732^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU732^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n012.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 16:43:37 EDT 2023
% Result : Theorem 3.60s 3.92s
% Output : Proof 3.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU732^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n012.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 20:52:12 EDT 2023
% 0.14/0.35 % CPUTime :
% 3.60/3.92 SZS status Theorem for theBenchmark.p
% 3.60/3.92 SZS output start Proof for theBenchmark.p
% 3.60/3.92 Clause #0 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True
% 3.60/3.92 Clause #1 (by assumption #[]): Eq
% 3.60/3.92 (Eq binintersectTELcontra
% 3.60/3.92 (∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y))))
% 3.60/3.92 True
% 3.60/3.92 Clause #2 (by assumption #[]): Eq
% 3.60/3.92 (Not
% 3.60/3.92 (setminusER →
% 3.60/3.92 binintersectTELcontra →
% 3.60/3.92 ∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota),
% 3.60/3.92 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y))))
% 3.60/3.92 True
% 3.60/3.92 Clause #3 (by clausification #[0]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 3.60/3.92 Clause #20 (by clausification #[1]): Eq binintersectTELcontra
% 3.60/3.92 (∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 Clause #24 (by clausification #[2]): Eq
% 3.60/3.92 (setminusER →
% 3.60/3.92 binintersectTELcontra →
% 3.60/3.92 ∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota),
% 3.60/3.92 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 False
% 3.60/3.92 Clause #25 (by clausification #[24]): Eq setminusER True
% 3.60/3.92 Clause #26 (by clausification #[24]): Eq
% 3.60/3.92 (binintersectTELcontra →
% 3.60/3.92 ∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota),
% 3.60/3.92 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 False
% 3.60/3.92 Clause #27 (by backward demodulation #[25, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 3.60/3.92 Clause #30 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True
% 3.60/3.92 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True
% 3.60/3.92 Clause #32 (by clausification #[31]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → Not (in a a_2)) True
% 3.60/3.92 Clause #33 (by clausification #[32]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (Not (in a a_2)) True)
% 3.60/3.92 Clause #34 (by clausification #[33]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_2) False)
% 3.60/3.92 Clause #35 (by clausification #[26]): Eq binintersectTELcontra True
% 3.60/3.92 Clause #36 (by clausification #[26]): Eq
% 3.60/3.92 (∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 False
% 3.60/3.92 Clause #37 (by backward demodulation #[35, 20]): Eq True
% 3.60/3.92 (∀ (A X : Iota),
% 3.60/3.92 in X (powerset A) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 Clause #38 (by clausification #[37]): ∀ (a : Iota),
% 3.60/3.92 Eq
% 3.60/3.92 (∀ (X : Iota),
% 3.60/3.92 in X (powerset a) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx X) → Not (in Xx (binintersect X Y)))
% 3.60/3.92 True
% 3.60/3.92 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 3.60/3.92 Eq
% 3.60/3.92 (in a (powerset a_1) →
% 3.60/3.92 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y)))
% 3.60/3.92 True
% 3.60/3.92 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 3.60/3.92 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.92 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a Y)))
% 3.60/3.92 True)
% 3.60/3.92 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.92 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.92 (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)
% 3.60/3.92 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.92 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.92 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.60/3.92 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx a) → Not (in Xx (binintersect a a_2))) True))
% 3.60/3.94 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.94 (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))
% 3.60/3.94 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 a) → Not (in a_3 (binintersect a a_2))) True)))
% 3.60/3.94 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.60/3.94 (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))))
% 3.60/3.94 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.60/3.94 (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))))
% 3.60/3.94 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq (in a (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.60/3.94 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 a) True) (Eq (in a_3 (binintersect a a_2)) False))))
% 3.60/3.94 Clause #48 (by clausification #[36]): ∀ (a : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (Not
% 3.60/3.94 (∀ (X : Iota),
% 3.60/3.94 in X (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Y : Iota),
% 3.60/3.94 in Y (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) X) → Not (in Xx (binintersect X Y))))
% 3.60/3.94 True
% 3.60/3.94 Clause #49 (by clausification #[48]): ∀ (a : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (∀ (X : Iota),
% 3.60/3.94 in X (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Y : Iota),
% 3.60/3.94 in Y (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) X) → Not (in Xx (binintersect X Y)))
% 3.60/3.94 False
% 3.60/3.94 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (Not
% 3.60/3.94 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Y : Iota),
