TSTP Solution File: SEU759^2 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU759^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n026.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 16:43:46 EDT 2023
% Result : Theorem 5.18s 5.34s
% Output : Proof 5.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU759^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n026.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 23:19:01 EDT 2023
% 0.13/0.35 % CPUTime :
% 5.18/5.34 SZS status Theorem for theBenchmark.p
% 5.18/5.34 SZS output start Proof for theBenchmark.p
% 5.18/5.34 Clause #0 (by assumption #[]): Eq (Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)) True
% 5.18/5.34 Clause #1 (by assumption #[]): Eq (Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)) True
% 5.18/5.34 Clause #2 (by assumption #[]): Eq (Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)) True
% 5.18/5.34 Clause #3 (by assumption #[]): Eq
% 5.18/5.34 (Not
% 5.18/5.34 (subsetI1 →
% 5.18/5.34 subsetE →
% 5.18/5.34 binintersectEL →
% 5.18/5.34 ∀ (A X : Iota),
% 5.18/5.34 in X (powerset A) →
% 5.18/5.34 ∀ (Y : Iota),
% 5.18/5.34 in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset X Z → subset (binintersect X Y) Z))
% 5.18/5.34 True
% 5.18/5.34 Clause #4 (by clausification #[0]): Eq subsetI1 (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B)
% 5.18/5.34 Clause #6 (by clausify Prop equality #[4]): Or (Eq subsetI1 False) (Eq (∀ (A B : Iota), (∀ (Xx : Iota), in Xx A → in Xx B) → subset A B) True)
% 5.18/5.34 Clause #8 (by clausification #[6]): ∀ (a : Iota), Or (Eq subsetI1 False) (Eq (∀ (B : Iota), (∀ (Xx : Iota), in Xx a → in Xx B) → subset a B) True)
% 5.18/5.34 Clause #9 (by clausification #[8]): ∀ (a a_1 : Iota), Or (Eq subsetI1 False) (Eq ((∀ (Xx : Iota), in Xx a → in Xx a_1) → subset a a_1) True)
% 5.18/5.34 Clause #10 (by clausification #[9]): ∀ (a a_1 : Iota), Or (Eq subsetI1 False) (Or (Eq (∀ (Xx : Iota), in Xx a → in Xx a_1) False) (Eq (subset a a_1) True))
% 5.18/5.34 Clause #11 (by clausification #[10]): ∀ (a a_1 a_2 : Iota),
% 5.18/5.34 Or (Eq subsetI1 False)
% 5.18/5.34 (Or (Eq (subset a a_1) True) (Eq (Not (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1)) True))
% 5.18/5.34 Clause #12 (by clausification #[11]): ∀ (a a_1 a_2 : Iota),
% 5.18/5.34 Or (Eq subsetI1 False)
% 5.18/5.34 (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a → in (skS.0 0 a a_1 a_2) a_1) False))
% 5.18/5.34 Clause #13 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI1 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True))
% 5.18/5.34 Clause #14 (by clausification #[12]): ∀ (a a_1 a_2 : Iota), Or (Eq subsetI1 False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False))
% 5.18/5.34 Clause #23 (by clausification #[2]): Eq binintersectEL (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)
% 5.18/5.34 Clause #27 (by clausification #[1]): Eq subsetE (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 5.18/5.34 Clause #56 (by clausification #[3]): Eq
% 5.18/5.34 (subsetI1 →
% 5.18/5.34 subsetE →
% 5.18/5.34 binintersectEL →
% 5.18/5.34 ∀ (A X : Iota),
% 5.18/5.34 in X (powerset A) →
% 5.18/5.34 ∀ (Y : Iota),
% 5.18/5.34 in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset X Z → subset (binintersect X Y) Z)
% 5.18/5.34 False
% 5.18/5.34 Clause #57 (by clausification #[56]): Eq subsetI1 True
% 5.18/5.34 Clause #58 (by clausification #[56]): Eq
% 5.18/5.34 (subsetE →
% 5.18/5.34 binintersectEL →
% 5.18/5.34 ∀ (A X : Iota),
% 5.18/5.34 in X (powerset A) →
% 5.18/5.34 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset X Z → subset (binintersect X Y) Z)
% 5.18/5.34 False
% 5.18/5.34 Clause #60 (by backward demodulation #[57, 13]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True))
% 5.18/5.34 Clause #69 (by clausification #[58]): Eq subsetE True
% 5.18/5.34 Clause #70 (by clausification #[58]): Eq
% 5.18/5.34 (binintersectEL →
% 5.18/5.34 ∀ (A X : Iota),
% 5.18/5.34 in X (powerset A) →
% 5.18/5.34 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset X Z → subset (binintersect X Y) Z)
% 5.18/5.34 False
