TSTP Solution File: SEU628^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU628^2 : 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 16:43:05 EDT 2023
% Result : Theorem 4.36s 4.53s
% Output : Proof 4.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SEU628^2 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.36 % Computer : n010.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Wed Aug 23 20:25:36 EDT 2023
% 0.14/0.36 % CPUTime :
% 4.36/4.53 SZS status Theorem for theBenchmark.p
% 4.36/4.53 SZS output start Proof for theBenchmark.p
% 4.36/4.53 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True
% 4.36/4.53 Clause #1 (by assumption #[]): Eq
% 4.36/4.53 (Eq ubforcartprodlem1
% 4.36/4.53 (∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion A B))))
% 4.36/4.53 True
% 4.36/4.53 Clause #2 (by assumption #[]): Eq
% 4.36/4.53 (Not
% 4.36/4.53 (powersetI1 →
% 4.36/4.53 ubforcartprodlem1 →
% 4.36/4.53 ∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (powerset (binunion A B)))))
% 4.36/4.53 True
% 4.36/4.53 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))
% 4.36/4.53 Clause #16 (by clausification #[1]): Eq ubforcartprodlem1
% 4.36/4.53 (∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion A B)))
% 4.36/4.53 Clause #34 (by clausification #[2]): Eq
% 4.36/4.53 (powersetI1 →
% 4.36/4.53 ubforcartprodlem1 →
% 4.36/4.53 ∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (powerset (binunion A B))))
% 4.36/4.53 False
% 4.36/4.53 Clause #35 (by clausification #[34]): Eq powersetI1 True
% 4.36/4.53 Clause #36 (by clausification #[34]): Eq
% 4.36/4.53 (ubforcartprodlem1 →
% 4.36/4.53 ∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (powerset (binunion A B))))
% 4.36/4.53 False
% 4.36/4.53 Clause #37 (by backward demodulation #[35, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A))
% 4.36/4.53 Clause #41 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True
% 4.36/4.53 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True
% 4.36/4.53 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True)
% 4.36/4.53 Clause #48 (by clausification #[36]): Eq ubforcartprodlem1 True
% 4.36/4.53 Clause #49 (by clausification #[36]): Eq
% 4.36/4.53 (∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (powerset (binunion A B))))
% 4.36/4.53 False
% 4.36/4.53 Clause #50 (by backward demodulation #[48, 16]): Eq True
% 4.36/4.53 (∀ (A B Xx : Iota),
% 4.36/4.53 in Xx A →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion A B)))
% 4.36/4.53 Clause #55 (by clausification #[50]): ∀ (a : Iota),
% 4.36/4.53 Eq
% 4.36/4.53 (∀ (B Xx : Iota),
% 4.36/4.53 in Xx a →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy B →
% 4.36/4.53 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion a B)))
% 4.36/4.53 True
% 4.36/4.53 Clause #56 (by clausification #[55]): ∀ (a a_1 : Iota),
% 4.36/4.53 Eq
% 4.36/4.53 (∀ (Xx : Iota),
% 4.36/4.53 in Xx a →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy a_1 →
% 4.36/4.53 subset (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion a a_1)))
% 4.36/4.53 True
% 4.36/4.53 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 4.36/4.53 Eq
% 4.36/4.53 (in a a_1 →
% 4.36/4.53 ∀ (Xy : Iota),
% 4.36/4.53 in Xy a_2 →
% 4.36/4.53 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))
% 4.36/4.53 (powerset (binunion a_1 a_2)))
% 4.36/4.53 True
% 4.36/4.53 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 : Iota),
% 4.36/4.53 Or (Eq (in a a_1) False)
% 4.37/4.55 (Eq
% 4.37/4.55 (∀ (Xy : Iota),
% 4.37/4.55 in Xy a_2 →
% 4.37/4.55 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (binunion a_1 a_2)))
% 4.37/4.55 True)
% 4.37/4.55 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.37/4.55 Or (Eq (in a a_1) False)
% 4.37/4.55 (Eq
% 4.37/4.55 (in a_2 a_3 →
% 4.37/4.55 subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset))
% 4.37/4.55 (powerset (binunion a_1 a_3)))
% 4.37/4.55 True)
% 4.37/4.55 Clause #60 (by clausification #[59]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.37/4.55 Or (Eq (in a a_1) False)
% 4.37/4.55 (Or (Eq (in a_2 a_3) False)
% 4.37/4.55 (Eq
% 4.37/4.55 (subset (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_2 emptyset)) emptyset))
% 4.37/4.55 (powerset (binunion a_1 a_3)))
% 4.37/4.55 True))
% 4.37/4.55 Clause #61 (by clausification #[49]): ∀ (a : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (Not
% 4.37/4.55 (∀ (B Xx : Iota),
% 4.37/4.55 in Xx (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy B →
% 4.37/4.55 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) B)))))
% 4.37/4.55 True
% 4.37/4.55 Clause #62 (by clausification #[61]): ∀ (a : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (∀ (B Xx : Iota),