% 3.60/3.94 in Y (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota),
% 3.60/3.94 in Xx (skS.0 3 a) →
% 3.60/3.94 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y))))
% 3.60/3.94 True
% 3.60/3.94 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Y : Iota),
% 3.60/3.94 in Y (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota),
% 3.60/3.94 in Xx (skS.0 3 a) →
% 3.60/3.94 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y)))
% 3.60/3.94 False
% 3.60/3.94 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (powerset (skS.0 3 a))) True
% 3.60/3.94 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (∀ (Y : Iota),
% 3.60/3.94 in Y (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota),
% 3.60/3.94 in Xx (skS.0 3 a) →
% 3.60/3.94 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) Y)))
% 3.60/3.94 False
% 3.60/3.94 Clause #54 (by superposition #[52, 47]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.94 Or (Eq True False)
% 3.60/3.94 (Or (Eq (in a (powerset (skS.0 3 a_1))) False)
% 3.60/3.94 (Or (Eq (in a_2 (skS.0 3 a_1)) False)
% 3.60/3.94 (Or (Eq (in a_2 (skS.0 4 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 4 a_1 a_3) a)) False))))
% 3.60/3.94 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (Not
% 3.60/3.94 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota),
% 3.60/3.94 in Xx (skS.0 3 a) →
% 3.60/3.94 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) →
% 3.60/3.94 Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))))
% 3.60/3.94 True
% 3.60/3.94 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.94 Eq
% 3.60/3.94 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.60/3.94 ∀ (Xx : Iota),
% 3.60/3.94 in Xx (skS.0 3 a) →
% 3.60/3.94 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))
% 3.60/3.94 False
% 3.60/3.94 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a))) True
% 3.60/3.97 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota),
% 3.60/3.97 Eq
% 3.60/3.97 (∀ (Xx : Iota),
% 3.60/3.97 in Xx (skS.0 3 a) →
% 3.60/3.97 in Xx (setminus (skS.0 3 a) (skS.0 4 a a_1)) → Not (in Xx (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))
% 3.60/3.97 False
% 3.60/3.97 Clause #85 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.97 Eq
% 3.60/3.97 (Not
% 3.60/3.97 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.60/3.97 in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) →
% 3.60/3.97 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))))
% 3.60/3.97 True
% 3.60/3.97 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.97 Eq
% 3.60/3.97 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.60/3.97 in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) →
% 3.60/3.97 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))
% 3.60/3.97 False
% 3.60/3.97 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 3 a)) True
% 3.60/3.97 Clause #88 (by clausification #[86]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.97 Eq
% 3.60/3.97 (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1)) →
% 3.60/3.97 Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))))
% 3.60/3.97 False
% 3.60/3.97 Clause #94 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (setminus (skS.0 3 a) (skS.0 4 a a_1))) True
% 3.60/3.97 Clause #95 (by clausification #[88]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) False
% 3.60/3.97 Clause #96 (by superposition #[94, 34]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) False)
% 3.60/3.97 Clause #97 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) False
% 3.60/3.97 Clause #98 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) True
% 3.60/3.97 Clause #99 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.60/3.97 Or (Eq (in a (powerset (skS.0 3 a_1))) False)
% 3.60/3.97 (Or (Eq (in a_2 (skS.0 3 a_1)) False)
% 3.60/3.97 (Or (Eq (in a_2 (skS.0 4 a_1 a_3)) True) (Eq (in a_2 (binintersect (skS.0 4 a_1 a_3) a)) False)))
% 3.60/3.97 Clause #101 (by superposition #[99, 77]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.60/3.97 Or (Eq (in a (skS.0 3 a_1)) False)
% 3.60/3.97 (Or (Eq (in a (skS.0 4 a_1 a_2)) True)
% 3.60/3.97 (Or (Eq (in a (binintersect (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) False) (Eq False True)))
% 3.60/3.97 Clause #110 (by clausification #[101]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.60/3.97 Or (Eq (in a (skS.0 3 a_1)) False)
% 3.60/3.97 (Or (Eq (in a (skS.0 4 a_1 a_2)) True) (Eq (in a (binintersect (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) False))
% 3.60/3.97 Clause #111 (by superposition #[110, 87]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.60/3.97 Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_4)) True)
% 3.60/3.97 (Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) False) (Eq False True))
% 3.60/3.97 Clause #120 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.60/3.97 Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_4)) True)
% 3.60/3.97 (Eq (in (skS.0 9 a a_1 a_2 a_3) (binintersect (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) False)
% 3.60/3.97 Clause #121 (by superposition #[120, 98]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) True) (Eq False True)
% 3.60/3.97 Clause #122 (by clausification #[121]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 4 a a_1)) True
% 3.60/3.97 Clause #123 (by superposition #[122, 97]): Eq True False
% 3.60/3.97 Clause #124 (by clausification #[123]): False
% 3.60/3.97 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------