TSTP Solution File: SEU359+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU359+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n028.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 16:41:37 EDT 2023
% Result : Theorem 12.04s 12.22s
% Output : Proof 12.45s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU359+1 : TPTP v8.1.2. Released v3.3.0.
% 0.13/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n028.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 16:05:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 12.04/12.22 SZS status Theorem for theBenchmark.p
% 12.04/12.22 SZS output start Proof for theBenchmark.p
% 12.04/12.22 Clause #0 (by assumption #[]): Eq
% 12.04/12.22 (∀ (A : Iota),
% 12.04/12.22 rel_str A →
% 12.04/12.22 ∀ (B C : Iota),
% 12.04/12.22 element C (the_carrier A) →
% 12.04/12.22 ex_sup_of_relstr_set A B →
% 12.04/12.22 Iff (Eq C (join_on_relstr A B))
% 12.04/12.22 (And (relstr_set_smaller A B C)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A B D → related A C D)))
% 12.04/12.22 True
% 12.04/12.22 Clause #1 (by assumption #[]): Eq (∀ (A B : Iota), rel_str A → element (join_on_relstr A B) (the_carrier A)) True
% 12.04/12.22 Clause #7 (by assumption #[]): Eq
% 12.04/12.22 (∀ (A : Iota),
% 12.04/12.22 And (antisymmetric_relstr A) (rel_str A) →
% 12.04/12.22 ∀ (B : Iota),
% 12.04/12.22 Iff (ex_sup_of_relstr_set A B)
% 12.04/12.22 (Exists fun C =>
% 12.04/12.22 And (And (element C (the_carrier A)) (relstr_set_smaller A B C))
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A B D → related A C D)))
% 12.04/12.22 True
% 12.04/12.22 Clause #8 (by assumption #[]): Eq
% 12.04/12.22 (Not
% 12.04/12.22 (∀ (A : Iota),
% 12.04/12.22 And (antisymmetric_relstr A) (rel_str A) →
% 12.04/12.22 ∀ (B : Iota),
% 12.04/12.22 element B (the_carrier A) →
% 12.04/12.22 ∀ (C : Iota),
% 12.04/12.22 And
% 12.04/12.22 (And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C) →
% 12.04/12.22 And (relstr_set_smaller A C B)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D))
% 12.04/12.22 (And (relstr_set_smaller A C B)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D) →
% 12.04/12.22 And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C))))
% 12.04/12.22 True
% 12.04/12.22 Clause #18 (by clausification #[0]): ∀ (a : Iota),
% 12.04/12.22 Eq
% 12.04/12.22 (rel_str a →
% 12.04/12.22 ∀ (B C : Iota),
% 12.04/12.22 element C (the_carrier a) →
% 12.04/12.22 ex_sup_of_relstr_set a B →
% 12.04/12.22 Iff (Eq C (join_on_relstr a B))
% 12.04/12.22 (And (relstr_set_smaller a B C)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a B D → related a C D)))
% 12.04/12.22 True
% 12.04/12.22 Clause #19 (by clausification #[18]): ∀ (a : Iota),
% 12.04/12.22 Or (Eq (rel_str a) False)
% 12.04/12.22 (Eq
% 12.04/12.22 (∀ (B C : Iota),
% 12.04/12.22 element C (the_carrier a) →
% 12.04/12.22 ex_sup_of_relstr_set a B →
% 12.04/12.22 Iff (Eq C (join_on_relstr a B))
% 12.04/12.22 (And (relstr_set_smaller a B C)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a B D → related a C D)))
% 12.04/12.22 True)
% 12.04/12.22 Clause #20 (by clausification #[19]): ∀ (a a_1 : Iota),
% 12.04/12.22 Or (Eq (rel_str a) False)
% 12.04/12.22 (Eq
% 12.04/12.22 (∀ (C : Iota),
% 12.04/12.22 element C (the_carrier a) →
% 12.04/12.22 ex_sup_of_relstr_set a a_1 →
% 12.04/12.22 Iff (Eq C (join_on_relstr a a_1))
% 12.04/12.22 (And (relstr_set_smaller a a_1 C)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a C D)))
% 12.04/12.22 True)
% 12.04/12.22 Clause #21 (by clausification #[20]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.22 Or (Eq (rel_str a) False)
% 12.04/12.22 (Eq
% 12.04/12.22 (element a_1 (the_carrier a) →
% 12.04/12.22 ex_sup_of_relstr_set a a_2 →
% 12.04/12.22 Iff (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.22 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)))
% 12.04/12.22 True)
% 12.04/12.22 Clause #22 (by clausification #[21]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.22 Or (Eq (rel_str a) False)
% 12.04/12.22 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.22 (Eq
% 12.04/12.22 (ex_sup_of_relstr_set a a_2 →
% 12.04/12.22 Iff (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.22 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)))
% 12.04/12.22 True))
% 12.04/12.22 Clause #23 (by clausification #[22]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.22 Or (Eq (rel_str a) False)
% 12.04/12.22 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.22 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.22 (Eq
% 12.04/12.22 (Iff (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.22 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.22 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D)))
% 12.04/12.22 True)))
% 12.04/12.24 Clause #24 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) True)
% 12.04/12.24 (Eq
% 12.04/12.24 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.24 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 12.04/12.24 False))))
% 12.04/12.24 Clause #25 (by clausification #[23]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) False)
% 12.04/12.24 (Eq
