TSTP Solution File: SEU744^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU744^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n021.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 16:43:41 EDT 2023
% Result : Theorem 3.92s 4.20s
% Output : Proof 3.92s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU744^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 12:56:24 EDT 2023
% 0.19/0.34 % CPUTime :
% 3.92/4.20 SZS status Theorem for theBenchmark.p
% 3.92/4.20 SZS output start Proof for theBenchmark.p
% 3.92/4.20 Clause #0 (by assumption #[]): Eq (Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))) True
% 3.92/4.20 Clause #1 (by assumption #[]): Eq
% 3.92/4.20 (Eq binunionTILcontra
% 3.92/4.20 (∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X)))
% 3.92/4.20 True
% 3.92/4.20 Clause #2 (by assumption #[]): Eq
% 3.92/4.20 (Not
% 3.92/4.20 (setminusER →
% 3.92/4.20 binunionTILcontra →
% 3.92/4.20 ∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota),
% 3.92/4.20 in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X)))
% 3.92/4.20 True
% 3.92/4.20 Clause #3 (by clausification #[0]): Eq setminusER (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 3.92/4.20 Clause #20 (by clausification #[1]): Eq binunionTILcontra
% 3.92/4.20 (∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 Clause #24 (by clausification #[2]): Eq
% 3.92/4.20 (setminusER →
% 3.92/4.20 binunionTILcontra →
% 3.92/4.20 ∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 False
% 3.92/4.20 Clause #25 (by clausification #[24]): Eq setminusER True
% 3.92/4.20 Clause #26 (by clausification #[24]): Eq
% 3.92/4.20 (binunionTILcontra →
% 3.92/4.20 ∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 False
% 3.92/4.20 Clause #27 (by backward demodulation #[25, 3]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → Not (in Xx B))
% 3.92/4.20 Clause #30 (by clausification #[27]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → Not (in Xx B)) True
% 3.92/4.20 Clause #31 (by clausification #[30]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → Not (in Xx a_1)) True
% 3.92/4.20 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
% 3.92/4.20 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)
% 3.92/4.20 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)
% 3.92/4.20 Clause #35 (by clausification #[26]): Eq binunionTILcontra True
% 3.92/4.20 Clause #36 (by clausification #[26]): Eq
% 3.92/4.20 (∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (setminus A (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 False
% 3.92/4.20 Clause #37 (by backward demodulation #[35, 20]): Eq True
% 3.92/4.20 (∀ (A X : Iota),
% 3.92/4.20 in X (powerset A) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset A) → ∀ (Xx : Iota), in Xx A → Not (in Xx (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 Clause #38 (by clausification #[37]): ∀ (a : Iota),
% 3.92/4.20 Eq
% 3.92/4.20 (∀ (X : Iota),
% 3.92/4.20 in X (powerset a) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset a) → ∀ (Xx : Iota), in Xx a → Not (in Xx (binunion X Y)) → Not (in Xx X))
% 3.92/4.20 True
% 3.92/4.20 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota),
% 3.92/4.20 Eq
% 3.92/4.20 (in a (powerset a_1) →
% 3.92/4.20 ∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a))
% 3.92/4.20 True
% 3.92/4.20 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota),
% 3.92/4.20 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.20 (Eq (∀ (Y : Iota), in Y (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a Y)) → Not (in Xx a))
% 3.92/4.20 True)
% 3.92/4.20 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.20 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.20 (Eq (in a_2 (powerset a_1) → ∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True)
% 3.92/4.20 Clause #42 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.20 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.20 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.92/4.20 (Eq (∀ (Xx : Iota), in Xx a_1 → Not (in Xx (binunion a a_2)) → Not (in Xx a)) True))
% 3.92/4.20 Clause #43 (by clausification #[42]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (in a_3 a_1 → Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True))
% 3.92/4.23 Clause #44 (by clausification #[43]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_3 a_1) False) (Eq (Not (in a_3 (binunion a a_2)) → Not (in a_3 a)) True)))
% 3.92/4.23 Clause #45 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 (binunion a a_2))) False) (Eq (Not (in a_3 a)) True))))
% 3.92/4.23 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (Not (in a_3 a)) True) (Eq (in a_3 (binunion a a_2)) True))))
% 3.92/4.23 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq (in a (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (powerset a_1)) False)
% 3.92/4.23 (Or (Eq (in a_3 a_1) False) (Or (Eq (in a_3 (binunion a a_2)) True) (Eq (in a_3 a) False))))
% 3.92/4.23 Clause #48 (by clausification #[36]): ∀ (a : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (Not
% 3.92/4.23 (∀ (X : Iota),
% 3.92/4.23 in X (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Y : Iota),
% 3.92/4.23 in Y (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → Not (in Xx X)))
% 3.92/4.23 True
% 3.92/4.23 Clause #49 (by clausification #[48]): ∀ (a : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (∀ (X : Iota),
% 3.92/4.23 in X (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Y : Iota),
% 3.92/4.23 in Y (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota), in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion X Y)) → Not (in Xx X))
% 3.92/4.23 False
% 3.92/4.23 Clause #50 (by clausification #[49]): ∀ (a a_1 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (Not
