TSTP Solution File: SEU651^2 by Duper---1.0
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%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU651^2 : TPTP v8.1.2. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n017.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 16:43:13 EDT 2023
% Result : Theorem 4.33s 4.49s
% Output : Proof 4.33s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU651^2 : TPTP v8.1.2. Released v3.7.0.
% 0.11/0.13 % Command : duper %s
% 0.13/0.35 % Computer : n017.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 19:14:54 EDT 2023
% 0.13/0.35 % CPUTime :
% 4.33/4.49 SZS status Theorem for theBenchmark.p
% 4.33/4.49 SZS output start Proof for theBenchmark.p
% 4.33/4.49 Clause #0 (by assumption #[]): Eq (Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)) True
% 4.33/4.49 Clause #1 (by assumption #[]): Eq (Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))) True
% 4.33/4.49 Clause #2 (by assumption #[]): Eq
% 4.33/4.49 (Eq setukpairinjR12
% 4.33/4.49 (∀ (Xx Xy : Iota),
% 4.33/4.49 Eq Xx Xy →
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xx emptyset) emptyset)))
% 4.33/4.49 True
% 4.33/4.49 Clause #3 (by assumption #[]): Eq
% 4.33/4.49 (Not
% 4.33/4.49 (uniqinunit →
% 4.33/4.49 secondinupair →
% 4.33/4.49 setukpairinjR12 →
% 4.33/4.49 ∀ (Xx Xy Xz Xu : Iota),
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.49 Eq Xz Xu → Eq Xy Xu))
% 4.33/4.49 True
% 4.33/4.49 Clause #4 (by clausification #[0]): Eq uniqinunit (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)
% 4.33/4.49 Clause #18 (by clausification #[1]): Eq secondinupair (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset)))
% 4.33/4.49 Clause #20 (by clausify Prop equality #[18]): Or (Eq secondinupair False) (Eq (∀ (Xx Xy : Iota), in Xy (setadjoin Xx (setadjoin Xy emptyset))) True)
% 4.33/4.49 Clause #22 (by clausification #[2]): Eq setukpairinjR12
% 4.33/4.49 (∀ (Xx Xy : Iota),
% 4.33/4.49 Eq Xx Xy →
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xx emptyset) emptyset))
% 4.33/4.49 Clause #26 (by clausification #[20]): ∀ (a : Iota), Or (Eq secondinupair False) (Eq (∀ (Xy : Iota), in Xy (setadjoin a (setadjoin Xy emptyset))) True)
% 4.33/4.49 Clause #27 (by clausification #[26]): ∀ (a a_1 : Iota), Or (Eq secondinupair False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True)
% 4.33/4.49 Clause #32 (by clausification #[3]): Eq
% 4.33/4.49 (uniqinunit →
% 4.33/4.49 secondinupair →
% 4.33/4.49 setukpairinjR12 →
% 4.33/4.49 ∀ (Xx Xy Xz Xu : Iota),
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.49 Eq Xz Xu → Eq Xy Xu)
% 4.33/4.49 False
% 4.33/4.49 Clause #33 (by clausification #[32]): Eq uniqinunit True
% 4.33/4.49 Clause #34 (by clausification #[32]): Eq
% 4.33/4.49 (secondinupair →
% 4.33/4.49 setukpairinjR12 →
% 4.33/4.49 ∀ (Xx Xy Xz Xu : Iota),
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.49 Eq Xz Xu → Eq Xy Xu)
% 4.33/4.49 False
% 4.33/4.49 Clause #35 (by backward demodulation #[33, 4]): Eq True (∀ (Xx Xy : Iota), in Xx (setadjoin Xy emptyset) → Eq Xx Xy)
% 4.33/4.49 Clause #38 (by clausification #[35]): ∀ (a : Iota), Eq (∀ (Xy : Iota), in a (setadjoin Xy emptyset) → Eq a Xy) True
% 4.33/4.49 Clause #39 (by clausification #[38]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 emptyset) → Eq a a_1) True
% 4.33/4.49 Clause #40 (by clausification #[39]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq (Eq a a_1) True)
% 4.33/4.49 Clause #41 (by clausification #[40]): ∀ (a a_1 : Iota), Or (Eq (in a (setadjoin a_1 emptyset)) False) (Eq a a_1)
% 4.33/4.49 Clause #44 (by clausification #[34]): Eq secondinupair True
% 4.33/4.49 Clause #45 (by clausification #[34]): Eq
% 4.33/4.49 (setukpairinjR12 →
% 4.33/4.49 ∀ (Xx Xy Xz Xu : Iota),
% 4.33/4.49 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.49 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.49 Eq Xz Xu → Eq Xy Xu)
% 4.33/4.49 False
% 4.33/4.49 Clause #47 (by backward demodulation #[44, 27]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True)
% 4.33/4.49 Clause #49 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (in a (setadjoin a_1 (setadjoin a emptyset))) True
