TSTP Solution File: SET600+3 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n009.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 14:46:59 EDT 2023
% Result : Theorem 147.60s 147.81s
% Output : Proof 147.98s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET600+3 : TPTP v8.1.2. Released v2.2.0.
% 0.07/0.13 % Command : duper %s
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sat Aug 26 09:35:20 EDT 2023
% 0.14/0.35 % CPUTime :
% 147.60/147.81 SZS status Theorem for theBenchmark.p
% 147.60/147.81 SZS output start Proof for theBenchmark.p
% 147.60/147.81 Clause #0 (by assumption #[]): Eq (∀ (B C D : Iota), Iff (member D (union B C)) (Or (member D B) (member D C))) True
% 147.60/147.81 Clause #1 (by assumption #[]): Eq (∀ (B : Iota), Not (member B empty_set)) True
% 147.60/147.81 Clause #2 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (And (subset B C) (subset C B))) True
% 147.60/147.81 Clause #3 (by assumption #[]): Eq (∀ (B C : Iota), Eq (union B C) (union C B)) True
% 147.60/147.81 Clause #4 (by assumption #[]): Eq (∀ (B C : Iota), Iff (subset B C) (∀ (D : Iota), member D B → member D C)) True
% 147.60/147.81 Clause #6 (by assumption #[]): Eq (∀ (B : Iota), Iff (empty B) (∀ (C : Iota), Not (member C B))) True
% 147.60/147.81 Clause #7 (by assumption #[]): Eq (∀ (B C : Iota), Iff (Eq B C) (∀ (D : Iota), Iff (member D B) (member D C))) True
% 147.60/147.81 Clause #8 (by assumption #[]): Eq (Not (∀ (B C : Iota), Iff (Eq (union B C) empty_set) (And (Eq B empty_set) (Eq C empty_set)))) True
% 147.60/147.81 Clause #10 (by clausification #[1]): ∀ (a : Iota), Eq (Not (member a empty_set)) True
% 147.60/147.81 Clause #11 (by clausification #[10]): ∀ (a : Iota), Eq (member a empty_set) False
% 147.60/147.81 Clause #12 (by clausification #[6]): ∀ (a : Iota), Eq (Iff (empty a) (∀ (C : Iota), Not (member C a))) True
% 147.60/147.81 Clause #13 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) True) (Eq (∀ (C : Iota), Not (member C a)) False)
% 147.60/147.81 Clause #14 (by clausification #[12]): ∀ (a : Iota), Or (Eq (empty a) False) (Eq (∀ (C : Iota), Not (member C a)) True)
% 147.60/147.81 Clause #15 (by clausification #[13]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (Not (member (skS.0 0 a a_1) a))) True)
% 147.60/147.81 Clause #16 (by clausification #[15]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (Not (member (skS.0 0 a a_1) a)) False)
% 147.60/147.81 Clause #17 (by clausification #[16]): ∀ (a a_1 : Iota), Or (Eq (empty a) True) (Eq (member (skS.0 0 a a_1) a) True)
% 147.60/147.81 Clause #20 (by clausification #[14]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (Not (member a_1 a)) True)
% 147.60/147.81 Clause #21 (by clausification #[20]): ∀ (a a_1 : Iota), Or (Eq (empty a) False) (Eq (member a_1 a) False)
% 147.60/147.81 Clause #23 (by clausification #[0]): ∀ (a : Iota), Eq (∀ (C D : Iota), Iff (member D (union a C)) (Or (member D a) (member D C))) True
% 147.60/147.81 Clause #24 (by clausification #[23]): ∀ (a a_1 : Iota), Eq (∀ (D : Iota), Iff (member D (union a a_1)) (Or (member D a) (member D a_1))) True
% 147.60/147.81 Clause #25 (by clausification #[24]): ∀ (a a_1 a_2 : Iota), Eq (Iff (member a (union a_1 a_2)) (Or (member a a_1) (member a a_2))) True
% 147.60/147.81 Clause #26 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (Or (member a a_1) (member a a_2)) False)
% 147.60/147.81 Clause #27 (by clausification #[25]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Eq (Or (member a a_1) (member a a_2)) True)
% 147.60/147.81 Clause #28 (by clausification #[26]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) True) (Eq (member a a_2) False)