% 5.18/5.34 Clause #71 (by backward demodulation #[69, 27]): Eq True (∀ (A B Xx : Iota), subset A B → in Xx A → in Xx B)
% 5.18/5.34 Clause #74 (by clausification #[71]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), subset a B → in Xx a → in Xx B) True
% 5.18/5.34 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), subset a a_1 → in Xx a → in Xx a_1) True
% 5.18/5.34 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 : Iota), Eq (subset a a_1 → in a_2 a → in a_2 a_1) True
% 5.18/5.34 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Eq (in a_2 a → in a_2 a_1) True)
% 5.20/5.36 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) False) (Or (Eq (in a_2 a) False) (Eq (in a_2 a_1) True))
% 5.20/5.36 Clause #79 (by forward demodulation #[14, 57]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False))
% 5.20/5.36 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a_1) False)
% 5.20/5.36 Clause #81 (by clausification #[70]): Eq binintersectEL True
% 5.20/5.36 Clause #82 (by clausification #[70]): Eq
% 5.20/5.36 (∀ (A X : Iota),
% 5.20/5.36 in X (powerset A) →
% 5.20/5.36 ∀ (Y : Iota), in Y (powerset A) → ∀ (Z : Iota), in Z (powerset A) → subset X Z → subset (binintersect X Y) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #83 (by backward demodulation #[81, 23]): Eq True (∀ (A B Xx : Iota), in Xx (binintersect A B) → in Xx A)
% 5.20/5.36 Clause #86 (by clausification #[83]): ∀ (a : Iota), Eq (∀ (B Xx : Iota), in Xx (binintersect a B) → in Xx a) True
% 5.20/5.36 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota), Eq (∀ (Xx : Iota), in Xx (binintersect a a_1) → in Xx a) True
% 5.20/5.36 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota), Eq (in a (binintersect a_1 a_2) → in a a_1) True
% 5.20/5.36 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota), Or (Eq (in a (binintersect a_1 a_2)) False) (Eq (in a a_1) True)
% 5.20/5.36 Clause #91 (by clausification #[82]): ∀ (a : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (Not
% 5.20/5.36 (∀ (X : Iota),
% 5.20/5.36 in X (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Y : Iota),
% 5.20/5.36 in Y (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset X Z → subset (binintersect X Y) Z))
% 5.20/5.36 True
% 5.20/5.36 Clause #92 (by clausification #[91]): ∀ (a : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (∀ (X : Iota),
% 5.20/5.36 in X (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Y : Iota),
% 5.20/5.36 in Y (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota), in Z (powerset (skS.0 10 a)) → subset X Z → subset (binintersect X Y) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #93 (by clausification #[92]): ∀ (a a_1 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (Not
% 5.20/5.36 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Y : Iota),
% 5.20/5.36 in Y (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) → subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) Y) Z))
% 5.20/5.36 True
% 5.20/5.36 Clause #94 (by clausification #[93]): ∀ (a a_1 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (in (skS.0 11 a a_1) (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Y : Iota),
% 5.20/5.36 in Y (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) → subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) Y) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #96 (by clausification #[94]): ∀ (a a_1 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (∀ (Y : Iota),
% 5.20/5.36 in Y (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) → subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) Y) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #103 (by clausification #[96]): ∀ (a a_1 a_2 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (Not
% 5.20/5.36 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) →
% 5.20/5.36 subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z))
% 5.20/5.36 True
% 5.20/5.36 Clause #104 (by clausification #[103]): ∀ (a a_1 a_2 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (in (skS.0 12 a a_1 a_2) (powerset (skS.0 10 a)) →
% 5.20/5.36 ∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) →