% 12.04/12.24 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.24 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 12.04/12.24 True))))
% 12.04/12.24 Clause #26 (by clausification #[24]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or
% 12.04/12.24 (Eq
% 12.04/12.24 (And (relstr_set_smaller a a_2 a_1)
% 12.04/12.24 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 12.04/12.24 False)
% 12.04/12.24 (Eq a_1 (join_on_relstr a a_2)))))
% 12.04/12.24 Clause #27 (by clausification #[26]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.24 (Or (Eq (relstr_set_smaller a a_2 a_1) False)
% 12.04/12.24 (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) False)))))
% 12.04/12.24 Clause #28 (by clausification #[27]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.24 (Or (Eq (relstr_set_smaller a a_2 a_1) False)
% 12.04/12.24 (Eq
% 12.04/12.24 (Not
% 12.04/12.24 (element (skS.0 3 a a_2 a_1 a_3) (the_carrier a) →
% 12.04/12.24 relstr_set_smaller a a_2 (skS.0 3 a a_2 a_1 a_3) → related a a_1 (skS.0 3 a a_2 a_1 a_3)))
% 12.04/12.24 True)))))
% 12.04/12.24 Clause #29 (by clausification #[28]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.24 (Or (Eq (relstr_set_smaller a a_2 a_1) False)
% 12.04/12.24 (Eq
% 12.04/12.24 (element (skS.0 3 a a_2 a_1 a_3) (the_carrier a) →
% 12.04/12.24 relstr_set_smaller a a_2 (skS.0 3 a a_2 a_1 a_3) → related a a_1 (skS.0 3 a a_2 a_1 a_3))
% 12.04/12.24 False)))))
% 12.04/12.24 Clause #30 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.24 (Or (Eq (relstr_set_smaller a a_2 a_1) False) (Eq (element (skS.0 3 a a_2 a_1 a_3) (the_carrier a)) True)))))
% 12.04/12.24 Clause #31 (by clausification #[29]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.24 Or (Eq (rel_str a) False)
% 12.04/12.24 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.04/12.24 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.04/12.24 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.04/12.24 (Or (Eq (relstr_set_smaller a a_2 a_1) False)
% 12.04/12.24 (Eq (relstr_set_smaller a a_2 (skS.0 3 a a_2 a_1 a_3) → related a a_1 (skS.0 3 a a_2 a_1 a_3)) False)))))
% 12.04/12.24 Clause #34 (by clausification #[1]): ∀ (a : Iota), Eq (∀ (B : Iota), rel_str a → element (join_on_relstr a B) (the_carrier a)) True
% 12.04/12.24 Clause #35 (by clausification #[34]): ∀ (a a_1 : Iota), Eq (rel_str a → element (join_on_relstr a a_1) (the_carrier a)) True
% 12.04/12.24 Clause #36 (by clausification #[35]): ∀ (a a_1 : Iota), Or (Eq (rel_str a) False) (Eq (element (join_on_relstr a a_1) (the_carrier a)) True)
% 12.04/12.24 Clause #39 (by clausification #[7]): ∀ (a : Iota),
% 12.04/12.24 Eq
% 12.04/12.24 (And (antisymmetric_relstr a) (rel_str a) →
% 12.04/12.24 ∀ (B : Iota),
% 12.04/12.24 Iff (ex_sup_of_relstr_set a B)
% 12.04/12.26 (Exists fun C =>
% 12.04/12.26 And (And (element C (the_carrier a)) (relstr_set_smaller a B C))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a B D → related a C D)))
% 12.04/12.26 True
% 12.04/12.26 Clause #40 (by clausification #[39]): ∀ (a : Iota),
% 12.04/12.26 Or (Eq (And (antisymmetric_relstr a) (rel_str a)) False)
% 12.04/12.26 (Eq
% 12.04/12.26 (∀ (B : Iota),
% 12.04/12.26 Iff (ex_sup_of_relstr_set a B)
% 12.04/12.26 (Exists fun C =>
% 12.04/12.26 And (And (element C (the_carrier a)) (relstr_set_smaller a B C))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a B D → related a C D)))
% 12.04/12.26 True)
% 12.04/12.26 Clause #41 (by clausification #[40]): ∀ (a : Iota),
% 12.04/12.26 Or
% 12.04/12.26 (Eq
% 12.04/12.26 (∀ (B : Iota),
% 12.04/12.26 Iff (ex_sup_of_relstr_set a B)
% 12.04/12.26 (Exists fun C =>
% 12.04/12.26 And (And (element C (the_carrier a)) (relstr_set_smaller a B C))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a B D → related a C D)))
% 12.04/12.26 True)
% 12.04/12.26 (Or (Eq (antisymmetric_relstr a) False) (Eq (rel_str a) False))
% 12.04/12.26 Clause #42 (by clausification #[41]): ∀ (a a_1 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Eq
% 12.04/12.26 (Iff (ex_sup_of_relstr_set a a_1)
% 12.04/12.26 (Exists fun C =>
% 12.04/12.26 And (And (element C (the_carrier a)) (relstr_set_smaller a a_1 C))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a C D)))
% 12.04/12.26 True))
% 12.04/12.26 Clause #43 (by clausification #[42]): ∀ (a a_1 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Eq
% 12.04/12.26 (Exists fun C =>
% 12.04/12.26 And (And (element C (the_carrier a)) (relstr_set_smaller a a_1 C))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a C D))
% 12.04/12.26 False)))
% 12.04/12.26 Clause #45 (by clausification #[43]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Eq
% 12.04/12.26 (And (And (element a_2 (the_carrier a)) (relstr_set_smaller a a_1 a_2))
% 12.04/12.26 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a a_2 D))
% 12.04/12.26 False)))
% 12.04/12.26 Clause #46 (by clausification #[45]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Or (Eq (And (element a_2 (the_carrier a)) (relstr_set_smaller a a_1 a_2)) False)
% 12.04/12.26 (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a a_2 D) False))))