% 147.60/147.81 Clause #32 (by clausification #[3]): ∀ (a : Iota), Eq (∀ (C : Iota), Eq (union a C) (union C a)) True
% 147.60/147.81 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota), Eq (Eq (union a a_1) (union a_1 a)) True
% 147.60/147.81 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota), Eq (union a a_1) (union a_1 a)
% 147.60/147.81 Clause #35 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (subset a C) (∀ (D : Iota), member D a → member D C)) True
% 147.60/147.81 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Eq (Iff (subset a a_1) (∀ (D : Iota), member D a → member D a_1)) True
% 147.60/147.81 Clause #37 (by clausification #[36]): ∀ (a a_1 : Iota), Or (Eq (subset a a_1) True) (Eq (∀ (D : Iota), member D a → member D a_1) False)
% 147.60/147.81 Clause #39 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 147.60/147.81 Or (Eq (subset a a_1) True) (Eq (Not (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1)) True)
% 147.60/147.81 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 147.60/147.81 Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a → member (skS.0 1 a a_1 a_2) a_1) False)
% 147.60/147.81 Clause #41 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a) True)
% 147.66/147.84 Clause #42 (by clausification #[40]): ∀ (a a_1 a_2 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) a_1) False)
% 147.66/147.84 Clause #43 (by superposition #[41, 11]): ∀ (a : Iota), Or (Eq (subset empty_set a) True) (Eq True False)
% 147.66/147.84 Clause #44 (by superposition #[41, 28]): ∀ (a a_1 a_2 a_3 : Iota),
% 147.66/147.84 Or (Eq (subset a a_1) True) (Or (Eq (member (skS.0 1 a a_1 a_2) (union a_3 a)) True) (Eq True False))
% 147.66/147.84 Clause #46 (by clausification #[43]): ∀ (a : Iota), Eq (subset empty_set a) True
% 147.66/147.84 Clause #47 (by clausification #[2]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (And (subset a C) (subset C a))) True
% 147.66/147.84 Clause #48 (by clausification #[47]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (And (subset a a_1) (subset a_1 a))) True
% 147.66/147.84 Clause #49 (by clausification #[48]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (And (subset a a_1) (subset a_1 a)) False)
% 147.66/147.84 Clause #51 (by clausification #[49]): ∀ (a a_1 : Iota), Or (Eq (And (subset a a_1) (subset a_1 a)) False) (Eq a a_1)
% 147.66/147.84 Clause #52 (by clausification #[51]): ∀ (a a_1 : Iota), Or (Eq a a_1) (Or (Eq (subset a a_1) False) (Eq (subset a_1 a) False))
% 147.66/147.84 Clause #53 (by superposition #[52, 46]): ∀ (a : Iota), Or (Eq empty_set a) (Or (Eq (subset a empty_set) False) (Eq False True))
% 147.66/147.84 Clause #56 (by clausification #[53]): ∀ (a : Iota), Or (Eq empty_set a) (Eq (subset a empty_set) False)
% 147.66/147.84 Clause #64 (by clausification #[7]): ∀ (a : Iota), Eq (∀ (C : Iota), Iff (Eq a C) (∀ (D : Iota), Iff (member D a) (member D C))) True
% 147.66/147.84 Clause #65 (by clausification #[64]): ∀ (a a_1 : Iota), Eq (Iff (Eq a a_1) (∀ (D : Iota), Iff (member D a) (member D a_1))) True
% 147.66/147.84 Clause #66 (by clausification #[65]): ∀ (a a_1 : Iota), Or (Eq (Eq a a_1) True) (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False)
% 147.66/147.84 Clause #68 (by clausification #[66]): ∀ (a a_1 : Iota), Or (Eq (∀ (D : Iota), Iff (member D a) (member D a_1)) False) (Eq a a_1)
% 147.66/147.84 Clause #69 (by clausification #[68]): ∀ (a a_1 a_2 : Iota),
% 147.66/147.84 Or (Eq a a_1) (Eq (Not (Iff (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1))) True)
