TSTP Solution File: SEU626^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU626^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 16:43:04 EDT 2023
% Result : Theorem 3.83s 4.03s
% Output : Proof 3.83s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEU626^2 : TPTP v8.1.2. Released v3.7.0.
% 0.07/0.13 % Command : duper %s
% 0.13/0.34 % Computer : n023.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 20:46:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 3.83/4.03 SZS status Theorem for theBenchmark.p
% 3.83/4.03 SZS output start Proof for theBenchmark.p
% 3.83/4.03 Clause #0 (by assumption #[]): Eq (Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))) True
% 3.83/4.03 Clause #1 (by assumption #[]): Eq
% 3.83/4.03 (Eq upairsubunion
% 3.83/4.03 (∀ (A B Xx : Iota),
% 3.83/4.03 in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B)))
% 3.83/4.03 True
% 3.83/4.03 Clause #2 (by assumption #[]): Eq
% 3.83/4.03 (Not
% 3.83/4.03 (powersetI1 →
% 3.83/4.03 upairsubunion →
% 3.83/4.03 ∀ (A B Xx : Iota),
% 3.83/4.03 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B))))
% 3.83/4.03 True
% 3.83/4.03 Clause #3 (by clausification #[0]): Eq powersetI1 (∀ (A B : Iota), subset B A → in B (powerset A))
% 3.83/4.03 Clause #16 (by clausification #[1]): Eq upairsubunion
% 3.83/4.03 (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B))
% 3.83/4.03 Clause #34 (by clausification #[2]): Eq
% 3.83/4.03 (powersetI1 →
% 3.83/4.03 upairsubunion →
% 3.83/4.03 ∀ (A B Xx : Iota),
% 3.83/4.03 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B)))
% 3.83/4.03 False
% 3.83/4.03 Clause #35 (by clausification #[34]): Eq powersetI1 True
% 3.83/4.03 Clause #36 (by clausification #[34]): Eq
% 3.83/4.03 (upairsubunion →
% 3.83/4.03 ∀ (A B Xx : Iota),
% 3.83/4.03 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B)))
% 3.83/4.03 False
% 3.83/4.03 Clause #37 (by backward demodulation #[35, 3]): Eq True (∀ (A B : Iota), subset B A → in B (powerset A))
% 3.83/4.03 Clause #41 (by clausification #[37]): ∀ (a : Iota), Eq (∀ (B : Iota), subset B a → in B (powerset a)) True
% 3.83/4.03 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota), Eq (subset a a_1 → in a (powerset a_1)) True
% 3.83/4.03 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) False) (Eq (in a (powerset a_1)) True)
% 3.83/4.03 Clause #48 (by clausification #[36]): Eq upairsubunion True
% 3.83/4.03 Clause #49 (by clausification #[36]): Eq
% 3.83/4.03 (∀ (A B Xx : Iota),
% 3.83/4.03 in Xx A → ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion A B)))
% 3.83/4.03 False
% 3.83/4.03 Clause #50 (by backward demodulation #[48, 16]): Eq True
% 3.83/4.03 (∀ (A B Xx : Iota), in Xx A → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion A B))
% 3.83/4.03 Clause #54 (by clausification #[50]): ∀ (a : Iota),
% 3.83/4.03 Eq (∀ (B Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy B → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion a B))
% 3.83/4.03 True
% 3.83/4.03 Clause #55 (by clausification #[54]): ∀ (a a_1 : Iota),
% 3.83/4.03 Eq
% 3.83/4.03 (∀ (Xx : Iota), in Xx a → ∀ (Xy : Iota), in Xy a_1 → subset (setadjoin Xx (setadjoin Xy emptyset)) (binunion a a_1))
% 3.83/4.03 True
% 3.83/4.03 Clause #56 (by clausification #[55]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.03 Eq (in a a_1 → ∀ (Xy : Iota), in Xy a_2 → subset (setadjoin a (setadjoin Xy emptyset)) (binunion a_1 a_2)) True
% 3.83/4.03 Clause #57 (by clausification #[56]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.03 Or (Eq (in a a_1) False)
% 3.83/4.03 (Eq (∀ (Xy : Iota), in Xy a_2 → subset (setadjoin a (setadjoin Xy emptyset)) (binunion a_1 a_2)) True)
% 3.83/4.03 Clause #58 (by clausification #[57]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.83/4.03 Or (Eq (in a a_1) False) (Eq (in a_2 a_3 → subset (setadjoin a (setadjoin a_2 emptyset)) (binunion a_1 a_3)) True)
% 3.83/4.03 Clause #59 (by clausification #[58]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.83/4.03 Or (Eq (in a a_1) False)
% 3.83/4.03 (Or (Eq (in a_2 a_3) False) (Eq (subset (setadjoin a (setadjoin a_2 emptyset)) (binunion a_1 a_3)) True))
% 3.83/4.03 Clause #60 (by clausification #[49]): ∀ (a : Iota),
% 3.83/4.03 Eq
% 3.83/4.03 (Not
% 3.83/4.03 (∀ (B Xx : Iota),
% 3.83/4.03 in Xx (skS.0 6 a) →