% 5.20/5.36 subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #106 (by clausification #[104]): ∀ (a a_1 a_2 : Iota),
% 5.20/5.36 Eq
% 5.20/5.36 (∀ (Z : Iota),
% 5.20/5.36 in Z (powerset (skS.0 10 a)) →
% 5.20/5.36 subset (skS.0 11 a a_1) Z → subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) Z)
% 5.20/5.36 False
% 5.20/5.36 Clause #107 (by clausification #[60]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (in (skS.0 0 a a_1 a_2) a) True)
% 5.20/5.36 Clause #108 (by superposition #[107, 89]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.36 Or (Eq (subset (binintersect a a_1) a_2) True)
% 5.20/5.36 (Or (Eq True False) (Eq (in (skS.0 0 (binintersect a a_1) a_2 a_3) a) True))
% 5.20/5.38 Clause #111 (by clausification #[108]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.38 Or (Eq (subset (binintersect a a_1) a_2) True) (Eq (in (skS.0 0 (binintersect a a_1) a_2 a_3) a) True)
% 5.20/5.38 Clause #122 (by clausification #[106]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.38 Eq
% 5.20/5.38 (Not
% 5.20/5.38 (in (skS.0 13 a a_1 a_2 a_3) (powerset (skS.0 10 a)) →
% 5.20/5.38 subset (skS.0 11 a a_1) (skS.0 13 a a_1 a_2 a_3) →
% 5.20/5.38 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3)))
% 5.20/5.38 True
% 5.20/5.38 Clause #123 (by clausification #[122]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.38 Eq
% 5.20/5.38 (in (skS.0 13 a a_1 a_2 a_3) (powerset (skS.0 10 a)) →
% 5.20/5.38 subset (skS.0 11 a a_1) (skS.0 13 a a_1 a_2 a_3) →
% 5.20/5.38 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3))
% 5.20/5.38 False
% 5.20/5.38 Clause #125 (by clausification #[123]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.38 Eq
% 5.20/5.38 (subset (skS.0 11 a a_1) (skS.0 13 a a_1 a_2 a_3) →
% 5.20/5.38 subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3))
% 5.20/5.38 False
% 5.20/5.38 Clause #150 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota), Eq (subset (skS.0 11 a a_1) (skS.0 13 a a_1 a_2 a_3)) True
% 5.20/5.38 Clause #151 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.20/5.38 Eq (subset (binintersect (skS.0 11 a a_1) (skS.0 12 a a_1 a_2)) (skS.0 13 a a_1 a_2 a_3)) False
% 5.20/5.38 Clause #152 (by superposition #[150, 78]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.20/5.38 Or (Eq True False) (Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 13 a_1 a_2 a_3 a_4)) True))
% 5.20/5.38 Clause #160 (by clausification #[152]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (in a (skS.0 11 a_1 a_2)) False) (Eq (in a (skS.0 13 a_1 a_2 a_3 a_4)) True)
% 5.20/5.38 Clause #163 (by superposition #[160, 111]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.20/5.38 Or (Eq (in (skS.0 0 (binintersect (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 13 a a_1 a_5 a_6)) True)
% 5.20/5.38 (Or (Eq (subset (binintersect (skS.0 11 a a_1) a_2) a_3) True) (Eq False True))
% 5.20/5.38 Clause #253 (by clausification #[163]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 5.20/5.38 Or (Eq (in (skS.0 0 (binintersect (skS.0 11 a a_1) a_2) a_3 a_4) (skS.0 13 a a_1 a_5 a_6)) True)
% 5.20/5.38 (Eq (subset (binintersect (skS.0 11 a a_1) a_2) a_3) True)
% 5.20/5.38 Clause #254 (by superposition #[253, 80]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.20/5.38 Or (Eq (subset (binintersect (skS.0 11 a a_1) a_2) (skS.0 13 a a_1 a_3 a_4)) True)
% 5.20/5.38 (Or (Eq (subset (binintersect (skS.0 11 a a_1) a_2) (skS.0 13 a a_1 a_3 a_4)) True) (Eq True False))
% 5.20/5.38 Clause #272 (by clausification #[254]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 5.20/5.38 Or (Eq (subset (binintersect (skS.0 11 a a_1) a_2) (skS.0 13 a a_1 a_3 a_4)) True)
% 5.20/5.38 (Eq (subset (binintersect (skS.0 11 a a_1) a_2) (skS.0 13 a a_1 a_3 a_4)) True)
% 5.20/5.38 Clause #273 (by eliminate duplicate literals #[272]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Eq (subset (binintersect (skS.0 11 a a_1) a_2) (skS.0 13 a a_1 a_3 a_4)) True
% 5.20/5.38 Clause #274 (by superposition #[273, 151]): Eq True False
% 5.20/5.38 Clause #276 (by clausification #[274]): False
% 5.20/5.38 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------