% 12.04/12.26 Clause #47 (by clausification #[46]): ∀ (a a_1 a_2 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Or (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_1 D → related a a_2 D) False)
% 12.04/12.26 (Or (Eq (element a_2 (the_carrier a)) False) (Eq (relstr_set_smaller a a_1 a_2) False)))))
% 12.04/12.26 Clause #48 (by clausification #[47]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.04/12.26 (Or (Eq (relstr_set_smaller a a_1 a_2) False)
% 12.04/12.26 (Eq
% 12.04/12.26 (Not
% 12.04/12.26 (element (skS.0 4 a a_1 a_2 a_3) (the_carrier a) →
% 12.04/12.26 relstr_set_smaller a a_1 (skS.0 4 a a_1 a_2 a_3) → related a a_2 (skS.0 4 a a_1 a_2 a_3)))
% 12.04/12.26 True)))))
% 12.04/12.26 Clause #49 (by clausification #[48]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.04/12.26 Or (Eq (antisymmetric_relstr a) False)
% 12.04/12.26 (Or (Eq (rel_str a) False)
% 12.04/12.26 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.04/12.26 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.04/12.26 (Or (Eq (relstr_set_smaller a a_1 a_2) False)
% 12.04/12.26 (Eq
% 12.04/12.26 (element (skS.0 4 a a_1 a_2 a_3) (the_carrier a) →
% 12.04/12.26 relstr_set_smaller a a_1 (skS.0 4 a a_1 a_2 a_3) → related a a_2 (skS.0 4 a a_1 a_2 a_3))
% 12.12/12.28 False)))))
% 12.12/12.28 Clause #50 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.12/12.28 Or (Eq (antisymmetric_relstr a) False)
% 12.12/12.28 (Or (Eq (rel_str a) False)
% 12.12/12.28 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.12/12.28 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.12/12.28 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (element (skS.0 4 a a_1 a_2 a_3) (the_carrier a)) True)))))
% 12.12/12.28 Clause #51 (by clausification #[49]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.12/12.28 Or (Eq (antisymmetric_relstr a) False)
% 12.12/12.28 (Or (Eq (rel_str a) False)
% 12.12/12.28 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.12/12.28 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.12/12.28 (Or (Eq (relstr_set_smaller a a_1 a_2) False)
% 12.12/12.28 (Eq (relstr_set_smaller a a_1 (skS.0 4 a a_1 a_2 a_3) → related a a_2 (skS.0 4 a a_1 a_2 a_3)) False)))))
% 12.12/12.28 Clause #58 (by clausification #[8]): Eq
% 12.12/12.28 (∀ (A : Iota),
% 12.12/12.28 And (antisymmetric_relstr A) (rel_str A) →
% 12.12/12.28 ∀ (B : Iota),
% 12.12/12.28 element B (the_carrier A) →
% 12.12/12.28 ∀ (C : Iota),
% 12.12/12.28 And
% 12.12/12.28 (And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C) →
% 12.12/12.28 And (relstr_set_smaller A C B)
% 12.12/12.28 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D))
% 12.12/12.28 (And (relstr_set_smaller A C B)
% 12.12/12.28 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D) →
% 12.12/12.28 And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C)))
% 12.12/12.28 False
% 12.12/12.28 Clause #59 (by clausification #[58]): ∀ (a : Iota),
% 12.12/12.28 Eq
% 12.12/12.28 (Not
% 12.12/12.28 (And (antisymmetric_relstr (skS.0 6 a)) (rel_str (skS.0 6 a)) →
% 12.12/12.28 ∀ (B : Iota),
% 12.12/12.28 element B (the_carrier (skS.0 6 a)) →
% 12.12/12.28 ∀ (C : Iota),
% 12.12/12.28 And
% 12.12/12.28 (And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.12/12.28 And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) →
% 12.12/12.28 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D))
% 12.12/12.28 (And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) →
% 12.12/12.28 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D) →
% 12.12/12.28 And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C))))
% 12.12/12.28 True
% 12.12/12.28 Clause #60 (by clausification #[59]): ∀ (a : Iota),
% 12.12/12.28 Eq
% 12.12/12.28 (And (antisymmetric_relstr (skS.0 6 a)) (rel_str (skS.0 6 a)) →
% 12.12/12.28 ∀ (B : Iota),
% 12.12/12.28 element B (the_carrier (skS.0 6 a)) →
% 12.12/12.28 ∀ (C : Iota),
% 12.12/12.28 And
% 12.12/12.28 (And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.12/12.28 And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) → relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D))
% 12.12/12.28 (And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) →
% 12.12/12.28 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D) →
% 12.12/12.28 And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C)))
% 12.12/12.28 False
% 12.12/12.28 Clause #61 (by clausification #[60]): ∀ (a : Iota), Eq (And (antisymmetric_relstr (skS.0 6 a)) (rel_str (skS.0 6 a))) True
% 12.12/12.28 Clause #62 (by clausification #[60]): ∀ (a : Iota),
% 12.12/12.28 Eq
% 12.12/12.28 (∀ (B : Iota),
% 12.12/12.28 element B (the_carrier (skS.0 6 a)) →
% 12.12/12.28 ∀ (C : Iota),
% 12.12/12.28 And
% 12.12/12.28 (And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.12/12.28 And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) → relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D))
% 12.12/12.28 (And (relstr_set_smaller (skS.0 6 a) C B)
% 12.12/12.28 (∀ (D : Iota),
% 12.12/12.28 element D (the_carrier (skS.0 6 a)) → relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) B D) →
% 12.15/12.31 And (Eq B (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C)))
% 12.15/12.31 False
