TSTP Solution File: SEU735^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU735^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n007.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 16:43:38 EDT 2023
% Result : Theorem 3.94s 4.12s
% Output : Proof 3.97s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU735^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n007.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Aug 23 16:15:24 EDT 2023
% 0.13/0.35 % CPUTime :
% 3.94/4.12 SZS status Theorem for theBenchmark.p
% 3.94/4.12 SZS output start Proof for theBenchmark.p
% 3.94/4.12 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True
% 3.94/4.12 Clause #1 (by assumption #[]): Eq
% 3.94/4.12 (Eq complementSubsetComplementIntersect
% 3.94/4.12 (∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y))))
% 3.94/4.12 True
% 3.94/4.12 Clause #2 (by assumption #[]): Eq
% 3.94/4.12 (Not
% 3.94/4.12 (powersetI1 →
% 3.94/4.12 complementSubsetComplementIntersect →
% 3.94/4.12 ∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) →
% 3.94/4.12 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y)))))
% 3.94/4.12 True
% 3.94/4.12 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))
% 3.94/4.12 Clause #16 (by clausification #[1]): Eq complementSubsetComplementIntersect
% 3.94/4.12 (∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y)))
% 3.94/4.12 Clause #20 (by clausification #[2]): Eq
% 3.94/4.12 (powersetI1 →
% 3.94/4.12 complementSubsetComplementIntersect →
% 3.94/4.12 ∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) →
% 3.94/4.12 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y))))
% 3.94/4.12 False
% 3.94/4.12 Clause #21 (by clausification #[20]): Eq powersetI1 True
% 3.94/4.12 Clause #22 (by clausification #[20]): Eq
% 3.94/4.12 (complementSubsetComplementIntersect →
% 3.94/4.12 ∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) →
% 3.94/4.12 ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y))))
% 3.94/4.12 False
% 3.94/4.12 Clause #23 (by backward demodulation #[21, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A))
% 3.94/4.12 Clause #26 (by clausification #[23]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True
% 3.94/4.12 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True
% 3.94/4.12 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True)
% 3.94/4.12 Clause #40 (by clausification #[22]): Eq complementSubsetComplementIntersect True
% 3.94/4.12 Clause #41 (by clausification #[22]): Eq
% 3.94/4.12 (∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → in (setminus A X) (powerset (setminus A (binintersect X Y))))
% 3.94/4.12 False
% 3.94/4.12 Clause #42 (by backward demodulation #[40, 16]): Eq True
% 3.94/4.12 (∀ (A X : Iota),
% 3.94/4.12 in X (powerset A) → ∀ (Y : Iota), in Y (powerset A) → subset (setminus A X) (setminus A (binintersect X Y)))
% 3.94/4.12 Clause #46 (by clausification #[42]): ∀ (a : Iota),
% 3.94/4.12 Eq
% 3.94/4.12 (∀ (X : Iota),
% 3.94/4.12 in X (powerset a) → ∀ (Y : Iota), in Y (powerset a) → subset (setminus a X) (setminus a (binintersect X Y)))
% 3.94/4.12 True
% 3.94/4.12 Clause #47 (by clausification #[46]): ∀ (a a_1 : Iota),
% 3.94/4.12 Eq
% 3.94/4.12 (in a (powerset a_1) →
% 3.94/4.12 ∀ (Y : Iota), in Y (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a Y)))
% 3.94/4.12 True
% 3.94/4.12 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota),
% 3.94/4.12 Or (Eq (in a (powerset a_1)) False)
% 3.94/4.12 (Eq (∀ (Y : Iota), in Y (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a Y))) True)
% 3.94/4.12 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.12 Or (Eq (in a (powerset a_1)) False)
% 3.94/4.12 (Eq (in a_2 (powerset a_1) → subset (setminus a_1 a) (setminus a_1 (binintersect a a_2))) True)
% 3.94/4.12 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 : Iota),
% 3.94/4.12 Or (Eq (in a (powerset a_1)) False)
% 3.94/4.12 (Or (Eq (in a_2 (powerset a_1)) False) (Eq (subset (setminus a_1 a) (setminus a_1 (binintersect a a_2))) True))
