TSTP Solution File: SEU284+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU284+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n014.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 16:41:13 EDT 2023
% Result : Theorem 14.88s 15.06s
% Output : Proof 15.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU284+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Aug 23 20:07:49 EDT 2023
% 0.14/0.35 % CPUTime :
% 14.88/15.06 SZS status Theorem for theBenchmark.p
% 14.88/15.06 SZS output start Proof for theBenchmark.p
% 14.88/15.06 Clause #0 (by assumption #[]): Eq
% 14.88/15.06 (Not
% 14.88/15.06 (∀ (A : Iota),
% 14.88/15.06 Exists fun B =>
% 14.88/15.06 And (And (And (relation B) (function B)) (Eq (relation_dom B) A))
% 14.88/15.06 (∀ (C : Iota), in C A → Eq (apply B C) (singleton C))))
% 14.88/15.06 True
% 14.88/15.06 Clause #4 (by assumption #[]): Eq
% 14.88/15.06 (∀ (A : Iota),
% 14.88/15.06 And (∀ (B C D : Iota), And (And (in B A) (Eq C (singleton B))) (Eq D (singleton B)) → Eq C D)
% 14.88/15.06 (∀ (B : Iota), Not (And (in B A) (∀ (C : Iota), Ne C (singleton B)))) →
% 14.88/15.06 Exists fun B =>
% 14.88/15.06 And (And (And (relation B) (function B)) (Eq (relation_dom B) A))
% 14.88/15.06 (∀ (C : Iota), in C A → Eq (apply B C) (singleton C)))
% 14.88/15.06 True
% 14.88/15.06 Clause #30 (by clausification #[0]): Eq
% 14.88/15.06 (∀ (A : Iota),
% 14.88/15.06 Exists fun B =>
% 14.88/15.06 And (And (And (relation B) (function B)) (Eq (relation_dom B) A))
% 14.88/15.06 (∀ (C : Iota), in C A → Eq (apply B C) (singleton C)))
% 14.88/15.06 False
% 14.88/15.06 Clause #31 (by clausification #[30]): ∀ (a : Iota),
% 14.88/15.06 Eq
% 14.88/15.06 (Not
% 14.88/15.06 (Exists fun B =>
% 14.88/15.06 And (And (And (relation B) (function B)) (Eq (relation_dom B) (skS.0 0 a)))
% 14.88/15.06 (∀ (C : Iota), in C (skS.0 0 a) → Eq (apply B C) (singleton C))))
% 14.88/15.06 True
% 14.88/15.06 Clause #32 (by clausification #[31]): ∀ (a : Iota),
% 14.88/15.06 Eq
% 14.88/15.06 (Exists fun B =>
% 14.88/15.06 And (And (And (relation B) (function B)) (Eq (relation_dom B) (skS.0 0 a)))
% 14.88/15.06 (∀ (C : Iota), in C (skS.0 0 a) → Eq (apply B C) (singleton C)))
% 14.88/15.06 False
% 14.88/15.06 Clause #33 (by clausification #[32]): ∀ (a a_1 : Iota),
% 14.88/15.06 Eq
% 14.88/15.06 (And (And (And (relation a) (function a)) (Eq (relation_dom a) (skS.0 0 a_1)))
% 14.88/15.06 (∀ (C : Iota), in C (skS.0 0 a_1) → Eq (apply a C) (singleton C)))
% 14.88/15.06 False
% 14.88/15.06 Clause #34 (by clausification #[33]): ∀ (a a_1 : Iota),
% 14.88/15.06 Or (Eq (And (And (relation a) (function a)) (Eq (relation_dom a) (skS.0 0 a_1))) False)
% 14.88/15.06 (Eq (∀ (C : Iota), in C (skS.0 0 a_1) → Eq (apply a C) (singleton C)) False)
% 14.88/15.06 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota),
% 14.88/15.06 Or (Eq (∀ (C : Iota), in C (skS.0 0 a) → Eq (apply a_1 C) (singleton C)) False)
% 14.88/15.06 (Or (Eq (And (relation a_1) (function a_1)) False) (Eq (Eq (relation_dom a_1) (skS.0 0 a)) False))
% 14.88/15.06 Clause #36 (by clausification #[35]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or (Eq (And (relation a) (function a)) False)
% 14.88/15.06 (Or (Eq (Eq (relation_dom a) (skS.0 0 a_1)) False)
% 14.88/15.06 (Eq
% 14.88/15.06 (Not (in (skS.0 1 a_1 a a_2) (skS.0 0 a_1) → Eq (apply a (skS.0 1 a_1 a a_2)) (singleton (skS.0 1 a_1 a a_2))))
% 14.88/15.06 True))
% 14.88/15.06 Clause #37 (by clausification #[36]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or (Eq (Eq (relation_dom a) (skS.0 0 a_1)) False)
% 14.88/15.06 (Or
% 14.88/15.06 (Eq
% 14.88/15.06 (Not (in (skS.0 1 a_1 a a_2) (skS.0 0 a_1) → Eq (apply a (skS.0 1 a_1 a a_2)) (singleton (skS.0 1 a_1 a a_2))))
% 14.88/15.06 True)
% 14.88/15.06 (Or (Eq (relation a) False) (Eq (function a) False)))
% 14.88/15.06 Clause #38 (by clausification #[37]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or
% 14.88/15.06 (Eq (Not (in (skS.0 1 a a_1 a_2) (skS.0 0 a) → Eq (apply a_1 (skS.0 1 a a_1 a_2)) (singleton (skS.0 1 a a_1 a_2))))
% 14.88/15.06 True)
% 14.88/15.06 (Or (Eq (relation a_1) False) (Or (Eq (function a_1) False) (Ne (relation_dom a_1) (skS.0 0 a))))
% 14.88/15.06 Clause #39 (by clausification #[38]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or (Eq (relation a) False)
% 14.88/15.06 (Or (Eq (function a) False)
% 14.88/15.06 (Or (Ne (relation_dom a) (skS.0 0 a_1))
% 14.88/15.06 (Eq (in (skS.0 1 a_1 a a_2) (skS.0 0 a_1) → Eq (apply a (skS.0 1 a_1 a a_2)) (singleton (skS.0 1 a_1 a a_2)))
% 14.88/15.06 False)))
% 14.88/15.06 Clause #40 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or (Eq (relation a) False)
% 14.88/15.06 (Or (Eq (function a) False)
% 14.88/15.06 (Or (Ne (relation_dom a) (skS.0 0 a_1)) (Eq (in (skS.0 1 a_1 a a_2) (skS.0 0 a_1)) True)))
% 14.88/15.06 Clause #41 (by clausification #[39]): ∀ (a a_1 a_2 : Iota),
% 14.88/15.06 Or (Eq (relation a) False)
% 14.88/15.06 (Or (Eq (function a) False)
% 14.88/15.06 (Or (Ne (relation_dom a) (skS.0 0 a_1))
% 14.88/15.06 (Eq (Eq (apply a (skS.0 1 a_1 a a_2)) (singleton (skS.0 1 a_1 a a_2))) False)))
% 14.88/15.06 Clause #74 (by clausification #[4]): ∀ (a : Iota),
% 14.88/15.06 Eq
% 14.88/15.06 (And (∀ (B C D : Iota), And (And (in B a) (Eq C (singleton B))) (Eq D (singleton B)) → Eq C D)
% 14.88/15.06 (∀ (B : Iota), Not (And (in B a) (∀ (C : Iota), Ne C (singleton B)))) →
% 14.92/15.09 Exists fun B =>
% 14.92/15.09 And (And (And (relation B) (function B)) (Eq (relation_dom B) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply B C) (singleton C)))
% 14.92/15.09 True
% 14.92/15.09 Clause #75 (by clausification #[74]): ∀ (a : Iota),
% 14.92/15.09 Or
% 14.92/15.09 (Eq
% 14.92/15.09 (And (∀ (B C D : Iota), And (And (in B a) (Eq C (singleton B))) (Eq D (singleton B)) → Eq C D)
% 14.92/15.09 (∀ (B : Iota), Not (And (in B a) (∀ (C : Iota), Ne C (singleton B)))))
% 14.92/15.09 False)
% 14.92/15.09 (Eq
% 14.92/15.09 (Exists fun B =>
% 14.92/15.09 And (And (And (relation B) (function B)) (Eq (relation_dom B) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply B C) (singleton C)))
% 14.92/15.09 True)
% 14.92/15.09 Clause #76 (by clausification #[75]): ∀ (a : Iota),
% 14.92/15.09 Or
% 14.92/15.09 (Eq