% 12.15/12.31 Clause #63 (by clausification #[61]): ∀ (a : Iota), Eq (rel_str (skS.0 6 a)) True
% 12.15/12.31 Clause #64 (by clausification #[61]): ∀ (a : Iota), Eq (antisymmetric_relstr (skS.0 6 a)) True
% 12.15/12.31 Clause #66 (by superposition #[63, 30]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq True False)
% 12.15/12.31 (Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.15/12.31 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.15/12.31 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.15/12.31 (Eq (element (skS.0 3 (skS.0 6 a_1) a_2 a a_3) (the_carrier (skS.0 6 a_1))) True)))))
% 12.15/12.31 Clause #67 (by superposition #[63, 36]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) True)
% 12.15/12.31 Clause #68 (by superposition #[64, 50]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq True False)
% 12.15/12.31 (Or (Eq (rel_str (skS.0 6 a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.15/12.31 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.15/12.31 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.15/12.31 (Eq (element (skS.0 4 (skS.0 6 a) a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True)))))
% 12.15/12.31 Clause #71 (by clausification #[67]): ∀ (a a_1 : Iota), Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) True
% 12.15/12.31 Clause #72 (by clausification #[25]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or
% 12.15/12.31 (Eq
% 12.15/12.31 (And (relstr_set_smaller a a_2 a_1)
% 12.15/12.31 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 12.15/12.31 True)
% 12.15/12.31 (Ne a_1 (join_on_relstr a a_2)))))
% 12.15/12.31 Clause #73 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or (Ne a_1 (join_on_relstr a a_2))
% 12.15/12.31 (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) True))))
% 12.15/12.31 Clause #74 (by clausification #[72]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or (Ne a_1 (join_on_relstr a a_2)) (Eq (relstr_set_smaller a a_2 a_1) True))))
% 12.15/12.31 Clause #75 (by clausification #[73]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or (Ne a_1 (join_on_relstr a a_2))
% 12.15/12.31 (Eq (element a_3 (the_carrier a) → relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True))))
% 12.15/12.31 Clause #76 (by clausification #[75]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or (Ne a_1 (join_on_relstr a a_2))
% 12.15/12.31 (Or (Eq (element a_3 (the_carrier a)) False) (Eq (relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True)))))
% 12.15/12.31 Clause #77 (by clausification #[76]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.15/12.31 (Or (Ne a_1 (join_on_relstr a a_2))
% 12.15/12.31 (Or (Eq (element a_3 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (relstr_set_smaller a a_2 a_3) False) (Eq (related a a_1 a_3) True))))))
% 12.15/12.31 Clause #78 (by destructive equality resolution #[77]): ∀ (a a_1 a_2 : Iota),
% 12.15/12.31 Or (Eq (rel_str a) False)
% 12.15/12.31 (Or (Eq (element (join_on_relstr a a_1) (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (ex_sup_of_relstr_set a a_1) False)
% 12.15/12.31 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.15/12.31 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (related a (join_on_relstr a a_1) a_2) True)))))
% 12.15/12.31 Clause #80 (by superposition #[78, 63]): ∀ (a a_1 a_2 : Iota),
% 12.17/12.33 Or (Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.33 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.33 (Or (Eq (related (skS.0 6 a) (join_on_relstr (skS.0 6 a) a_1) a_2) True) (Eq False True)))))
% 12.17/12.33 Clause #81 (by destructive equality resolution #[74]): ∀ (a a_1 : Iota),
% 12.17/12.33 Or (Eq (rel_str a) False)
% 12.17/12.33 (Or (Eq (element (join_on_relstr a a_1) (the_carrier a)) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set a a_1) False) (Eq (relstr_set_smaller a a_1 (join_on_relstr a a_1)) True)))
% 12.17/12.33 Clause #83 (by superposition #[81, 63]): ∀ (a a_1 : Iota),
% 12.17/12.33 Or (Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (join_on_relstr (skS.0 6 a) a_1)) True) (Eq False True)))
% 12.17/12.33 Clause #84 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (rel_str a) False)
% 12.17/12.33 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.17/12.33 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.17/12.33 (Or (Eq (relstr_set_smaller a a_2 a_1) False) (Eq (relstr_set_smaller a a_2 (skS.0 3 a a_2 a_1 a_3)) True)))))
% 12.17/12.33 Clause #85 (by clausification #[31]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (rel_str a) False)
% 12.17/12.33 (Or (Eq (element a_1 (the_carrier a)) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 12.17/12.33 (Or (Eq a_1 (join_on_relstr a a_2))
% 12.17/12.33 (Or (Eq (relstr_set_smaller a a_2 a_1) False) (Eq (related a a_1 (skS.0 3 a a_2 a_1 a_3)) False)))))
% 12.17/12.33 Clause #87 (by superposition #[84, 63]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.17/12.33 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 (skS.0 3 (skS.0 6 a_1) a_2 a a_3)) True) (Eq False True)))))
% 12.17/12.33 Clause #88 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (antisymmetric_relstr a) False)