% 147.66/147.84 Clause #70 (by clausification #[69]): ∀ (a a_1 a_2 : Iota), Or (Eq a a_1) (Eq (Iff (member (skS.0 2 a a_1 a_2) a) (member (skS.0 2 a a_1 a_2) a_1)) False)
% 147.66/147.84 Clause #72 (by clausification #[70]): ∀ (a a_1 a_2 : Iota),
% 147.66/147.84 Or (Eq a a_1) (Or (Eq (member (skS.0 2 a a_1 a_2) a) True) (Eq (member (skS.0 2 a a_1 a_2) a_1) True))
% 147.66/147.84 Clause #82 (by clausification #[8]): Eq (∀ (B C : Iota), Iff (Eq (union B C) empty_set) (And (Eq B empty_set) (Eq C empty_set))) False
% 147.66/147.84 Clause #83 (by clausification #[82]): ∀ (a : Iota),
% 147.66/147.84 Eq (Not (∀ (C : Iota), Iff (Eq (union (skS.0 3 a) C) empty_set) (And (Eq (skS.0 3 a) empty_set) (Eq C empty_set))))
% 147.66/147.84 True
% 147.66/147.84 Clause #84 (by clausification #[83]): ∀ (a : Iota),
% 147.66/147.84 Eq (∀ (C : Iota), Iff (Eq (union (skS.0 3 a) C) empty_set) (And (Eq (skS.0 3 a) empty_set) (Eq C empty_set))) False
% 147.66/147.84 Clause #85 (by clausification #[84]): ∀ (a a_1 : Iota),
% 147.66/147.84 Eq
% 147.66/147.84 (Not
% 147.66/147.84 (Iff (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.84 (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set))))
% 147.66/147.84 True
% 147.66/147.84 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota),
% 147.66/147.84 Eq
% 147.66/147.84 (Iff (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.84 (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set)))
% 147.66/147.84 False
% 147.66/147.84 Clause #87 (by clausification #[86]): ∀ (a a_1 : Iota),
% 147.66/147.84 Or (Eq (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) False)
% 147.66/147.84 (Eq (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set)) False)
% 147.66/147.84 Clause #88 (by clausification #[86]): ∀ (a a_1 : Iota),
% 147.66/147.84 Or (Eq (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) True)
% 147.66/147.84 (Eq (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set)) True)
% 147.66/147.84 Clause #89 (by clausification #[87]): ∀ (a a_1 : Iota),
% 147.66/147.84 Or (Eq (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set)) False)
% 147.66/147.84 (Ne (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.84 Clause #90 (by clausification #[89]): ∀ (a a_1 : Iota),
% 147.66/147.84 Or (Ne (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.84 (Or (Eq (Eq (skS.0 3 a) empty_set) False) (Eq (Eq (skS.0 4 a a_1) empty_set) False))
% 147.66/147.86 Clause #91 (by clausification #[90]): ∀ (a a_1 : Iota),
% 147.66/147.86 Or (Ne (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.86 (Or (Eq (Eq (skS.0 4 a a_1) empty_set) False) (Ne (skS.0 3 a) empty_set))
% 147.66/147.86 Clause #92 (by clausification #[91]): ∀ (a a_1 : Iota),
% 147.66/147.86 Or (Ne (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Or (Ne (skS.0 3 a) empty_set) (Ne (skS.0 4 a a_1) empty_set))
% 147.66/147.86 Clause #93 (by clausification #[27]): ∀ (a a_1 a_2 : Iota), Or (Eq (member a (union a_1 a_2)) False) (Or (Eq (member a a_1) True) (Eq (member a a_2) True))
% 147.66/147.86 Clause #94 (by superposition #[93, 17]): ∀ (a a_1 a_2 : Iota),
% 147.66/147.86 Or (Eq (member (skS.0 0 (union a a_1) a_2) a) True)
% 147.66/147.86 (Or (Eq (member (skS.0 0 (union a a_1) a_2) a_1) True) (Or (Eq (empty (union a a_1)) True) (Eq False True)))
% 147.66/147.86 Clause #119 (by clausification #[44]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (subset a a_1) True) (Eq (member (skS.0 1 a a_1 a_2) (union a_3 a)) True)
% 147.66/147.86 Clause #120 (by superposition #[119, 42]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Or (Eq (subset a (union a_1 a)) True) (Eq True False))