% 14.92/15.09 (Exists fun B =>
% 14.92/15.09 And (And (And (relation B) (function B)) (Eq (relation_dom B) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply B C) (singleton C)))
% 14.92/15.09 True)
% 14.92/15.09 (Or (Eq (∀ (B C D : Iota), And (And (in B a) (Eq C (singleton B))) (Eq D (singleton B)) → Eq C D) False)
% 14.92/15.09 (Eq (∀ (B : Iota), Not (And (in B a) (∀ (C : Iota), Ne C (singleton B)))) False))
% 14.92/15.09 Clause #77 (by clausification #[76]): ∀ (a a_1 : Iota),
% 14.92/15.09 Or (Eq (∀ (B C D : Iota), And (And (in B a) (Eq C (singleton B))) (Eq D (singleton B)) → Eq C D) False)
% 14.92/15.09 (Or (Eq (∀ (B : Iota), Not (And (in B a) (∀ (C : Iota), Ne C (singleton B)))) False)
% 14.92/15.09 (Eq
% 14.92/15.09 (And (And (And (relation (skS.0 6 a a_1)) (function (skS.0 6 a a_1))) (Eq (relation_dom (skS.0 6 a a_1)) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_1) C) (singleton C)))
% 14.92/15.09 True))
% 14.92/15.09 Clause #78 (by clausification #[77]): ∀ (a a_1 a_2 : Iota),
% 14.92/15.09 Or (Eq (∀ (B : Iota), Not (And (in B a) (∀ (C : Iota), Ne C (singleton B)))) False)
% 14.92/15.09 (Or
% 14.92/15.09 (Eq
% 14.92/15.09 (And (And (And (relation (skS.0 6 a a_1)) (function (skS.0 6 a a_1))) (Eq (relation_dom (skS.0 6 a a_1)) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_1) C) (singleton C)))
% 14.92/15.09 True)
% 14.92/15.09 (Eq
% 14.92/15.09 (Not
% 14.92/15.09 (∀ (C D : Iota),
% 14.92/15.09 And (And (in (skS.0 7 a a_2) a) (Eq C (singleton (skS.0 7 a a_2)))) (Eq D (singleton (skS.0 7 a a_2))) →
% 14.92/15.09 Eq C D))
% 14.92/15.09 True))
% 14.92/15.09 Clause #79 (by clausification #[78]): ∀ (a a_1 a_2 a_3 : Iota),
% 14.92/15.09 Or
% 14.92/15.09 (Eq
% 14.92/15.09 (And (And (And (relation (skS.0 6 a a_1)) (function (skS.0 6 a a_1))) (Eq (relation_dom (skS.0 6 a a_1)) a))
% 14.92/15.09 (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_1) C) (singleton C)))
% 14.92/15.09 True)
% 14.92/15.09 (Or
% 14.92/15.09 (Eq
% 14.92/15.09 (Not
% 14.92/15.09 (∀ (C D : Iota),
% 14.92/15.09 And (And (in (skS.0 7 a a_2) a) (Eq C (singleton (skS.0 7 a a_2)))) (Eq D (singleton (skS.0 7 a a_2))) →
% 14.92/15.09 Eq C D))
% 14.92/15.09 True)
% 14.92/15.09 (Eq (Not (Not (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3)))))) True))
% 14.92/15.09 Clause #80 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 14.92/15.09 Or
% 14.92/15.09 (Eq
% 14.92/15.09 (Not
% 14.92/15.09 (∀ (C D : Iota),
% 14.92/15.09 And (And (in (skS.0 7 a a_1) a) (Eq C (singleton (skS.0 7 a a_1)))) (Eq D (singleton (skS.0 7 a a_1))) →
% 14.92/15.09 Eq C D))
% 14.92/15.09 True)
% 14.92/15.09 (Or (Eq (Not (Not (And (in (skS.0 8 a a_2) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2)))))) True)
% 14.92/15.09 (Eq (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_3) C) (singleton C)) True))
% 14.92/15.09 Clause #81 (by clausification #[79]): ∀ (a a_1 a_2 a_3 : Iota),
% 14.92/15.09 Or
% 14.92/15.09 (Eq
% 14.92/15.09 (Not
% 14.92/15.09 (∀ (C D : Iota),
% 14.92/15.09 And (And (in (skS.0 7 a a_1) a) (Eq C (singleton (skS.0 7 a a_1)))) (Eq D (singleton (skS.0 7 a a_1))) →
% 14.92/15.09 Eq C D))
% 14.92/15.09 True)
% 14.92/15.09 (Or (Eq (Not (Not (And (in (skS.0 8 a a_2) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2)))))) True)
% 14.92/15.09 (Eq (And (And (relation (skS.0 6 a a_3)) (function (skS.0 6 a a_3))) (Eq (relation_dom (skS.0 6 a a_3)) a)) True))
% 14.92/15.09 Clause #82 (by clausification #[80]): ∀ (a a_1 a_2 a_3 : Iota),
% 14.92/15.09 Or (Eq (Not (Not (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))))) True)
% 14.92/15.09 (Or (Eq (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_2) C) (singleton C)) True)
% 14.92/15.09 (Eq
% 14.92/15.09 (∀ (C D : Iota),
% 14.92/15.09 And (And (in (skS.0 7 a a_3) a) (Eq C (singleton (skS.0 7 a a_3)))) (Eq D (singleton (skS.0 7 a a_3))) →
% 14.92/15.11 Eq C D)
% 14.92/15.11 False))
% 14.92/15.11 Clause #83 (by clausification #[82]): ∀ (a a_1 a_2 a_3 : Iota),
% 14.92/15.11 Or (Eq (∀ (C : Iota), in C a → Eq (apply (skS.0 6 a a_1) C) (singleton C)) True)
% 14.92/15.11 (Or
% 14.92/15.11 (Eq
% 14.92/15.11 (∀ (C D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a a_2) a) (Eq C (singleton (skS.0 7 a a_2)))) (Eq D (singleton (skS.0 7 a a_2))) →
% 14.92/15.11 Eq C D)
% 14.92/15.11 False)
% 14.92/15.11 (Eq (Not (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3))))) False))
% 14.92/15.11 Clause #84 (by clausification #[83]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 14.92/15.11 Or
% 14.92/15.11 (Eq
% 14.92/15.11 (∀ (C D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a a_1) a) (Eq C (singleton (skS.0 7 a a_1)))) (Eq D (singleton (skS.0 7 a a_1))) → Eq C D)
% 14.92/15.11 False)
% 14.92/15.11 (Or (Eq (Not (And (in (skS.0 8 a a_2) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))))) False)
% 14.92/15.11 (Eq (in a_3 a → Eq (apply (skS.0 6 a a_4) a_3) (singleton a_3)) True))
% 14.92/15.11 Clause #85 (by clausification #[84]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or (Eq (Not (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1))))) False)
% 14.92/15.11 (Or (Eq (in a_2 a → Eq (apply (skS.0 6 a a_3) a_2) (singleton a_2)) True)
% 14.92/15.11 (Eq
% 14.92/15.11 (Not
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 9 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a a_4))) →
% 14.92/15.11 Eq (skS.0 9 a a_4 a_5) D))
% 14.92/15.11 True))
% 14.92/15.11 Clause #86 (by clausification #[85]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or (Eq (in a a_1 → Eq (apply (skS.0 6 a_1 a_2) a) (singleton a)) True)
% 14.92/15.11 (Or
% 14.92/15.11 (Eq
% 14.92/15.11 (Not
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a_1 a_3) a_1) (Eq (skS.0 9 a_1 a_3 a_4) (singleton (skS.0 7 a_1 a_3))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a_1 a_3))) →
% 14.92/15.11 Eq (skS.0 9 a_1 a_3 a_4) D))
% 14.92/15.11 True)
% 14.92/15.11 (Eq (And (in (skS.0 8 a_1 a_5) a_1) (∀ (C : Iota), Ne C (singleton (skS.0 8 a_1 a_5)))) True))
% 14.92/15.11 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or
% 14.92/15.11 (Eq
% 14.92/15.11 (Not
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a a_1) a) (Eq (skS.0 9 a a_1 a_2) (singleton (skS.0 7 a a_1))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a a_1))) →