% 12.17/12.33 (Or (Eq (rel_str a) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.17/12.33 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (relstr_set_smaller a a_1 (skS.0 4 a a_1 a_2 a_3)) True)))))
% 12.17/12.33 Clause #89 (by clausification #[51]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (antisymmetric_relstr a) False)
% 12.17/12.33 (Or (Eq (rel_str a) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set a a_1) True)
% 12.17/12.33 (Or (Eq (element a_2 (the_carrier a)) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (related a a_2 (skS.0 4 a a_1 a_2 a_3)) False)))))
% 12.17/12.33 Clause #90 (by superposition #[88, 64]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (rel_str (skS.0 6 a)) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.33 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) True) (Eq False True)))))
% 12.17/12.33 Clause #91 (by superposition #[89, 64]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (rel_str (skS.0 6 a)) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.33 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.33 (Or (Eq (related (skS.0 6 a) a_2 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) False) (Eq False True)))))
% 12.17/12.33 Clause #93 (by superposition #[85, 63]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.33 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.17/12.33 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.17/12.33 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.17/12.33 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.17/12.33 (Or (Eq (related (skS.0 6 a_1) a (skS.0 3 (skS.0 6 a_1) a_2 a a_3)) False) (Eq False True)))))
% 12.17/12.33 Clause #107 (by clausification #[83]): ∀ (a a_1 : Iota),
% 12.17/12.35 Or (Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) False)
% 12.17/12.35 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.35 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (join_on_relstr (skS.0 6 a) a_1)) True))
% 12.17/12.35 Clause #108 (by forward demodulation #[107, 71]): ∀ (a a_1 : Iota),
% 12.17/12.35 Or (Eq True False)
% 12.17/12.35 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.35 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (join_on_relstr (skS.0 6 a) a_1)) True))
% 12.17/12.35 Clause #109 (by clausification #[108]): ∀ (a a_1 : Iota),
% 12.17/12.35 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.35 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (join_on_relstr (skS.0 6 a) a_1)) True)
% 12.17/12.35 Clause #113 (by clausification #[62]): ∀ (a a_1 : Iota),
% 12.17/12.35 Eq
% 12.17/12.35 (Not
% 12.17/12.35 (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a)) →
% 12.17/12.35 ∀ (C : Iota),
% 12.17/12.35 And
% 12.17/12.35 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.17/12.35 And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.17/12.35 (And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.17/12.35 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C))))
% 12.17/12.35 True
% 12.17/12.35 Clause #114 (by clausification #[113]): ∀ (a a_1 : Iota),
% 12.17/12.35 Eq
% 12.17/12.35 (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a)) →
% 12.17/12.35 ∀ (C : Iota),
% 12.17/12.35 And
% 12.17/12.35 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.17/12.35 And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.17/12.35 (And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.17/12.35 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C)))
% 12.17/12.35 False
% 12.17/12.35 Clause #115 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a))) True
% 12.17/12.35 Clause #116 (by clausification #[114]): ∀ (a a_1 : Iota),
% 12.17/12.35 Eq
% 12.17/12.35 (∀ (C : Iota),
% 12.17/12.35 And
% 12.17/12.35 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C) →
% 12.17/12.35 And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.17/12.35 (And (relstr_set_smaller (skS.0 6 a) C (skS.0 7 a a_1))
% 12.17/12.35 (∀ (D : Iota),
% 12.17/12.35 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.35 relstr_set_smaller (skS.0 6 a) C D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.17/12.35 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) C)) (ex_sup_of_relstr_set (skS.0 6 a) C)))
% 12.17/12.35 False
% 12.17/12.35 Clause #117 (by clausification #[66]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.35 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.17/12.35 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.17/12.35 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.17/12.35 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.17/12.35 (Eq (element (skS.0 3 (skS.0 6 a_1) a_2 a a_3) (the_carrier (skS.0 6 a_1))) True))))
% 12.17/12.35 Clause #119 (by superposition #[117, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.35 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.35 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.17/12.35 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.35 (Or (Eq (element (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3) (the_carrier (skS.0 6 a))) True)
% 12.17/12.38 (Eq False True))))