% 3.92/4.23 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Y : Iota),
% 3.92/4.23 in Y (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) →
% 3.92/4.23 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1))))
% 3.92/4.23 True
% 3.92/4.23 Clause #51 (by clausification #[50]): ∀ (a a_1 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (in (skS.0 4 a a_1) (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Y : Iota),
% 3.92/4.23 in Y (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1)))
% 3.92/4.23 False
% 3.92/4.23 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Eq (in (skS.0 4 a a_1) (powerset (skS.0 3 a))) True
% 3.92/4.23 Clause #53 (by clausification #[51]): ∀ (a a_1 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (∀ (Y : Iota),
% 3.92/4.23 in Y (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) → in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) Y)) → Not (in Xx (skS.0 4 a a_1)))
% 3.92/4.23 False
% 3.92/4.23 Clause #54 (by superposition #[52, 47]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.23 Or (Eq True False)
% 3.92/4.23 (Or (Eq (in a (powerset (skS.0 3 a_1))) False)
% 3.92/4.23 (Or (Eq (in a_2 (skS.0 3 a_1)) False)
% 3.92/4.23 (Or (Eq (in a_2 (binunion (skS.0 4 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 4 a_1 a_3)) False))))
% 3.92/4.23 Clause #75 (by clausification #[53]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (Not
% 3.92/4.23 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) →
% 3.92/4.23 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1))))
% 3.92/4.23 True
% 3.92/4.23 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 3 a)) →
% 3.92/4.23 ∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) →
% 3.92/4.23 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1)))
% 3.92/4.23 False
% 3.92/4.23 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
% 3.92/4.23 Clause #78 (by clausification #[76]): ∀ (a a_1 a_2 : Iota),
% 3.92/4.23 Eq
% 3.92/4.23 (∀ (Xx : Iota),
% 3.92/4.23 in Xx (skS.0 3 a) →
% 3.92/4.23 in Xx (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) → Not (in Xx (skS.0 4 a a_1)))
% 3.92/4.25 False
% 3.92/4.25 Clause #80 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Eq
% 3.92/4.25 (Not
% 3.92/4.25 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.92/4.25 in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) →
% 3.92/4.25 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1))))
% 3.92/4.25 True
% 3.92/4.25 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Eq
% 3.92/4.25 (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a) →
% 3.92/4.25 in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) →
% 3.92/4.25 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1)))
% 3.92/4.25 False
% 3.92/4.25 Clause #82 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 3 a)) True
% 3.92/4.25 Clause #83 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Eq
% 3.92/4.25 (in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) →
% 3.92/4.25 Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1)))
% 3.92/4.25 False
% 3.92/4.25 Clause #94 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Eq (in (skS.0 8 a a_1 a_2 a_3) (setminus (skS.0 3 a) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2)))) True
% 3.92/4.25 Clause #95 (by clausification #[83]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Not (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1))) False
% 3.92/4.25 Clause #96 (by superposition #[94, 34]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Or (Eq True False) (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) False)
% 3.92/4.25 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_1)) True
% 3.92/4.25 Clause #102 (by clausification #[54]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.92/4.25 Or (Eq (in a (powerset (skS.0 3 a_1))) False)
% 3.92/4.25 (Or (Eq (in a_2 (skS.0 3 a_1)) False)
% 3.92/4.25 (Or (Eq (in a_2 (binunion (skS.0 4 a_1 a_3) a)) True) (Eq (in a_2 (skS.0 4 a_1 a_3)) False)))
% 3.92/4.25 Clause #104 (by superposition #[102, 77]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.92/4.25 Or (Eq (in a (skS.0 3 a_1)) False)
% 3.92/4.25 (Or (Eq (in a (binunion (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) True)
% 3.92/4.25 (Or (Eq (in a (skS.0 4 a_1 a_2)) False) (Eq False True)))
% 3.92/4.25 Clause #107 (by clausification #[96]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_1 a_2))) False
% 3.92/4.25 Clause #110 (by clausification #[104]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.92/4.25 Or (Eq (in a (skS.0 3 a_1)) False)
% 3.92/4.25 (Or (Eq (in a (binunion (skS.0 4 a_1 a_2) (skS.0 7 a_1 a_3 a_4))) True) (Eq (in a (skS.0 4 a_1 a_2)) False))
% 3.92/4.25 Clause #111 (by superposition #[110, 82]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.92/4.25 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) True)
% 3.92/4.25 (Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_4)) False) (Eq False True))
% 3.92/4.25 Clause #122 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.92/4.25 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_4) (skS.0 7 a a_5 a_6))) True)
% 3.92/4.25 (Eq (in (skS.0 8 a a_1 a_2 a_3) (skS.0 4 a a_4)) False)
% 3.92/4.25 Clause #123 (by superposition #[122, 97]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 3.92/4.25 Or (Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_4 a_5))) True) (Eq False True)
% 3.92/4.25 Clause #124 (by clausification #[123]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (in (skS.0 8 a a_1 a_2 a_3) (binunion (skS.0 4 a a_1) (skS.0 7 a a_4 a_5))) True
% 3.92/4.25 Clause #125 (by superposition #[124, 107]): Eq True False
% 3.92/4.25 Clause #127 (by clausification #[125]): False
% 3.92/4.25 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------