% 14.92/15.11 Eq (skS.0 9 a a_1 a_2) D))
% 14.92/15.11 True)
% 14.92/15.11 (Or (Eq (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3)))) True)
% 14.92/15.11 (Or (Eq (in a_4 a) False) (Eq (Eq (apply (skS.0 6 a a_5) a_4) (singleton a_4)) True)))
% 14.92/15.11 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or (Eq (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))) True)
% 14.92/15.11 (Or (Eq (in a_2 a) False)
% 14.92/15.11 (Or (Eq (Eq (apply (skS.0 6 a a_3) a_2) (singleton a_2)) True)
% 14.92/15.11 (Eq
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 9 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a a_4))) →
% 14.92/15.11 Eq (skS.0 9 a a_4 a_5) D)
% 14.92/15.11 False)))
% 14.92/15.11 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or (Eq (in a a_1) False)
% 14.92/15.11 (Or (Eq (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a)) True)
% 14.92/15.11 (Or
% 14.92/15.11 (Eq
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a_1 a_3) a_1) (Eq (skS.0 9 a_1 a_3 a_4) (singleton (skS.0 7 a_1 a_3))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a_1 a_3))) →
% 14.92/15.11 Eq (skS.0 9 a_1 a_3 a_4) D)
% 14.92/15.11 False)
% 14.92/15.11 (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a_1 a_5))) True)))
% 14.92/15.11 Clause #91 (by clausification #[89]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.11 Or (Eq (in a a_1) False)
% 14.92/15.11 (Or
% 14.92/15.11 (Eq
% 14.92/15.11 (∀ (D : Iota),
% 14.92/15.11 And (And (in (skS.0 7 a_1 a_2) a_1) (Eq (skS.0 9 a_1 a_2 a_3) (singleton (skS.0 7 a_1 a_2))))
% 14.92/15.11 (Eq D (singleton (skS.0 7 a_1 a_2))) →
% 14.92/15.11 Eq (skS.0 9 a_1 a_2 a_3) D)
% 14.92/15.11 False)
% 14.92/15.11 (Or (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a_1 a_4))) True) (Eq (apply (skS.0 6 a_1 a_5) a) (singleton a))))
% 14.92/15.14 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a_1 a_2))) True)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_3) a) (singleton a))
% 14.92/15.14 (Eq
% 14.92/15.14 (Not
% 14.92/15.14 (And (And (in (skS.0 7 a_1 a_4) a_1) (Eq (skS.0 9 a_1 a_4 a_5) (singleton (skS.0 7 a_1 a_4))))
% 14.92/15.14 (Eq (skS.0 10 a_1 a_4 a_5 a_6) (singleton (skS.0 7 a_1 a_4))) →
% 14.92/15.14 Eq (skS.0 9 a_1 a_4 a_5) (skS.0 10 a_1 a_4 a_5 a_6)))
% 14.92/15.14 True)))
% 14.92/15.14 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or
% 14.92/15.14 (Eq
% 14.92/15.14 (Not
% 14.92/15.14 (And (And (in (skS.0 7 a_1 a_3) a_1) (Eq (skS.0 9 a_1 a_3 a_4) (singleton (skS.0 7 a_1 a_3))))
% 14.92/15.14 (Eq (skS.0 10 a_1 a_3 a_4 a_5) (singleton (skS.0 7 a_1 a_3))) →
% 14.92/15.14 Eq (skS.0 9 a_1 a_3 a_4) (skS.0 10 a_1 a_3 a_4 a_5)))
% 14.92/15.14 True)
% 14.92/15.14 (Eq (Ne a_6 (singleton (skS.0 8 a_1 a_7))) True)))
% 14.92/15.14 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Eq (Ne a_3 (singleton (skS.0 8 a_1 a_4))) True)
% 14.92/15.14 (Eq
% 14.92/15.14 (And (And (in (skS.0 7 a_1 a_5) a_1) (Eq (skS.0 9 a_1 a_5 a_6) (singleton (skS.0 7 a_1 a_5))))
% 14.92/15.14 (Eq (skS.0 10 a_1 a_5 a_6 a_7) (singleton (skS.0 7 a_1 a_5))) →
% 14.92/15.14 Eq (skS.0 9 a_1 a_5 a_6) (skS.0 10 a_1 a_5 a_6 a_7))
% 14.92/15.14 False)))
% 14.92/15.14 Clause #95 (by clausification #[94]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or
% 14.92/15.14 (Eq
% 14.92/15.14 (And (And (in (skS.0 7 a_1 a_3) a_1) (Eq (skS.0 9 a_1 a_3 a_4) (singleton (skS.0 7 a_1 a_3))))
% 14.92/15.14 (Eq (skS.0 10 a_1 a_3 a_4 a_5) (singleton (skS.0 7 a_1 a_3))) →
% 14.92/15.14 Eq (skS.0 9 a_1 a_3 a_4) (skS.0 10 a_1 a_3 a_4 a_5))
% 14.92/15.14 False)
% 14.92/15.14 (Ne a_6 (singleton (skS.0 8 a_1 a_7)))))
% 14.92/15.14 Clause #96 (by clausification #[95]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4)))
% 14.92/15.14 (Eq
% 14.92/15.14 (And (And (in (skS.0 7 a_1 a_5) a_1) (Eq (skS.0 9 a_1 a_5 a_6) (singleton (skS.0 7 a_1 a_5))))
% 14.92/15.14 (Eq (skS.0 10 a_1 a_5 a_6 a_7) (singleton (skS.0 7 a_1 a_5))))
% 14.92/15.14 True)))
% 14.92/15.14 Clause #97 (by clausification #[95]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4))) (Eq (Eq (skS.0 9 a_1 a_5 a_6) (skS.0 10 a_1 a_5 a_6 a_7)) False)))
% 14.92/15.14 Clause #98 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4)))
% 14.92/15.14 (Eq (Eq (skS.0 10 a_1 a_5 a_6 a_7) (singleton (skS.0 7 a_1 a_5))) True)))
% 14.92/15.14 Clause #99 (by clausification #[96]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4)))
% 14.92/15.14 (Eq (And (in (skS.0 7 a_1 a_5) a_1) (Eq (skS.0 9 a_1 a_5 a_6) (singleton (skS.0 7 a_1 a_5)))) True)))
% 14.92/15.14 Clause #100 (by clausification #[98]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 14.92/15.14 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4))) (Eq (skS.0 10 a_1 a_5 a_6 a_7) (singleton (skS.0 7 a_1 a_5)))))
% 14.92/15.14 Clause #101 (by destructive equality resolution #[100]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 14.92/15.14 Or (Eq (in a a_1) False)
% 14.92/15.14 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a)) (Eq (skS.0 10 a_1 a_3 a_4 a_5) (singleton (skS.0 7 a_1 a_3))))
% 14.92/15.14 Clause #168 (by clausification #[41]): ∀ (a a_1 a_2 : Iota),
% 14.92/15.14 Or (Eq (relation a) False)
% 14.92/15.14 (Or (Eq (function a) False)
% 14.92/15.14 (Or (Ne (relation_dom a) (skS.0 0 a_1)) (Ne (apply a (skS.0 1 a_1 a a_2)) (singleton (skS.0 1 a_1 a a_2)))))
% 15.01/15.16 Clause #204 (by clausification #[81]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.01/15.16 Or (Eq (Not (Not (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))))) True)
% 15.01/15.16 (Or
% 15.01/15.16 (Eq (And (And (relation (skS.0 6 a a_2)) (function (skS.0 6 a a_2))) (Eq (relation_dom (skS.0 6 a a_2)) a)) True)
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (C D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_3) a) (Eq C (singleton (skS.0 7 a a_3)))) (Eq D (singleton (skS.0 7 a a_3))) →
% 15.01/15.16 Eq C D)
% 15.01/15.16 False))
% 15.01/15.16 Clause #205 (by clausification #[204]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.01/15.16 Or (Eq (And (And (relation (skS.0 6 a a_1)) (function (skS.0 6 a a_1))) (Eq (relation_dom (skS.0 6 a a_1)) a)) True)
% 15.01/15.16 (Or