% 12.17/12.38 Clause #124 (by clausification #[68]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (rel_str (skS.0 6 a)) False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (element (skS.0 4 (skS.0 6 a) a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True))))
% 12.17/12.38 Clause #125 (by forward demodulation #[124, 63]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq True False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (element (skS.0 4 (skS.0 6 a) a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True))))
% 12.17/12.38 Clause #126 (by clausification #[125]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (element (skS.0 4 (skS.0 6 a) a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True)))
% 12.17/12.38 Clause #128 (by superposition #[126, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.38 (Or (Eq (element (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3) (the_carrier (skS.0 6 a))) True) (Eq False True)))
% 12.17/12.38 Clause #130 (by clausification #[128]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.38 (Eq (element (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3) (the_carrier (skS.0 6 a))) True))
% 12.17/12.38 Clause #132 (by clausification #[80]): ∀ (a a_1 a_2 : Iota),
% 12.17/12.38 Or (Eq (element (join_on_relstr (skS.0 6 a) a_1) (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) (join_on_relstr (skS.0 6 a) a_1) a_2) True))))
% 12.17/12.38 Clause #133 (by forward demodulation #[132, 71]): ∀ (a a_1 a_2 : Iota),
% 12.17/12.38 Or (Eq True False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) (join_on_relstr (skS.0 6 a) a_1) a_2) True))))
% 12.17/12.38 Clause #134 (by clausification #[133]): ∀ (a a_1 a_2 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) (join_on_relstr (skS.0 6 a) a_1) a_2) True)))
% 12.17/12.38 Clause #138 (by clausification #[91]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (rel_str (skS.0 6 a)) False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) a_2 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) False))))
% 12.17/12.38 Clause #139 (by forward demodulation #[138, 63]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq True False)
% 12.17/12.38 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) a_2 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) False))))
% 12.17/12.38 Clause #140 (by clausification #[139]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.38 (Eq (related (skS.0 6 a) a_2 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) False)))
% 12.17/12.38 Clause #142 (by superposition #[140, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.38 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.38 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.40 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_2) (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) False)
% 12.17/12.40 (Eq False True)))
% 12.17/12.40 Clause #144 (by clausification #[90]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (rel_str (skS.0 6 a)) False)
% 12.17/12.40 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.40 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.40 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) True))))
% 12.17/12.40 Clause #145 (by forward demodulation #[144, 63]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq True False)
% 12.17/12.40 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.40 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.40 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) True))))
% 12.17/12.40 Clause #146 (by clausification #[145]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.40 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 a_2) False)
% 12.17/12.40 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 a_2 a_3)) True)))
% 12.17/12.40 Clause #148 (by superposition #[146, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) True) (Eq False True)))
% 12.17/12.40 Clause #150 (by clausification #[148]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.40 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) True))
% 12.17/12.40 Clause #155 (by clausification #[87]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.17/12.40 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.17/12.40 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.17/12.40 (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 (skS.0 3 (skS.0 6 a_1) a_2 a a_3)) True))))
% 12.17/12.40 Clause #157 (by superposition #[155, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.40 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) True)
% 12.17/12.40 (Eq False True))))
% 12.17/12.40 Clause #159 (by clausification #[93]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.17/12.40 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a_1) a_2) False)
% 12.17/12.40 (Or (Eq a (join_on_relstr (skS.0 6 a_1) a_2))
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) a_2 a) False)
% 12.17/12.40 (Eq (related (skS.0 6 a_1) a (skS.0 3 (skS.0 6 a_1) a_2 a a_3)) False))))