% 4.33/4.49 Clause #51 (by clausification #[45]): Eq setukpairinjR12 True
% 4.33/4.51 Clause #52 (by clausification #[45]): Eq
% 4.33/4.51 (∀ (Xx Xy Xz Xu : Iota),
% 4.33/4.51 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq Xz Xu → Eq Xy Xu)
% 4.33/4.51 False
% 4.33/4.51 Clause #53 (by backward demodulation #[51, 22]): Eq True
% 4.33/4.51 (∀ (Xx Xy : Iota),
% 4.33/4.51 Eq Xx Xy →
% 4.33/4.51 Eq (setadjoin (setadjoin Xx emptyset) (setadjoin (setadjoin Xx (setadjoin Xy emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xx emptyset) emptyset))
% 4.33/4.51 Clause #62 (by clausification #[52]): ∀ (a : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (Not
% 4.33/4.51 (∀ (Xy Xz Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq Xz Xu → Eq Xy Xu))
% 4.33/4.51 True
% 4.33/4.51 Clause #63 (by clausification #[62]): ∀ (a : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (∀ (Xy Xz Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin Xy emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq Xz Xu → Eq Xy Xu)
% 4.33/4.51 False
% 4.33/4.51 Clause #64 (by clausification #[63]): ∀ (a a_1 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (Not
% 4.33/4.51 (∀ (Xz Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq Xz Xu → Eq (skS.0 7 a a_1) Xu))
% 4.33/4.51 True
% 4.33/4.51 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (∀ (Xz Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin Xz emptyset) (setadjoin (setadjoin Xz (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq Xz Xu → Eq (skS.0 7 a a_1) Xu)
% 4.33/4.51 False
% 4.33/4.51 Clause #66 (by clausification #[65]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (Not
% 4.33/4.51 (∀ (Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq (skS.0 8 a a_1 a_2) Xu → Eq (skS.0 7 a a_1) Xu))
% 4.33/4.51 True
% 4.33/4.51 Clause #67 (by clausification #[66]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (∀ (Xu : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin Xu emptyset)) emptyset)) →
% 4.33/4.51 Eq (skS.0 8 a a_1 a_2) Xu → Eq (skS.0 7 a a_1) Xu)
% 4.33/4.51 False
% 4.33/4.51 Clause #68 (by clausification #[67]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (Not
% 4.33/4.51 (Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)) →
% 4.33/4.51 Eq (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3) → Eq (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)))
% 4.33/4.51 True
% 4.33/4.51 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.51 Eq
% 4.33/4.51 (Eq
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.51 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)) →
% 4.33/4.53 Eq (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3) → Eq (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3))
% 4.33/4.53 False
% 4.33/4.53 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (Eq
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset)))
% 4.33/4.53 True
% 4.33/4.53 Clause #71 (by clausification #[69]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.53 Eq (Eq (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3) → Eq (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)) False
% 4.33/4.53 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 9 a a_1 a_2 a_3) emptyset)) emptyset))
% 4.33/4.53 Clause #74 (by clausification #[53]): ∀ (a : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (∀ (Xy : Iota),
% 4.33/4.53 Eq a Xy →
% 4.33/4.53 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin Xy emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset))
% 4.33/4.53 True
% 4.33/4.53 Clause #75 (by clausification #[74]): ∀ (a a_1 : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (Eq a a_1 →
% 4.33/4.53 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset))
% 4.33/4.53 True
% 4.33/4.53 Clause #76 (by clausification #[75]): ∀ (a a_1 : Iota),
% 4.33/4.53 Or (Eq (Eq a a_1) False)
% 4.33/4.53 (Eq
% 4.33/4.53 (Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset))
% 4.33/4.53 True)
% 4.33/4.53 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota),
% 4.33/4.53 Or
% 4.33/4.53 (Eq