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (C D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_2) a) (Eq C (singleton (skS.0 7 a a_2)))) (Eq D (singleton (skS.0 7 a a_2))) →
% 15.01/15.16 Eq C D)
% 15.01/15.16 False)
% 15.01/15.16 (Eq (Not (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3))))) False))
% 15.01/15.16 Clause #206 (by clausification #[205]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.01/15.16 Or
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (C D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_1) a) (Eq C (singleton (skS.0 7 a a_1)))) (Eq D (singleton (skS.0 7 a a_1))) → Eq C D)
% 15.01/15.16 False)
% 15.01/15.16 (Or (Eq (Not (And (in (skS.0 8 a a_2) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))))) False)
% 15.01/15.16 (Eq (Eq (relation_dom (skS.0 6 a a_3)) a) True))
% 15.01/15.16 Clause #207 (by clausification #[205]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.01/15.16 Or
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (C D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_1) a) (Eq C (singleton (skS.0 7 a a_1)))) (Eq D (singleton (skS.0 7 a a_1))) → Eq C D)
% 15.01/15.16 False)
% 15.01/15.16 (Or (Eq (Not (And (in (skS.0 8 a a_2) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))))) False)
% 15.01/15.16 (Eq (And (relation (skS.0 6 a a_3)) (function (skS.0 6 a a_3))) True))
% 15.01/15.16 Clause #208 (by clausification #[206]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.16 Or (Eq (Not (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1))))) False)
% 15.01/15.16 (Or (Eq (Eq (relation_dom (skS.0 6 a a_2)) a) True)
% 15.01/15.16 (Eq
% 15.01/15.16 (Not
% 15.01/15.16 (∀ (D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 14 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.01/15.16 (Eq D (singleton (skS.0 7 a a_3))) →
% 15.01/15.16 Eq (skS.0 14 a a_3 a_4) D))
% 15.01/15.16 True))
% 15.01/15.16 Clause #209 (by clausification #[208]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.16 Or (Eq (Eq (relation_dom (skS.0 6 a a_1)) a) True)
% 15.01/15.16 (Or
% 15.01/15.16 (Eq
% 15.01/15.16 (Not
% 15.01/15.16 (∀ (D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 14 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.01/15.16 (Eq D (singleton (skS.0 7 a a_2))) →
% 15.01/15.16 Eq (skS.0 14 a a_2 a_3) D))
% 15.01/15.16 True)
% 15.01/15.16 (Eq (And (in (skS.0 8 a a_4) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_4)))) True))
% 15.01/15.16 Clause #210 (by clausification #[209]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.16 Or
% 15.01/15.16 (Eq
% 15.01/15.16 (Not
% 15.01/15.16 (∀ (D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_1) a) (Eq (skS.0 14 a a_1 a_2) (singleton (skS.0 7 a a_1))))
% 15.01/15.16 (Eq D (singleton (skS.0 7 a a_1))) →
% 15.01/15.16 Eq (skS.0 14 a a_1 a_2) D))
% 15.01/15.16 True)
% 15.01/15.16 (Or (Eq (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3)))) True)
% 15.01/15.16 (Eq (relation_dom (skS.0 6 a a_4)) a))
% 15.01/15.16 Clause #211 (by clausification #[210]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.16 Or (Eq (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))) True)
% 15.01/15.16 (Or (Eq (relation_dom (skS.0 6 a a_2)) a)
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 14 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.01/15.16 (Eq D (singleton (skS.0 7 a a_3))) →
% 15.01/15.16 Eq (skS.0 14 a a_3 a_4) D)
% 15.01/15.16 False))
% 15.01/15.16 Clause #212 (by clausification #[211]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.16 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.16 (Or
% 15.01/15.16 (Eq
% 15.01/15.16 (∀ (D : Iota),
% 15.01/15.16 And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 14 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.01/15.16 (Eq D (singleton (skS.0 7 a a_2))) →
% 15.01/15.16 Eq (skS.0 14 a a_2 a_3) D)
% 15.01/15.19 False)
% 15.01/15.19 (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_4))) True))
% 15.01/15.19 Clause #214 (by clausification #[212]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))) True)
% 15.01/15.19 (Eq
% 15.01/15.19 (Not
% 15.01/15.19 (And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 14 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.01/15.19 (Eq (skS.0 15 a a_3 a_4 a_5) (singleton (skS.0 7 a a_3))) →
% 15.01/15.19 Eq (skS.0 14 a a_3 a_4) (skS.0 15 a a_3 a_4 a_5)))
% 15.01/15.19 True))
% 15.01/15.19 Clause #215 (by clausification #[214]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or
% 15.01/15.19 (Eq
% 15.01/15.19 (Not
% 15.01/15.19 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 14 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.01/15.19 (Eq (skS.0 15 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.01/15.19 Eq (skS.0 14 a a_2 a_3) (skS.0 15 a a_2 a_3 a_4)))
% 15.01/15.19 True)
% 15.01/15.19 (Eq (Ne a_5 (singleton (skS.0 8 a a_6))) True))
% 15.01/15.19 Clause #216 (by clausification #[215]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Eq (Ne a_2 (singleton (skS.0 8 a a_3))) True)
% 15.01/15.19 (Eq
% 15.01/15.19 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 14 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.01/15.19 (Eq (skS.0 15 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) →
% 15.01/15.19 Eq (skS.0 14 a a_4 a_5) (skS.0 15 a a_4 a_5 a_6))
% 15.01/15.19 False))
% 15.01/15.19 Clause #217 (by clausification #[216]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or
% 15.01/15.19 (Eq
% 15.01/15.19 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 14 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.01/15.19 (Eq (skS.0 15 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.01/15.19 Eq (skS.0 14 a a_2 a_3) (skS.0 15 a a_2 a_3 a_4))
% 15.01/15.19 False)
% 15.01/15.19 (Ne a_5 (singleton (skS.0 8 a a_6))))
% 15.01/15.19 Clause #218 (by clausification #[217]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.01/15.19 (Eq
% 15.01/15.19 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 14 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.01/15.19 (Eq (skS.0 15 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.01/15.19 True))