% 12.17/12.40 Clause #161 (by superposition #[159, 115]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.17/12.40 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.17/12.40 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.17/12.40 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.17/12.40 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_2) (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) False)
% 12.17/12.40 (Eq False True))))
% 12.17/12.40 Clause #166 (by clausification #[116]): ∀ (a a_1 a_2 : Iota),
% 12.17/12.40 Eq
% 12.17/12.40 (Not
% 12.17/12.40 (And
% 12.17/12.40 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.17/12.40 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) →
% 12.17/12.40 And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.17/12.40 (∀ (D : Iota),
% 12.17/12.40 element D (the_carrier (skS.0 6 a)) →
% 12.17/12.40 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.17/12.40 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.17/12.40 (∀ (D : Iota),
% 12.17/12.40 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.26/12.42 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.26/12.42 True
% 12.26/12.42 Clause #167 (by clausification #[166]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.42 Eq
% 12.26/12.42 (And
% 12.26/12.42 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) →
% 12.26/12.42 And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.26/12.42 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2))))
% 12.26/12.42 False
% 12.26/12.42 Clause #168 (by clausification #[167]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.42 Or
% 12.26/12.42 (Eq
% 12.26/12.42 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) →
% 12.26/12.42 And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.42 False)
% 12.26/12.42 (Eq
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.26/12.42 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 False)
% 12.26/12.42 Clause #169 (by clausification #[168]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.42 Or
% 12.26/12.42 (Eq
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.26/12.42 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 False)
% 12.26/12.42 (Eq
% 12.26/12.42 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 True)
% 12.26/12.42 Clause #170 (by clausification #[168]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.42 Or
% 12.26/12.42 (Eq
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D) →
% 12.26/12.42 And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 False)
% 12.26/12.42 (Eq
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.42 False)
% 12.26/12.42 Clause #171 (by clausification #[169]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.42 Or
% 12.26/12.42 (Eq
% 12.26/12.42 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.42 True)
% 12.26/12.42 (Eq
% 12.26/12.42 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.42 (∀ (D : Iota),
% 12.26/12.42 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.42 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.45 True)
% 12.26/12.45 Clause #173 (by clausification #[171]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or
% 12.26/12.45 (Eq
% 12.26/12.45 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.45 (∀ (D : Iota),
% 12.26/12.45 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.45 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.45 True)
% 12.26/12.45 (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 Clause #174 (by clausification #[171]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or
% 12.26/12.45 (Eq
% 12.26/12.45 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.26/12.45 (∀ (D : Iota),
% 12.26/12.45 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.45 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.26/12.45 True)
% 12.26/12.45 (Eq (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) True)
% 12.26/12.45 Clause #175 (by clausification #[173]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Eq
% 12.26/12.45 (∀ (D : Iota),
% 12.26/12.45 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.45 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D)
% 12.26/12.45 True)
% 12.26/12.45 Clause #176 (by clausification #[173]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True)
% 12.26/12.45 Clause #177 (by clausification #[175]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Eq
% 12.26/12.45 (element a_3 (the_carrier (skS.0 6 a)) →
% 12.26/12.45 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3 → related (skS.0 6 a) (skS.0 7 a a_1) a_3)
% 12.26/12.45 True)
% 12.26/12.45 Clause #178 (by clausification #[177]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq (element a_3 (the_carrier (skS.0 6 a))) False)
% 12.26/12.45 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3 → related (skS.0 6 a) (skS.0 7 a a_1) a_3) True))
% 12.26/12.45 Clause #179 (by clausification #[178]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq (element a_3 (the_carrier (skS.0 6 a))) False)
% 12.26/12.45 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3) False)
% 12.26/12.45 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) a_3) True)))
% 12.26/12.45 Clause #183 (by superposition #[176, 130]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq True False)