% 3.83/4.03 ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) B))))
% 3.83/4.03 True
% 3.83/4.03 Clause #61 (by clausification #[60]): ∀ (a : Iota),
% 3.83/4.03 Eq
% 3.83/4.03 (∀ (B Xx : Iota),
% 3.83/4.03 in Xx (skS.0 6 a) →
% 3.83/4.03 ∀ (Xy : Iota), in Xy B → in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) B)))
% 3.83/4.03 False
% 3.83/4.03 Clause #62 (by clausification #[61]): ∀ (a a_1 : Iota),
% 3.83/4.03 Eq
% 3.83/4.03 (Not
% 3.83/4.03 (∀ (Xx : Iota),
% 3.83/4.03 in Xx (skS.0 6 a) →
% 3.83/4.03 ∀ (Xy : Iota),
% 3.83/4.03 in Xy (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 3.83/4.05 True
% 3.83/4.05 Clause #63 (by clausification #[62]): ∀ (a a_1 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (∀ (Xx : Iota),
% 3.83/4.05 in Xx (skS.0 6 a) →
% 3.83/4.05 ∀ (Xy : Iota),
% 3.83/4.05 in Xy (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin Xx (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))
% 3.83/4.05 False
% 3.83/4.05 Clause #64 (by clausification #[63]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (Not
% 3.83/4.05 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) →
% 3.83/4.05 ∀ (Xy : Iota),
% 3.83/4.05 in Xy (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 3.83/4.05 True
% 3.83/4.05 Clause #65 (by clausification #[64]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (in (skS.0 8 a a_1 a_2) (skS.0 6 a) →
% 3.83/4.05 ∀ (Xy : Iota),
% 3.83/4.05 in Xy (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))
% 3.83/4.05 False
% 3.83/4.05 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 8 a a_1 a_2) (skS.0 6 a)) True
% 3.83/4.05 Clause #67 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (∀ (Xy : Iota),
% 3.83/4.05 in Xy (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xy emptyset)) (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))
% 3.83/4.05 False
% 3.83/4.05 Clause #68 (by superposition #[66, 59]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.83/4.05 Or (Eq True False)
% 3.83/4.05 (Or (Eq (in a a_1) False)
% 3.83/4.05 (Eq (subset (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) (binunion (skS.0 6 a_2) a_1)) True))
% 3.83/4.05 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 3.83/4.05 Or (Eq (in a a_1) False)
% 3.83/4.05 (Eq (subset (setadjoin (skS.0 8 a_2 a_3 a_4) (setadjoin a emptyset)) (binunion (skS.0 6 a_2) a_1)) True)
% 3.83/4.05 Clause #71 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (Not
% 3.83/4.05 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1)))))
% 3.83/4.05 True
% 3.83/4.05 Clause #72 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (in (skS.0 9 a a_1 a_2 a_3) (skS.0 7 a a_1) →
% 3.83/4.05 in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))
% 3.83/4.05 False
% 3.83/4.05 Clause #73 (by clausification #[72]): ∀ (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
% 3.83/4.05 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 a_3 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a a_1))))
% 3.83/4.05 False
% 3.83/4.05 Clause #76 (by superposition #[73, 69]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.83/4.05 Or (Eq True False)
% 3.83/4.05 (Eq
% 3.83/4.05 (subset (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset))
% 3.83/4.05 (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))
% 3.83/4.05 True)
% 3.83/4.05 Clause #89 (by clausification #[76]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (subset (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset))
% 3.83/4.05 (binunion (skS.0 6 a) (skS.0 7 a_3 a_4)))
% 3.83/4.05 True
% 3.83/4.05 Clause #90 (by superposition #[89, 43]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.83/4.05 Or (Eq True False)
% 3.83/4.05 (Eq
% 3.83/4.05 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))
% 3.83/4.05 True)
% 3.83/4.05 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 3.83/4.05 Eq
% 3.83/4.05 (in (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a_3 a_4 a_5 a_6) emptyset))
% 3.83/4.05 (powerset (binunion (skS.0 6 a) (skS.0 7 a_3 a_4))))
% 3.83/4.05 True
% 3.83/4.05 Clause #92 (by superposition #[91, 74]): Eq True False
% 3.83/4.05 Clause #96 (by clausification #[92]): False
% 3.83/4.05 SZS output end Proof for theBenchmark.p
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