% 15.01/15.19 Clause #219 (by clausification #[217]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 14 a a_4 a_5) (skS.0 15 a a_4 a_5 a_6)) False))
% 15.01/15.19 Clause #220 (by clausification #[218]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 15 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) True))
% 15.01/15.19 Clause #221 (by clausification #[218]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.01/15.19 (Eq (And (in (skS.0 7 a a_4) a) (Eq (skS.0 14 a a_4 a_5) (singleton (skS.0 7 a a_4)))) True))
% 15.01/15.19 Clause #222 (by clausification #[220]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 15 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.01/15.19 Clause #223 (by destructive equality resolution #[222]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a) (Eq (skS.0 15 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2)))
% 15.01/15.19 Clause #251 (by clausification #[219]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Ne (skS.0 14 a a_4 a_5) (skS.0 15 a a_4 a_5 a_6)))
% 15.01/15.19 Clause #252 (by destructive equality resolution #[251]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a) (Ne (skS.0 14 a a_2 a_3) (skS.0 15 a a_2 a_3 a_4))
% 15.01/15.19 Clause #253 (by superposition #[252, 223]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.19 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.19 (Or (Eq (relation_dom (skS.0 6 a a_2)) a) (Ne (skS.0 14 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.01/15.19 Clause #262 (by clausification #[97]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 a_7 : Iota),
% 15.01/15.19 Or (Eq (in a a_1) False)
% 15.01/15.21 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 15.01/15.21 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4))) (Ne (skS.0 9 a_1 a_5 a_6) (skS.0 10 a_1 a_5 a_6 a_7))))
% 15.01/15.21 Clause #263 (by destructive equality resolution #[262]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.01/15.21 Or (Eq (in a a_1) False)
% 15.01/15.21 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a)) (Ne (skS.0 9 a_1 a_3 a_4) (skS.0 10 a_1 a_3 a_4 a_5)))
% 15.01/15.21 Clause #275 (by clausification #[99]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.21 Or (Eq (in a a_1) False)
% 15.01/15.21 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 15.01/15.21 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4))) (Eq (Eq (skS.0 9 a_1 a_5 a_6) (singleton (skS.0 7 a_1 a_5))) True)))
% 15.01/15.21 Clause #277 (by clausification #[275]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.01/15.21 Or (Eq (in a a_1) False)
% 15.01/15.21 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a))
% 15.01/15.21 (Or (Ne a_3 (singleton (skS.0 8 a_1 a_4))) (Eq (skS.0 9 a_1 a_5 a_6) (singleton (skS.0 7 a_1 a_5)))))
% 15.01/15.21 Clause #278 (by destructive equality resolution #[277]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.21 Or (Eq (in a a_1) False)
% 15.01/15.21 (Or (Eq (apply (skS.0 6 a_1 a_2) a) (singleton a)) (Eq (skS.0 9 a_1 a_3 a_4) (singleton (skS.0 7 a_1 a_3))))
% 15.01/15.21 Clause #309 (by clausification #[221]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.01/15.21 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.21 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 14 a a_4 a_5) (singleton (skS.0 7 a a_4))) True))
% 15.01/15.21 Clause #311 (by clausification #[309]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.01/15.21 Or (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.21 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 14 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.01/15.21 Clause #312 (by destructive equality resolution #[311]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (relation_dom (skS.0 6 a a_1)) a) (Eq (skS.0 14 a a_2 a_3) (singleton (skS.0 7 a a_2)))
% 15.01/15.21 Clause #313 (by backward contextual literal cutting #[312, 253]): ∀ (a a_1 a_2 : Iota), Or (Eq (relation_dom (skS.0 6 a a_1)) a) (Eq (relation_dom (skS.0 6 a a_2)) a)
% 15.01/15.21 Clause #315 (by equality factoring #[313]): ∀ (a a_1 : Iota), Or (Ne a a) (Eq (relation_dom (skS.0 6 a a_1)) a)
% 15.01/15.21 Clause #316 (by eliminate resolved literals #[315]): ∀ (a a_1 : Iota), Eq (relation_dom (skS.0 6 a a_1)) a
% 15.01/15.21 Clause #322 (by clausification #[207]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.21 Or (Eq (Not (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1))))) False)
% 15.01/15.21 (Or (Eq (And (relation (skS.0 6 a a_2)) (function (skS.0 6 a a_2))) True)
% 15.01/15.21 (Eq
% 15.01/15.21 (Not
% 15.01/15.21 (∀ (D : Iota),
% 15.01/15.21 And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.01/15.21 (Eq D (singleton (skS.0 7 a a_3))) →
% 15.01/15.21 Eq (skS.0 18 a a_3 a_4) D))
% 15.01/15.21 True))
% 15.01/15.21 Clause #323 (by clausification #[322]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.21 Or (Eq (And (relation (skS.0 6 a a_1)) (function (skS.0 6 a a_1))) True)
% 15.01/15.21 (Or
% 15.01/15.21 (Eq
% 15.01/15.21 (Not
% 15.01/15.21 (∀ (D : Iota),
% 15.01/15.21 And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.01/15.21 (Eq D (singleton (skS.0 7 a a_2))) →
% 15.01/15.21 Eq (skS.0 18 a a_2 a_3) D))
% 15.01/15.21 True)
% 15.01/15.21 (Eq (And (in (skS.0 8 a a_4) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_4)))) True))
% 15.01/15.21 Clause #324 (by clausification #[323]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.21 Or
% 15.01/15.21 (Eq
% 15.01/15.21 (Not
% 15.01/15.21 (∀ (D : Iota),
% 15.01/15.21 And (And (in (skS.0 7 a a_1) a) (Eq (skS.0 18 a a_1 a_2) (singleton (skS.0 7 a a_1))))
% 15.01/15.21 (Eq D (singleton (skS.0 7 a a_1))) →
% 15.01/15.21 Eq (skS.0 18 a a_1 a_2) D))
% 15.01/15.21 True)
% 15.01/15.21 (Or (Eq (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3)))) True)
% 15.01/15.21 (Eq (function (skS.0 6 a a_4)) True))
% 15.01/15.21 Clause #325 (by clausification #[323]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.01/15.21 Or
% 15.01/15.21 (Eq
% 15.01/15.21 (Not
% 15.01/15.21 (∀ (D : Iota),
% 15.01/15.21 And (And (in (skS.0 7 a a_1) a) (Eq (skS.0 18 a a_1 a_2) (singleton (skS.0 7 a a_1))))
% 15.01/15.21 (Eq D (singleton (skS.0 7 a a_1))) →
% 15.01/15.21 Eq (skS.0 18 a a_1 a_2) D))
% 15.01/15.21 True)
