TSTP Solution File: SEU713^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU713^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n004.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 16:43:31 EDT 2023
% Result : Theorem 7.07s 7.29s
% Output : Proof 7.07s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU713^2 : TPTP v8.1.2. Released v3.7.0.
% 0.14/0.14 % Command : duper %s
% 0.15/0.35 % Computer : n004.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 18:34:23 EDT 2023
% 0.15/0.35 % CPUTime :
% 7.07/7.29 SZS status Theorem for theBenchmark.p
% 7.07/7.29 SZS output start Proof for theBenchmark.p
% 7.07/7.29 Clause #0 (by assumption #[]): Eq (Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))) True
% 7.07/7.29 Clause #1 (by assumption #[]): Eq (Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)) True
% 7.07/7.29 Clause #2 (by assumption #[]): Eq (Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)) True
% 7.07/7.29 Clause #3 (by assumption #[]): Eq
% 7.07/7.29 (Not
% 7.07/7.29 (powersetI →
% 7.07/7.29 powersetE →
% 7.07/7.29 setminusEL →
% 7.07/7.29 ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)))
% 7.07/7.29 True
% 7.07/7.29 Clause #4 (by clausification #[2]): Eq setminusEL (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)
% 7.07/7.29 Clause #20 (by clausification #[0]): Eq powersetI (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))
% 7.07/7.29 Clause #24 (by clausification #[1]): Eq powersetE (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)
% 7.07/7.29 Clause #56 (by clausification #[3]): Eq
% 7.07/7.29 (powersetI →
% 7.07/7.29 powersetE →
% 7.07/7.29 setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A))
% 7.07/7.29 False
% 7.07/7.29 Clause #57 (by clausification #[56]): Eq powersetI True
% 7.07/7.29 Clause #58 (by clausification #[56]): Eq
% 7.07/7.29 (powersetE →
% 7.07/7.29 setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A))
% 7.07/7.29 False
% 7.07/7.29 Clause #59 (by backward demodulation #[57, 20]): Eq True (∀ (A B : Iota), (∀ (Xx : Iota), in Xx B → in Xx A) → in B (powerset A))
% 7.07/7.29 Clause #62 (by clausification #[59]): ∀ (a : Iota), Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx B → in Xx a) → in B (powerset a)) True
% 7.07/7.29 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota), Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → in a (powerset a_1)) True
% 7.07/7.29 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota), Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (in a (powerset a_1)) True)
% 7.07/7.29 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.29 Or (Eq (in a (powerset a_1)) True) (Eq (Not (in (skS.0 9 a a_1 a_2) a → in (skS.0 9 a a_1 a_2) a_1)) True)
% 7.07/7.29 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.29 Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a → in (skS.0 9 a a_1 a_2) a_1) False)
% 7.07/7.29 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a) True)
% 7.07/7.29 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) True) (Eq (in (skS.0 9 a a_1 a_2) a_1) False)
% 7.07/7.29 Clause #69 (by clausification #[58]): Eq powersetE True
% 7.07/7.29 Clause #70 (by clausification #[58]): Eq (setminusEL → ∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A))
% 7.07/7.29 False
% 7.07/7.29 Clause #71 (by backward demodulation #[69, 24]): Eq True (∀ (A B Xx : Iota), in B (powerset A) → in Xx B → in Xx A)
% 7.07/7.29 Clause #74 (by clausification #[71]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in B (powerset a) → in Xx B → in Xx a) True
% 7.07/7.29 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in a (powerset a_1) → in Xx a → in Xx a_1) True
% 7.07/7.29 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (in a (powerset a_1) → in a_2 a → in a_2 a_1) True
% 7.07/7.29 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Eq (in a_2 a → in a_2 a_1) True)
% 7.07/7.29 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (powerset a_1)) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 7.07/7.29 Clause #80 (by clausification #[70]): Eq setminusEL True
% 7.07/7.29 Clause #81 (by clausification #[70]): Eq (∀ (A X : Iota), in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus X Y) (powerset A)) False
% 7.07/7.29 Clause #82 (by backward demodulation #[80, 4]): Eq True (∀ (A B Xx : Iota), in Xx (setminus A B) → in Xx A)
% 7.07/7.29 Clause #86 (by clausification #[82]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (setminus a B) → in Xx a) True