% 147.66/147.86 Clause #124 (by clausification #[120]): ∀ (a a_1 : Iota), Or (Eq (subset a (union a_1 a)) True) (Eq (subset a (union a_1 a)) True)
% 147.66/147.86 Clause #125 (by eliminate duplicate literals #[124]): ∀ (a a_1 : Iota), Eq (subset a (union a_1 a)) True
% 147.66/147.86 Clause #128 (by superposition #[125, 34]): ∀ (a a_1 : Iota), Eq (subset a (union a a_1)) True
% 147.66/147.86 Clause #181 (by superposition #[72, 92]): ∀ (a a_1 a_2 a_3 : Iota),
% 147.66/147.86 Or (Eq (member (skS.0 2 a (skS.0 3 a_1) a_2) a) True)
% 147.66/147.86 (Or (Eq (member (skS.0 2 a (skS.0 3 a_1) a_2) (skS.0 3 a_1)) True)
% 147.66/147.86 (Or (Ne (union a (skS.0 4 a_1 a_3)) empty_set) (Or (Ne a empty_set) (Ne (skS.0 4 a_1 a_3) empty_set))))
% 147.66/147.86 Clause #215 (by superposition #[72, 11]): ∀ (a a_1 : Iota), Or (Eq empty_set a) (Or (Eq (member (skS.0 2 empty_set a a_1) a) True) (Eq True False))
% 147.66/147.86 Clause #259 (by clausification #[88]): ∀ (a a_1 : Iota),
% 147.66/147.86 Or (Eq (And (Eq (skS.0 3 a) empty_set) (Eq (skS.0 4 a a_1) empty_set)) True)
% 147.66/147.86 (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set)
% 147.66/147.86 Clause #260 (by clausification #[259]): ∀ (a a_1 : Iota), Or (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Eq (Eq (skS.0 4 a a_1) empty_set) True)
% 147.66/147.86 Clause #261 (by clausification #[259]): ∀ (a a_1 : Iota), Or (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Eq (Eq (skS.0 3 a) empty_set) True)
% 147.66/147.86 Clause #262 (by clausification #[260]): ∀ (a a_1 : Iota), Or (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Eq (skS.0 4 a a_1) empty_set)
% 147.66/147.86 Clause #271 (by superposition #[262, 125]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 a a_1) empty_set) (Eq (subset (skS.0 4 a a_1) empty_set) True)
% 147.66/147.86 Clause #296 (by clausification #[215]): ∀ (a a_1 : Iota), Or (Eq empty_set a) (Eq (member (skS.0 2 empty_set a a_1) a) True)
% 147.66/147.86 Clause #338 (by clausification #[94]): ∀ (a a_1 a_2 : Iota),
% 147.66/147.86 Or (Eq (member (skS.0 0 (union a a_1) a_2) a) True)
% 147.66/147.86 (Or (Eq (member (skS.0 0 (union a a_1) a_2) a_1) True) (Eq (empty (union a a_1)) True))
% 147.66/147.86 Clause #355 (by equality factoring #[338]): ∀ (a a_1 : Iota), Or (Eq (empty (union a a)) True) (Or (Ne True True) (Eq (member (skS.0 0 (union a a) a_1) a) True))
% 147.66/147.86 Clause #858 (by clausification #[355]): ∀ (a a_1 : Iota),
% 147.66/147.86 Or (Eq (empty (union a a)) True)
% 147.66/147.86 (Or (Eq (member (skS.0 0 (union a a) a_1) a) True) (Or (Eq True False) (Eq True False)))
% 147.66/147.86 Clause #860 (by clausification #[858]): ∀ (a a_1 : Iota), Or (Eq (empty (union a a)) True) (Or (Eq (member (skS.0 0 (union a a) a_1) a) True) (Eq True False))
% 147.66/147.86 Clause #861 (by clausification #[860]): ∀ (a a_1 : Iota), Or (Eq (empty (union a a)) True) (Eq (member (skS.0 0 (union a a) a_1) a) True)
% 147.66/147.86 Clause #862 (by superposition #[861, 11]): Or (Eq (empty (union empty_set empty_set)) True) (Eq True False)
% 147.66/147.86 Clause #875 (by clausification #[862]): Eq (empty (union empty_set empty_set)) True
% 147.66/147.86 Clause #876 (by superposition #[875, 21]): ∀ (a : Iota), Or (Eq True False) (Eq (member a (union empty_set empty_set)) False)
% 147.66/147.86 Clause #887 (by clausification #[876]): ∀ (a : Iota), Eq (member a (union empty_set empty_set)) False
% 147.66/147.86 Clause #898 (by superposition #[887, 296]): Or (Eq empty_set (union empty_set empty_set)) (Eq False True)
% 147.98/148.19 Clause #927 (by clausification #[898]): Eq empty_set (union empty_set empty_set)