% 15.01/15.21 (Or (Eq (And (in (skS.0 8 a a_3) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_3)))) True)
% 15.07/15.24 (Eq (relation (skS.0 6 a a_4)) True))
% 15.07/15.24 Clause #326 (by clausification #[324]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.07/15.24 Or (Eq (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))) True)
% 15.07/15.24 (Or (Eq (function (skS.0 6 a a_2)) True)
% 15.07/15.24 (Eq
% 15.07/15.24 (∀ (D : Iota),
% 15.07/15.24 And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.07/15.24 (Eq D (singleton (skS.0 7 a a_3))) →
% 15.07/15.24 Eq (skS.0 18 a a_3 a_4) D)
% 15.07/15.24 False))
% 15.07/15.24 Clause #327 (by clausification #[326]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or
% 15.07/15.24 (Eq
% 15.07/15.24 (∀ (D : Iota),
% 15.07/15.24 And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.07/15.24 (Eq D (singleton (skS.0 7 a a_2))) →
% 15.07/15.24 Eq (skS.0 18 a a_2 a_3) D)
% 15.07/15.24 False)
% 15.07/15.24 (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_4))) True))
% 15.07/15.24 Clause #329 (by clausification #[327]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))) True)
% 15.07/15.24 (Eq
% 15.07/15.24 (Not
% 15.07/15.24 (And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.07/15.24 (Eq (skS.0 19 a a_3 a_4 a_5) (singleton (skS.0 7 a a_3))) →
% 15.07/15.24 Eq (skS.0 18 a a_3 a_4) (skS.0 19 a a_3 a_4 a_5)))
% 15.07/15.24 True))
% 15.07/15.24 Clause #330 (by clausification #[329]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or
% 15.07/15.24 (Eq
% 15.07/15.24 (Not
% 15.07/15.24 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.07/15.24 (Eq (skS.0 19 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.07/15.24 Eq (skS.0 18 a a_2 a_3) (skS.0 19 a a_2 a_3 a_4)))
% 15.07/15.24 True)
% 15.07/15.24 (Eq (Ne a_5 (singleton (skS.0 8 a a_6))) True))
% 15.07/15.24 Clause #331 (by clausification #[330]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Eq (Ne a_2 (singleton (skS.0 8 a a_3))) True)
% 15.07/15.24 (Eq
% 15.07/15.24 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.07/15.24 (Eq (skS.0 19 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) →
% 15.07/15.24 Eq (skS.0 18 a a_4 a_5) (skS.0 19 a a_4 a_5 a_6))
% 15.07/15.24 False))
% 15.07/15.24 Clause #332 (by clausification #[331]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or
% 15.07/15.24 (Eq
% 15.07/15.24 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.07/15.24 (Eq (skS.0 19 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.07/15.24 Eq (skS.0 18 a a_2 a_3) (skS.0 19 a a_2 a_3 a_4))
% 15.07/15.24 False)
% 15.07/15.24 (Ne a_5 (singleton (skS.0 8 a a_6))))
% 15.07/15.24 Clause #333 (by clausification #[332]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.07/15.24 (Eq
% 15.07/15.24 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.07/15.24 (Eq (skS.0 19 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.07/15.24 True))
% 15.07/15.24 Clause #334 (by clausification #[332]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 18 a a_4 a_5) (skS.0 19 a a_4 a_5 a_6)) False))
% 15.07/15.24 Clause #335 (by clausification #[333]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 19 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) True))
% 15.07/15.24 Clause #336 (by clausification #[333]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.07/15.24 (Eq (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4)))) True))
% 15.07/15.24 Clause #337 (by clausification #[335]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.07/15.24 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.07/15.24 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 19 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.07/15.24 Clause #338 (by destructive equality resolution #[337]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.27 Or (Eq (function (skS.0 6 a a_1)) True) (Eq (skS.0 19 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2)))
% 15.10/15.27 Clause #362 (by clausification #[334]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Ne (skS.0 18 a a_4 a_5) (skS.0 19 a a_4 a_5 a_6)))
% 15.10/15.27 Clause #363 (by destructive equality resolution #[362]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (function (skS.0 6 a a_1)) True) (Ne (skS.0 18 a a_2 a_3) (skS.0 19 a a_2 a_3 a_4))
% 15.10/15.27 Clause #364 (by superposition #[363, 338]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.27 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Eq (function (skS.0 6 a a_2)) True) (Ne (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.10/15.27 Clause #373 (by clausification #[325]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.27 Or (Eq (And (in (skS.0 8 a a_1) a) (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_1)))) True)
% 15.10/15.27 (Or (Eq (relation (skS.0 6 a a_2)) True)
% 15.10/15.27 (Eq
% 15.10/15.27 (∀ (D : Iota),
% 15.10/15.27 And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.10/15.27 (Eq D (singleton (skS.0 7 a a_3))) →
% 15.10/15.27 Eq (skS.0 18 a a_3 a_4) D)
% 15.10/15.27 False))
% 15.10/15.27 Clause #374 (by clausification #[373]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or
% 15.10/15.27 (Eq
% 15.10/15.27 (∀ (D : Iota),
% 15.10/15.27 And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.10/15.27 (Eq D (singleton (skS.0 7 a a_2))) →
% 15.10/15.27 Eq (skS.0 18 a a_2 a_3) D)
% 15.10/15.27 False)
% 15.10/15.27 (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_4))) True))
% 15.10/15.27 Clause #376 (by clausification #[374]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Eq (∀ (C : Iota), Ne C (singleton (skS.0 8 a a_2))) True)
% 15.10/15.27 (Eq
% 15.10/15.27 (Not
% 15.10/15.27 (And (And (in (skS.0 7 a a_3) a) (Eq (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.10/15.27 (Eq (skS.0 21 a a_3 a_4 a_5) (singleton (skS.0 7 a a_3))) →
% 15.10/15.27 Eq (skS.0 18 a a_3 a_4) (skS.0 21 a a_3 a_4 a_5)))
% 15.10/15.27 True))
% 15.10/15.27 Clause #377 (by clausification #[376]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or
% 15.10/15.27 (Eq
% 15.10/15.27 (Not
% 15.10/15.27 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.10/15.27 (Eq (skS.0 21 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.10/15.27 Eq (skS.0 18 a a_2 a_3) (skS.0 21 a a_2 a_3 a_4)))
