TSTP Solution File: SEU740^2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU740^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n010.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 16:43:40 EDT 2023
% Result : Theorem 4.75s 4.99s
% Output : Proof 4.85s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU740^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n010.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 12:55:36 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.75/4.99 SZS status Theorem for theBenchmark.p
% 4.75/4.99 SZS output start Proof for theBenchmark.p
% 4.75/4.99 Clause #0 (by assumption #[]): Eq (Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))) True
% 4.75/4.99 Clause #1 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True
% 4.75/4.99 Clause #2 (by assumption #[]): Eq
% 4.75/4.99 (Not
% 4.75/4.99 (binunionIL →
% 4.75/4.99 binintersectEL →
% 4.75/4.99 ∀ (A X : Iota),
% 4.75/4.99 in X (powerset A) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset A) →
% 4.75/4.99 ∀ (Z : Iota),
% 4.75/4.99 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z)))
% 4.75/4.99 True
% 4.75/4.99 Clause #3 (by clausification #[1]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)
% 4.75/4.99 Clause #19 (by clausification #[0]): Eq binunionIL (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))
% 4.75/4.99 Clause #23 (by clausification #[2]): Eq
% 4.75/4.99 (binunionIL →
% 4.75/4.99 binintersectEL →
% 4.75/4.99 ∀ (A X : Iota),
% 4.75/4.99 in X (powerset A) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset A) →
% 4.75/4.99 ∀ (Z : Iota),
% 4.75/4.99 in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z))
% 4.75/4.99 False
% 4.75/4.99 Clause #24 (by clausification #[23]): Eq binunionIL True
% 4.75/4.99 Clause #25 (by clausification #[23]): Eq
% 4.75/4.99 (binintersectEL →
% 4.75/4.99 ∀ (A X : Iota),
% 4.75/4.99 in X (powerset A) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset A) →
% 4.75/4.99 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z))
% 4.75/4.99 False
% 4.75/4.99 Clause #26 (by backward demodulation #[24, 19]): Eq True (∀ (A B Xx : Iota), in Xx A → in Xx (binunion A B))
% 4.75/4.99 Clause #27 (by clausification #[26]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx a → in Xx (binunion a B)) True
% 4.75/4.99 Clause #28 (by clausification #[27]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx a → in Xx (binunion a a_1)) True
% 4.75/4.99 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 : Iota), Eq (in a a_1 → in a (binunion a_1 a_2)) True
% 4.75/4.99 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a a_1) False) (Eq (in a (binunion a_1 a_2)) True)
% 4.75/4.99 Clause #46 (by clausification #[25]): Eq binintersectEL True
% 4.75/4.99 Clause #47 (by clausification #[25]): Eq
% 4.75/4.99 (∀ (A X : Iota),
% 4.75/4.99 in X (powerset A) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset A) →
% 4.75/4.99 ∀ (Z : Iota), in Z (powerset A) → ∀ (Xx : Iota), in Xx A → in Xx (binintersect X Y) → in Xx (binunion X Z))
% 4.75/4.99 False
% 4.75/4.99 Clause #48 (by backward demodulation #[46, 3]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)
% 4.75/4.99 Clause #52 (by clausification #[48]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True
% 4.75/4.99 Clause #53 (by clausification #[52]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True
% 4.75/4.99 Clause #54 (by clausification #[53]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True
% 4.75/4.99 Clause #55 (by clausification #[54]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True)
% 4.75/4.99 Clause #56 (by clausification #[47]): ∀ (a : Iota),
% 4.75/4.99 Eq
% 4.75/4.99 (Not
% 4.75/4.99 (∀ (X : Iota),
% 4.75/4.99 in X (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Z : Iota),
% 4.75/4.99 in Z (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion X Z)))
% 4.75/4.99 True
% 4.75/4.99 Clause #57 (by clausification #[56]): ∀ (a : Iota),
% 4.75/4.99 Eq
% 4.75/4.99 (∀ (X : Iota),
% 4.75/4.99 in X (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Z : Iota),
% 4.75/4.99 in Z (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Xx : Iota), in Xx (skS.0 6 a) → in Xx (binintersect X Y) → in Xx (binunion X Z))
% 4.75/4.99 False
% 4.75/4.99 Clause #58 (by clausification #[57]): ∀ (a a_1 : Iota),
% 4.75/4.99 Eq
% 4.75/4.99 (Not
% 4.75/4.99 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Y : Iota),
% 4.75/4.99 in Y (powerset (skS.0 6 a)) →
% 4.75/4.99 ∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z)))
% 4.85/5.02 True
% 4.85/5.02 Clause #59 (by clausification #[58]): ∀ (a a_1 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (in (skS.0 7 a a_1) (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Y : Iota),
% 4.85/5.02 in Y (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z))
% 4.85/5.02 False
% 4.85/5.02 Clause #61 (by clausification #[59]): ∀ (a a_1 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (∀ (Y : Iota),
% 4.85/5.02 in Y (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) → in Xx (binintersect (skS.0 7 a a_1) Y) → in Xx (binunion (skS.0 7 a a_1) Z))
% 4.85/5.02 False
% 4.85/5.02 Clause #63 (by clausification #[61]): ∀ (a a_1 a_2 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (Not
% 4.85/5.02 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z)))
% 4.85/5.02 True
% 4.85/5.02 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (in (skS.0 8 a a_1 a_2) (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z))
% 4.85/5.02 False
% 4.85/5.02 Clause #66 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (∀ (Z : Iota),
% 4.85/5.02 in Z (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) → in Xx (binunion (skS.0 7 a a_1) Z))
% 4.85/5.02 False
% 4.85/5.02 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (Not
% 4.85/5.02 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))))
% 4.85/5.02 True
% 4.85/5.02 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (in (skS.0 9 a a_1 a_2 a_3) (powerset (skS.0 6 a)) →
% 4.85/5.02 ∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))
% 4.85/5.02 False
% 4.85/5.02 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (∀ (Xx : Iota),
% 4.85/5.02 in Xx (skS.0 6 a) →
% 4.85/5.02 in Xx (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in Xx (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))
% 4.85/5.02 False
% 4.85/5.02 Clause #88 (by clausification #[71]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (Not
% 4.85/5.02 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) →
% 4.85/5.02 in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))))
% 4.85/5.02 True
% 4.85/5.02 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 6 a) →
% 4.85/5.02 in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))
% 4.85/5.02 False
% 4.85/5.02 Clause #91 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.85/5.02 Eq
% 4.85/5.02 (in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) →
% 4.85/5.02 in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))
% 4.85/5.02 False
% 4.85/5.02 Clause #109 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.85/5.02 Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binintersect (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))) True
% 4.85/5.02 Clause #110 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.85/5.02 Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))) False
% 4.85/5.02 Clause #111 (by superposition #[109, 55]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq True False) (Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1)) True)
% 4.85/5.02 Clause #113 (by clausification #[111]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (skS.0 7 a a_1)) True
% 4.85/5.02 Clause #114 (by superposition #[113, 30]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 4.85/5.02 Or (Eq True False) (Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) a_5)) True)
% 4.85/5.02 Clause #115 (by clausification #[114]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota), Eq (in (skS.0 10 a a_1 a_2 a_3 a_4) (binunion (skS.0 7 a a_1) a_5)) True
% 4.85/5.02 Clause #135 (by superposition #[110, 115]): Eq True False
% 4.85/5.02 Clause #136 (by clausification #[135]): False
% 4.85/5.02 SZS output end Proof for theBenchmark.p
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