% 147.98/148.19 Clause #2265 (by superposition #[271, 56]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 a a_1) empty_set) (Or (Eq empty_set (skS.0 4 a a_1)) (Eq True False))
% 147.98/148.19 Clause #2280 (by clausification #[2265]): ∀ (a a_1 : Iota), Or (Eq (skS.0 4 a a_1) empty_set) (Eq empty_set (skS.0 4 a a_1))
% 147.98/148.19 Clause #2281 (by eliminate duplicate literals #[2280]): ∀ (a a_1 : Iota), Eq (skS.0 4 a a_1) empty_set
% 147.98/148.19 Clause #8393 (by destructive equality resolution #[181]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) empty_set) True)
% 147.98/148.19 (Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True)
% 147.98/148.19 (Or (Ne (union empty_set (skS.0 4 a a_2)) empty_set) (Ne (skS.0 4 a a_2) empty_set)))
% 147.98/148.19 Clause #8394 (by forward demodulation #[8393, 11]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq False True)
% 147.98/148.19 (Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True)
% 147.98/148.19 (Or (Ne (union empty_set (skS.0 4 a a_2)) empty_set) (Ne (skS.0 4 a a_2) empty_set)))
% 147.98/148.19 Clause #8395 (by clausification #[8394]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True)
% 147.98/148.19 (Or (Ne (union empty_set (skS.0 4 a a_2)) empty_set) (Ne (skS.0 4 a a_2) empty_set))
% 147.98/148.19 Clause #8396 (by forward demodulation #[8395, 2281]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True)
% 147.98/148.19 (Or (Ne (union empty_set empty_set) empty_set) (Ne (skS.0 4 a a_2) empty_set))
% 147.98/148.19 Clause #8397 (by forward demodulation #[8396, 927]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True)
% 147.98/148.19 (Or (Ne empty_set empty_set) (Ne (skS.0 4 a a_2) empty_set))
% 147.98/148.19 Clause #8398 (by eliminate resolved literals #[8397]): ∀ (a a_1 a_2 : Iota),
% 147.98/148.19 Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True) (Ne (skS.0 4 a a_2) empty_set)
% 147.98/148.19 Clause #8399 (by forward demodulation #[8398, 2281]): ∀ (a a_1 : Iota), Or (Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True) (Ne empty_set empty_set)
% 147.98/148.19 Clause #8400 (by eliminate resolved literals #[8399]): ∀ (a a_1 : Iota), Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) (skS.0 3 a)) True
% 147.98/148.19 Clause #31088 (by clausification #[261]): ∀ (a a_1 : Iota), Or (Eq (union (skS.0 3 a) (skS.0 4 a a_1)) empty_set) (Eq (skS.0 3 a) empty_set)
% 147.98/148.19 Clause #31089 (by forward demodulation #[31088, 2281]): ∀ (a : Iota), Or (Eq (union (skS.0 3 a) empty_set) empty_set) (Eq (skS.0 3 a) empty_set)
% 147.98/148.19 Clause #31103 (by superposition #[31089, 128]): ∀ (a : Iota), Or (Eq (skS.0 3 a) empty_set) (Eq (subset (skS.0 3 a) empty_set) True)
% 147.98/148.19 Clause #31385 (by superposition #[31103, 56]): ∀ (a : Iota), Or (Eq (skS.0 3 a) empty_set) (Or (Eq empty_set (skS.0 3 a)) (Eq True False))
% 147.98/148.19 Clause #31459 (by clausification #[31385]): ∀ (a : Iota), Or (Eq (skS.0 3 a) empty_set) (Eq empty_set (skS.0 3 a))
% 147.98/148.19 Clause #31460 (by eliminate duplicate literals #[31459]): ∀ (a : Iota), Eq (skS.0 3 a) empty_set
% 147.98/148.19 Clause #31461 (by backward demodulation #[31460, 8400]): ∀ (a a_1 : Iota), Eq (member (skS.0 2 empty_set (skS.0 3 a) a_1) empty_set) True
% 147.98/148.19 Clause #31472 (by forward demodulation #[31461, 31460]): ∀ (a : Iota), Eq (member (skS.0 2 empty_set empty_set a) empty_set) True
% 147.98/148.19 Clause #31473 (by superposition #[31472, 11]): Eq True False
% 147.98/148.19 Clause #31558 (by clausification #[31473]): False
% 147.98/148.19 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------