% 7.07/7.32 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (setminus a a_1) → in Xx a) True
% 7.07/7.32 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Eq (in a (setminus a_1 a_2) → in a a_1) True
% 7.07/7.32 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (setminus a_1 a_2)) False) (Eq (in a a_1) True)
% 7.07/7.32 Clause #90 (by superposition #[89, 67]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.07/7.32 Or (Eq (in (skS.0 9 (setminus a a_1) a_2 a_3) a) True)
% 7.07/7.32 (Or (Eq (in (setminus a a_1) (powerset a_2)) True) (Eq False True))
% 7.07/7.32 Clause #91 (by clausification #[81]): ∀ (a : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (Not
% 7.07/7.32 (∀ (X : Iota),
% 7.07/7.32 in X (powerset (skS.0 10 a)) →
% 7.07/7.32 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus X Y) (powerset (skS.0 10 a))))
% 7.07/7.32 True
% 7.07/7.32 Clause #92 (by clausification #[91]): ∀ (a : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (∀ (X : Iota),
% 7.07/7.32 in X (powerset (skS.0 10 a)) →
% 7.07/7.32 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus X Y) (powerset (skS.0 10 a)))
% 7.07/7.32 False
% 7.07/7.32 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (Not
% 7.07/7.32 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) →
% 7.07/7.32 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a))))
% 7.07/7.32 True
% 7.07/7.32 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) →
% 7.07/7.32 ∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a)))
% 7.07/7.32 False
% 7.07/7.32 Clause #95 (by clausification #[94]): ∀ (a a_1 : Iota), Eq (in (skS.0 11 a a_1) (powerset (skS.0 10 a))) True
% 7.07/7.32 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota),
% 7.07/7.32 Eq (∀ (Y : Iota), in Y (powerset (skS.0 10 a)) → in (setminus (skS.0 11 a a_1) Y) (powerset (skS.0 10 a))) False
% 7.07/7.32 Clause #97 (by superposition #[95, 78]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 10 a_1)) True))
% 7.07/7.32 Clause #114 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (Not
% 7.07/7.32 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) →
% 7.07/7.32 in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a))))
% 7.07/7.32 True
% 7.07/7.32 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.32 Eq
% 7.07/7.32 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) →
% 7.07/7.32 in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a)))
% 7.07/7.32 False
% 7.07/7.32 Clause #117 (by clausification #[115]): ∀ (a a_1 a_2 : Iota), Eq (in (setminus (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (powerset (skS.0 10 a))) False
% 7.07/7.32 Clause #119 (by clausification #[97]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 10 a_1)) True)
% 7.07/7.32 Clause #137 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota),
% 7.07/7.32 Or (Eq (in (skS.0 9 (setminus a a_1) a_2 a_3) a) True) (Eq (in (setminus a a_1) (powerset a_2)) True)
% 7.07/7.32 Clause #140 (by superposition #[137, 119]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.07/7.32 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset a_3)) True)
% 7.07/7.32 (Or (Eq True False) (Eq (in (skS.0 9 (setminus (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 10 a)) True))
% 7.07/7.32 Clause #417 (by clausification #[140]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 7.07/7.32 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset a_3)) True)
% 7.07/7.32 (Eq (in (skS.0 9 (setminus (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 10 a)) True)
% 7.07/7.32 Clause #418 (by superposition #[417, 68]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.32 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True)
% 7.07/7.32 (Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True) (Eq True False))
% 7.07/7.32 Clause #420 (by clausification #[418]): ∀ (a a_1 a_2 : Iota),
% 7.07/7.32 Or (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True)
% 7.07/7.32 (Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True)
% 7.07/7.32 Clause #421 (by eliminate duplicate literals #[420]): ∀ (a a_1 a_2 : Iota), Eq (in (setminus (skS.0 11 a a_1) a_2) (powerset (skS.0 10 a))) True
% 7.07/7.32 Clause #422 (by superposition #[421, 117]): Eq True False
% 7.07/7.32 Clause #424 (by clausification #[422]): False
% 7.07/7.32 SZS output end Proof for theBenchmark.p
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