% 3.94/4.12 Clause #51 (by clausification #[41]): ∀ (a : Iota),
% 3.94/4.12 Eq
% 3.94/4.12 (Not
% 3.94/4.12 (∀ (X : Iota),
% 3.94/4.12 in X (powerset (skS.0 4 a)) →
% 3.94/4.12 ∀ (Y : Iota),
% 3.94/4.12 in Y (powerset (skS.0 4 a)) →
% 3.94/4.12 in (setminus (skS.0 4 a) X) (powerset (setminus (skS.0 4 a) (binintersect X Y)))))
% 3.94/4.12 True
% 3.94/4.12 Clause #52 (by clausification #[51]): ∀ (a : Iota),
% 3.94/4.12 Eq
% 3.94/4.12 (∀ (X : Iota),
% 3.94/4.12 in X (powerset (skS.0 4 a)) →
% 3.94/4.12 ∀ (Y : Iota),
% 3.94/4.12 in Y (powerset (skS.0 4 a)) →
% 3.94/4.12 in (setminus (skS.0 4 a) X) (powerset (setminus (skS.0 4 a) (binintersect X Y))))
% 3.97/4.14 False
% 3.97/4.14 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (Not
% 3.97/4.14 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) →
% 3.97/4.14 ∀ (Y : Iota),
% 3.97/4.14 in Y (powerset (skS.0 4 a)) →
% 3.97/4.14 in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y)))))
% 3.97/4.14 True
% 3.97/4.14 Clause #54 (by clausification #[53]): ∀ (a a_1 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (in (skS.0 5 a a_1) (powerset (skS.0 4 a)) →
% 3.97/4.14 ∀ (Y : Iota),
% 3.97/4.14 in Y (powerset (skS.0 4 a)) →
% 3.97/4.14 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y))))
% 3.97/4.14 False
% 3.97/4.14 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota), Eq (in (skS.0 5 a a_1) (powerset (skS.0 4 a))) True
% 3.97/4.14 Clause #56 (by clausification #[54]): ∀ (a a_1 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (∀ (Y : Iota),
% 3.97/4.14 in Y (powerset (skS.0 4 a)) →
% 3.97/4.14 in (setminus (skS.0 4 a) (skS.0 5 a a_1)) (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) Y))))
% 3.97/4.14 False
% 3.97/4.14 Clause #57 (by superposition #[55, 50]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.14 Or (Eq True False)
% 3.97/4.14 (Or (Eq (in a (powerset (skS.0 4 a_1))) False)
% 3.97/4.14 (Eq
% 3.97/4.14 (subset (setminus (skS.0 4 a_1) (skS.0 5 a_1 a_2)) (setminus (skS.0 4 a_1) (binintersect (skS.0 5 a_1 a_2) a)))
% 3.97/4.14 True))
% 3.97/4.14 Clause #63 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (Not
% 3.97/4.14 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a)) →
% 3.97/4.14 in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2))))))
% 3.97/4.14 True
% 3.97/4.14 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a)) →
% 3.97/4.14 in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2)))))
% 3.97/4.14 False
% 3.97/4.14 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1 a_2) (powerset (skS.0 4 a))) True
% 3.97/4.14 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_1 a_2)))))
% 3.97/4.14 False
% 3.97/4.14 Clause #69 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 3.97/4.14 Or (Eq (in a (powerset (skS.0 4 a_1))) False)
% 3.97/4.14 (Eq (subset (setminus (skS.0 4 a_1) (skS.0 5 a_1 a_2)) (setminus (skS.0 4 a_1) (binintersect (skS.0 5 a_1 a_2) a)))
% 3.97/4.14 True)
% 3.97/4.14 Clause #71 (by superposition #[69, 65]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.14 Or
% 3.97/4.14 (Eq
% 3.97/4.14 (subset (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3))))
% 3.97/4.14 True)
% 3.97/4.14 (Eq False True)
% 3.97/4.14 Clause #79 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (subset (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3))))
% 3.97/4.14 True
% 3.97/4.14 Clause #80 (by superposition #[79, 28]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.14 Or (Eq True False)
% 3.97/4.14 (Eq
% 3.97/4.14 (in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3)))))
% 3.97/4.14 True)
% 3.97/4.14 Clause #81 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.97/4.14 Eq
% 3.97/4.14 (in (setminus (skS.0 4 a) (skS.0 5 a a_1))
% 3.97/4.14 (powerset (setminus (skS.0 4 a) (binintersect (skS.0 5 a a_1) (skS.0 7 a a_2 a_3)))))
% 3.97/4.14 True
% 3.97/4.14 Clause #82 (by superposition #[81, 66]): Eq True False
% 3.97/4.14 Clause #84 (by clausification #[82]): False
% 3.97/4.14 SZS output end Proof for theBenchmark.p
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