% 15.10/15.27 True)
% 15.10/15.27 (Eq (Ne a_5 (singleton (skS.0 8 a a_6))) True))
% 15.10/15.27 Clause #378 (by clausification #[377]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Eq (Ne a_2 (singleton (skS.0 8 a a_3))) True)
% 15.10/15.27 (Eq
% 15.10/15.27 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.10/15.27 (Eq (skS.0 21 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) →
% 15.10/15.27 Eq (skS.0 18 a a_4 a_5) (skS.0 21 a a_4 a_5 a_6))
% 15.10/15.27 False))
% 15.10/15.27 Clause #379 (by clausification #[378]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or
% 15.10/15.27 (Eq
% 15.10/15.27 (And (And (in (skS.0 7 a a_2) a) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2))))
% 15.10/15.27 (Eq (skS.0 21 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2))) →
% 15.10/15.27 Eq (skS.0 18 a a_2 a_3) (skS.0 21 a a_2 a_3 a_4))
% 15.10/15.27 False)
% 15.10/15.27 (Ne a_5 (singleton (skS.0 8 a a_6))))
% 15.10/15.27 Clause #380 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.10/15.27 (Eq
% 15.10/15.27 (And (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.10/15.27 (Eq (skS.0 21 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.10/15.27 True))
% 15.10/15.27 Clause #381 (by clausification #[379]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.27 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 18 a a_4 a_5) (skS.0 21 a a_4 a_5 a_6)) False))
% 15.10/15.27 Clause #382 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.27 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 21 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))) True))
% 15.10/15.29 Clause #383 (by clausification #[380]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3)))
% 15.10/15.29 (Eq (And (in (skS.0 7 a a_4) a) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4)))) True))
% 15.10/15.29 Clause #384 (by clausification #[382]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 21 a a_4 a_5 a_6) (singleton (skS.0 7 a a_4))))
% 15.10/15.29 Clause #385 (by destructive equality resolution #[384]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True) (Eq (skS.0 21 a a_2 a_3 a_4) (singleton (skS.0 7 a a_2)))
% 15.10/15.29 Clause #522 (by clausification #[381]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Ne (skS.0 18 a a_4 a_5) (skS.0 21 a a_4 a_5 a_6)))
% 15.10/15.29 Clause #523 (by destructive equality resolution #[522]): ∀ (a a_1 a_2 a_3 a_4 : Iota), Or (Eq (relation (skS.0 6 a a_1)) True) (Ne (skS.0 18 a a_2 a_3) (skS.0 21 a a_2 a_3 a_4))
% 15.10/15.29 Clause #524 (by superposition #[523, 385]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Eq (relation (skS.0 6 a a_2)) True) (Ne (skS.0 18 a a_3 a_4) (singleton (skS.0 7 a a_3))))
% 15.10/15.29 Clause #553 (by clausification #[383]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))) True))
% 15.10/15.29 Clause #555 (by clausification #[553]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.29 Or (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.10/15.29 Clause #556 (by destructive equality resolution #[555]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (relation (skS.0 6 a a_1)) True) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2)))
% 15.10/15.29 Clause #557 (by backward contextual literal cutting #[556, 524]): ∀ (a a_1 a_2 : Iota), Or (Eq (relation (skS.0 6 a a_1)) True) (Eq (relation (skS.0 6 a a_2)) True)
% 15.10/15.29 Clause #632 (by equality factoring #[557]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (relation (skS.0 6 a a_1)) True)
% 15.10/15.29 Clause #634 (by clausification #[632]): ∀ (a a_1 : Iota), Or (Eq (relation (skS.0 6 a a_1)) True) (Or (Eq True False) (Eq True False))
% 15.10/15.29 Clause #636 (by clausification #[634]): ∀ (a a_1 : Iota), Or (Eq (relation (skS.0 6 a a_1)) True) (Eq True False)
% 15.10/15.29 Clause #637 (by clausification #[636]): ∀ (a a_1 : Iota), Eq (relation (skS.0 6 a a_1)) True
% 15.10/15.29 Clause #638 (by superposition #[637, 40]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.29 Or (Eq True False)
% 15.10/15.29 (Or (Eq (function (skS.0 6 a a_1)) False)
% 15.10/15.29 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.29 (Eq (in (skS.0 1 a_2 (skS.0 6 a a_1) a_3) (skS.0 0 a_2)) True)))
% 15.10/15.29 Clause #640 (by superposition #[637, 168]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.29 Or (Eq True False)
% 15.10/15.29 (Or (Eq (function (skS.0 6 a a_1)) False)
% 15.10/15.29 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.29 (Ne (apply (skS.0 6 a a_1) (skS.0 1 a_2 (skS.0 6 a a_1) a_3)) (singleton (skS.0 1 a_2 (skS.0 6 a a_1) a_3)))))
% 15.10/15.29 Clause #709 (by clausification #[336]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.29 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))) True))
% 15.10/15.29 Clause #711 (by clausification #[709]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.29 Or (Eq (function (skS.0 6 a a_1)) True)
% 15.10/15.29 (Or (Ne a_2 (singleton (skS.0 8 a a_3))) (Eq (skS.0 18 a a_4 a_5) (singleton (skS.0 7 a a_4))))
% 15.10/15.29 Clause #712 (by destructive equality resolution #[711]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (function (skS.0 6 a a_1)) True) (Eq (skS.0 18 a a_2 a_3) (singleton (skS.0 7 a a_2)))
% 15.10/15.29 Clause #713 (by backward contextual literal cutting #[712, 364]): ∀ (a a_1 a_2 : Iota), Or (Eq (function (skS.0 6 a a_1)) True) (Eq (function (skS.0 6 a a_2)) True)
% 15.10/15.29 Clause #717 (by equality factoring #[713]): ∀ (a a_1 : Iota), Or (Ne True True) (Eq (function (skS.0 6 a a_1)) True)
% 15.10/15.32 Clause #718 (by clausification #[717]): ∀ (a a_1 : Iota), Or (Eq (function (skS.0 6 a a_1)) True) (Or (Eq True False) (Eq True False))
% 15.10/15.32 Clause #720 (by clausification #[718]): ∀ (a a_1 : Iota), Or (Eq (function (skS.0 6 a a_1)) True) (Eq True False)
% 15.10/15.32 Clause #721 (by clausification #[720]): ∀ (a a_1 : Iota), Eq (function (skS.0 6 a a_1)) True
% 15.10/15.32 Clause #876 (by clausification #[638]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Eq (function (skS.0 6 a a_1)) False)
% 15.10/15.32 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.32 (Eq (in (skS.0 1 a_2 (skS.0 6 a a_1) a_3) (skS.0 0 a_2)) True))