% 4.37/4.55 in Xx (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy B →
% 4.37/4.55 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) B))))
% 4.37/4.55 False
% 4.37/4.55 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (Not
% 4.37/4.55 (∀ (Xx : Iota),
% 4.37/4.55 in Xx (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy (skS.0 7 a a_1) →
% 4.37/4.55 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))))
% 4.37/4.55 True
% 4.37/4.55 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (∀ (Xx : Iota),
% 4.37/4.55 in Xx (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy (skS.0 7 a a_1) →
% 4.37/4.55 in (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 4.37/4.55 False
% 4.37/4.55 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (Not
% 4.37/4.55 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy (skS.0 7 a a_1) →
% 4.37/4.55 in
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))))
% 4.37/4.55 True
% 4.37/4.55 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) →
% 4.37/4.55 ∀ (Xy : Iota),
% 4.37/4.55 in Xy (skS.0 7 a a_1) →
% 4.37/4.55 in
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 4.37/4.55 False
% 4.37/4.55 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 6 a)) True
% 4.37/4.55 Clause #68 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 4.37/4.55 Eq
% 4.37/4.55 (∀ (Xy : Iota),
% 4.37/4.55 in Xy (skS.0 7 a a_1) →
% 4.37/4.55 in
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) emptyset))
% 4.37/4.55 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 4.37/4.55 False
% 4.37/4.55 Clause #69 (by superposition #[67, 60]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.37/4.55 Or (Eq True False)
% 4.37/4.55 (Or (Eq (in a a_1) False)
% 4.37/4.55 (Eq
% 4.37/4.55 (subset
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) emptyset)
% 4.37/4.55 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset))
% 4.37/4.55 (powerset (binunion (skS.0 6 a_2) a_1)))
% 4.37/4.55 True))
% 4.37/4.55 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.37/4.55 Or (Eq (in a a_1) False)
% 4.37/4.56 (Eq
% 4.37/4.56 (subset
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) emptyset))
% 4.37/4.56 (powerset (binunion (skS.0 6 a_2) a_1)))
% 4.37/4.56 True)
% 4.37/4.56 Clause #72 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.37/4.56 Eq
% 4.37/4.56 (Not
% 4.37/4.56 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) →
% 4.37/4.56 in
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset))
% 4.37/4.56 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))))
% 4.37/4.56 True
% 4.37/4.56 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.37/4.56 Eq
% 4.37/4.56 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) →
% 4.37/4.56 in
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset))
% 4.37/4.56 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 4.37/4.56 False
% 4.37/4.56 Clause #74 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota), Eq (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1)) True
% 4.37/4.56 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.37/4.56 Eq
% 4.37/4.56 (in
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset))
% 4.37/4.56 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 4.37/4.56 False
% 4.37/4.56 Clause #77 (by superposition #[74, 70]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.37/4.56 Or (Eq True False)
% 4.37/4.56 (Eq
% 4.37/4.56 (subset
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset))
% 4.37/4.56 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))
% 4.37/4.56 True)
% 4.37/4.56 Clause #87 (by clausification #[77]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.37/4.56 Eq
% 4.37/4.56 (subset
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset))
% 4.37/4.56 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))
% 4.37/4.56 True
% 4.37/4.56 Clause #88 (by superposition #[87, 43]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.37/4.56 Or (Eq True False)
% 4.37/4.56 (Eq
% 4.37/4.56 (in
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset))
% 4.37/4.56 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))))
% 4.37/4.56 True)
% 4.37/4.56 Clause #91 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 4.37/4.56 Eq
% 4.37/4.56 (in
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.37/4.56 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset)) emptyset))
% 4.37/4.56 (powerset (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))))
% 4.37/4.56 True
% 4.37/4.56 Clause #95 (by superposition #[91, 75]): Eq True False
% 4.37/4.56 Clause #96 (by clausification #[95]): False
% 4.37/4.56 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------