% 4.33/4.53 (Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset))
% 4.33/4.53 True)
% 4.33/4.53 (Ne a a_1)
% 4.33/4.53 Clause #78 (by clausification #[77]): ∀ (a a_1 : Iota),
% 4.33/4.53 Or (Ne a a_1)
% 4.33/4.53 (Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a_1 emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset))
% 4.33/4.53 Clause #79 (by destructive equality resolution #[78]): ∀ (a : Iota),
% 4.33/4.53 Eq (setadjoin (setadjoin a emptyset) (setadjoin (setadjoin a (setadjoin a emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin a emptyset) emptyset)
% 4.33/4.53 Clause #80 (by superposition #[79, 49]): ∀ (a : Iota), Eq (in (setadjoin a (setadjoin a emptyset)) (setadjoin (setadjoin a emptyset) emptyset)) True
% 4.33/4.53 Clause #81 (by superposition #[80, 41]): ∀ (a : Iota), Or (Eq True False) (Eq (setadjoin a (setadjoin a emptyset)) (setadjoin a emptyset))
% 4.33/4.53 Clause #82 (by clausification #[81]): ∀ (a : Iota), Eq (setadjoin a (setadjoin a emptyset)) (setadjoin a emptyset)
% 4.33/4.53 Clause #93 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3)) True
% 4.33/4.53 Clause #94 (by clausification #[71]): ∀ (a a_1 a_2 a_3 : Iota), Eq (Eq (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)) False
% 4.33/4.53 Clause #95 (by clausification #[93]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 8 a a_1 a_2) (skS.0 9 a a_1 a_2 a_3)
% 4.33/4.53 Clause #96 (by backward demodulation #[95, 72]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) emptyset))
% 4.33/4.53 Clause #97 (by clausification #[94]): ∀ (a a_1 a_2 a_3 : Iota), Ne (skS.0 7 a a_1) (skS.0 9 a a_1 a_2 a_3)
% 4.33/4.53 Clause #98 (by forward demodulation #[97, 95]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)
% 4.33/4.53 Clause #103 (by forward demodulation #[96, 82]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.53 Eq
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.53 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.54 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) emptyset))
% 4.33/4.54 Clause #104 (by forward demodulation #[103, 82]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.54 Eq
% 4.33/4.54 (setadjoin (setadjoin (skS.0 6 a) emptyset)
% 4.33/4.54 (setadjoin (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) emptyset))
% 4.33/4.54 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) emptyset)
% 4.33/4.54 Clause #106 (by superposition #[104, 104]): ∀ (a a_1 a_2 a_3 : Iota),
% 4.33/4.54 Eq (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) emptyset)
% 4.33/4.54 (setadjoin (setadjoin (skS.0 8 a a_1 a_3) emptyset) emptyset)
% 4.33/4.54 Clause #107 (by superposition #[104, 49]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.54 Eq
% 4.33/4.54 (in (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset))
% 4.33/4.54 (setadjoin (setadjoin (skS.0 8 a a_1 a_2) emptyset) emptyset))
% 4.33/4.54 True
% 4.33/4.54 Clause #111 (by superposition #[106, 41]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 4.33/4.54 Or (Eq (in a (setadjoin (setadjoin (skS.0 8 a_1 a_2 a_3) emptyset) emptyset)) False)
% 4.33/4.54 (Eq a (setadjoin (skS.0 8 a_1 a_2 a_4) emptyset))
% 4.33/4.54 Clause #126 (by superposition #[111, 107]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.54 Or (Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset))
% 4.33/4.54 (Eq False True)
% 4.33/4.54 Clause #127 (by clausification #[126]): ∀ (a a_1 a_2 : Iota),
% 4.33/4.54 Eq (setadjoin (skS.0 6 a) (setadjoin (skS.0 7 a a_1) emptyset)) (setadjoin (skS.0 8 a a_1 a_2) emptyset)
% 4.33/4.54 Clause #130 (by superposition #[127, 49]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 7 a a_1) (setadjoin (skS.0 8 a a_1 a_2) emptyset)) True
% 4.33/4.54 Clause #142 (by superposition #[130, 41]): ∀ (a a_1 a_2 : Iota), Or (Eq True False) (Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 4.33/4.54 Clause #144 (by clausification #[142]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)
% 4.33/4.54 Clause #145 (by forward contextual literal cutting #[144, 98]): False
% 4.33/4.54 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------