% 15.10/15.32 Clause #877 (by forward demodulation #[876, 721]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Eq True False)
% 15.10/15.32 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.32 (Eq (in (skS.0 1 a_2 (skS.0 6 a a_1) a_3) (skS.0 0 a_2)) True))
% 15.10/15.32 Clause #878 (by clausification #[877]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2)) (Eq (in (skS.0 1 a_2 (skS.0 6 a a_1) a_3) (skS.0 0 a_2)) True)
% 15.10/15.32 Clause #879 (by forward demodulation #[878, 316]): ∀ (a a_1 a_2 a_3 : Iota), Or (Ne a (skS.0 0 a_1)) (Eq (in (skS.0 1 a_1 (skS.0 6 a a_2) a_3) (skS.0 0 a_1)) True)
% 15.10/15.32 Clause #880 (by destructive equality resolution #[879]): ∀ (a a_1 a_2 : Iota), Eq (in (skS.0 1 a (skS.0 6 (skS.0 0 a) a_1) a_2) (skS.0 0 a)) True
% 15.10/15.32 Clause #883 (by superposition #[880, 101]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.32 Or (Eq True False)
% 15.10/15.32 (Or
% 15.10/15.32 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.10/15.32 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.10/15.32 (Eq (skS.0 10 (skS.0 0 a) a_4 a_5 a_6) (singleton (skS.0 7 (skS.0 0 a) a_4))))
% 15.10/15.32 Clause #886 (by superposition #[880, 263]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.10/15.32 Or (Eq True False)
% 15.10/15.32 (Or
% 15.10/15.32 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.10/15.32 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.10/15.32 (Ne (skS.0 9 (skS.0 0 a) a_4 a_5) (skS.0 10 (skS.0 0 a) a_4 a_5 a_6)))
% 15.10/15.32 Clause #887 (by superposition #[880, 278]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.32 Or (Eq True False)
% 15.10/15.32 (Or
% 15.10/15.32 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.10/15.32 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.10/15.32 (Eq (skS.0 9 (skS.0 0 a) a_4 a_5) (singleton (skS.0 7 (skS.0 0 a) a_4))))
% 15.10/15.32 Clause #976 (by clausification #[640]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Eq (function (skS.0 6 a a_1)) False)
% 15.10/15.32 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.32 (Ne (apply (skS.0 6 a a_1) (skS.0 1 a_2 (skS.0 6 a a_1) a_3)) (singleton (skS.0 1 a_2 (skS.0 6 a a_1) a_3))))
% 15.10/15.32 Clause #977 (by forward demodulation #[976, 721]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Eq True False)
% 15.10/15.32 (Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.32 (Ne (apply (skS.0 6 a a_1) (skS.0 1 a_2 (skS.0 6 a a_1) a_3)) (singleton (skS.0 1 a_2 (skS.0 6 a a_1) a_3))))
% 15.10/15.32 Clause #978 (by clausification #[977]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Ne (relation_dom (skS.0 6 a a_1)) (skS.0 0 a_2))
% 15.10/15.32 (Ne (apply (skS.0 6 a a_1) (skS.0 1 a_2 (skS.0 6 a a_1) a_3)) (singleton (skS.0 1 a_2 (skS.0 6 a a_1) a_3)))
% 15.10/15.32 Clause #979 (by forward demodulation #[978, 316]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.10/15.32 Or (Ne a (skS.0 0 a_1))
% 15.10/15.32 (Ne (apply (skS.0 6 a a_2) (skS.0 1 a_1 (skS.0 6 a a_2) a_3)) (singleton (skS.0 1 a_1 (skS.0 6 a a_2) a_3)))
% 15.10/15.32 Clause #980 (by destructive equality resolution #[979]): ∀ (a a_1 a_2 : Iota),
% 15.10/15.32 Ne (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_1) a_2))
% 15.10/15.32 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_1) a_2))
% 15.10/15.32 Clause #1102 (by clausification #[887]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.10/15.32 Or
% 15.10/15.32 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.10/15.32 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.10/15.32 (Eq (skS.0 9 (skS.0 0 a) a_4 a_5) (singleton (skS.0 7 (skS.0 0 a) a_4)))
% 15.10/15.32 Clause #1103 (by superposition #[1102, 980]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.10/15.32 Or (Eq (skS.0 9 (skS.0 0 a) a_1 a_2) (singleton (skS.0 7 (skS.0 0 a) a_1)))
% 15.18/15.33 (Ne (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_3) a_4)) (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_3) a_4)))
% 15.18/15.33 Clause #1104 (by eliminate resolved literals #[1103]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 9 (skS.0 0 a) a_1 a_2) (singleton (skS.0 7 (skS.0 0 a) a_1))
% 15.18/15.33 Clause #1107 (by clausification #[883]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.18/15.33 Or
% 15.18/15.33 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.18/15.33 (Eq (skS.0 10 (skS.0 0 a) a_4 a_5 a_6) (singleton (skS.0 7 (skS.0 0 a) a_4)))
% 15.18/15.33 Clause #1108 (by superposition #[1107, 980]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 15.18/15.33 Or (Eq (skS.0 10 (skS.0 0 a) a_1 a_2 a_3) (singleton (skS.0 7 (skS.0 0 a) a_1)))
% 15.18/15.33 (Ne (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_4) a_5)) (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_4) a_5)))
% 15.18/15.33 Clause #1109 (by eliminate resolved literals #[1108]): ∀ (a a_1 a_2 a_3 : Iota), Eq (skS.0 10 (skS.0 0 a) a_1 a_2 a_3) (singleton (skS.0 7 (skS.0 0 a) a_1))
% 15.18/15.33 Clause #1111 (by clausification #[886]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.18/15.33 Or
% 15.18/15.33 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.18/15.33 (Ne (skS.0 9 (skS.0 0 a) a_4 a_5) (skS.0 10 (skS.0 0 a) a_4 a_5 a_6))
% 15.18/15.33 Clause #1112 (by forward demodulation #[1111, 1104]): ∀ (a a_1 a_2 a_3 a_4 a_5 a_6 : Iota),
% 15.18/15.33 Or
% 15.18/15.33 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.18/15.33 (Ne (singleton (skS.0 7 (skS.0 0 a) a_4)) (skS.0 10 (skS.0 0 a) a_4 a_5 a_6))
% 15.18/15.33 Clause #1113 (by forward demodulation #[1112, 1109]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 15.18/15.33 Or
% 15.18/15.33 (Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3)))
% 15.18/15.33 (Ne (singleton (skS.0 7 (skS.0 0 a) a_4)) (singleton (skS.0 7 (skS.0 0 a) a_4)))
% 15.18/15.33 Clause #1114 (by eliminate resolved literals #[1113]): ∀ (a a_1 a_2 a_3 : Iota),
% 15.18/15.33 Eq (apply (skS.0 6 (skS.0 0 a) a_1) (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 (singleton (skS.0 1 a (skS.0 6 (skS.0 0 a) a_2) a_3))
% 15.18/15.33 Clause #1116 (by backward contextual literal cutting #[1114, 980]): False
% 15.18/15.33 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------