% 12.26/12.45 (Eq (element (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True)))
% 12.26/12.45 Clause #184 (by superposition #[176, 150]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq True False)
% 12.26/12.45 (Eq
% 12.26/12.45 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2)
% 12.26/12.45 (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.26/12.45 True)))
% 12.26/12.45 Clause #185 (by clausification #[142]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) True)
% 12.26/12.45 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.26/12.45 (Eq (related (skS.0 6 a) (skS.0 7 a a_2) (skS.0 4 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) False))
% 12.26/12.45 Clause #186 (by superposition #[185, 176]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.45 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.45 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.26/12.45 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True) (Eq False True)))
% 12.26/12.45 Clause #216 (by clausification #[174]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.45 Or (Eq (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) True)
% 12.26/12.45 (Eq
% 12.26/12.45 (∀ (D : Iota),
% 12.26/12.45 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.47 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D)
% 12.26/12.47 True)
% 12.26/12.47 Clause #217 (by clausification #[174]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.47 Or (Eq (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) True)
% 12.26/12.47 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True)
% 12.26/12.47 Clause #218 (by clausification #[216]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.47 Or
% 12.26/12.47 (Eq
% 12.26/12.47 (∀ (D : Iota),
% 12.26/12.47 element D (the_carrier (skS.0 6 a)) →
% 12.26/12.47 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D)
% 12.26/12.47 True)
% 12.26/12.47 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.47 Clause #219 (by clausification #[218]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.47 (Eq
% 12.26/12.47 (element a_3 (the_carrier (skS.0 6 a)) →
% 12.26/12.47 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3 → related (skS.0 6 a) (skS.0 7 a a_1) a_3)
% 12.26/12.47 True)
% 12.26/12.47 Clause #220 (by clausification #[219]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.47 (Or (Eq (element a_3 (the_carrier (skS.0 6 a))) False)
% 12.26/12.47 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3 → related (skS.0 6 a) (skS.0 7 a a_1) a_3) True))
% 12.26/12.47 Clause #221 (by clausification #[220]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.47 (Or (Eq (element a_3 (the_carrier (skS.0 6 a))) False)
% 12.26/12.47 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) a_3) False)
% 12.26/12.47 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) a_3) True)))
% 12.26/12.47 Clause #228 (by clausification #[217]): ∀ (a a_1 a_2 : Iota),
% 12.26/12.47 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True)
% 12.26/12.47 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.26/12.47 Clause #239 (by clausification #[119]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.26/12.47 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.26/12.47 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.26/12.47 (Eq (element (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3) (the_carrier (skS.0 6 a))) True)))
% 12.26/12.47 Clause #241 (by clausification #[157]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.26/12.47 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.26/12.47 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.26/12.47 (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) True)))
% 12.26/12.47 Clause #270 (by clausification #[183]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.47 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.47 (Eq (element (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True))
% 12.26/12.47 Clause #271 (by eliminate duplicate literals #[270]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.47 (Eq (element (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True)
% 12.26/12.47 Clause #278 (by superposition #[271, 179]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.26/12.47 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_3 a_4)) True)
% 12.26/12.47 (Or (Eq True False)
% 12.26/12.47 (Or
% 12.26/12.47 (Eq
% 12.26/12.47 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_3 a_4)
% 12.26/12.47 (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.26/12.47 False)
% 12.26/12.47 (Eq (related (skS.0 6 a) (skS.0 7 a a_3) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.26/12.47 True))))
% 12.26/12.47 Clause #292 (by clausification #[161]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.26/12.47 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) a_1) False)
% 12.26/12.47 (Or (Eq (skS.0 7 a a_2) (join_on_relstr (skS.0 6 a) a_1))
% 12.26/12.47 (Or (Eq (relstr_set_smaller (skS.0 6 a) a_1 (skS.0 7 a a_2)) False)
% 12.26/12.47 (Eq (related (skS.0 6 a) (skS.0 7 a a_2) (skS.0 3 (skS.0 6 a) a_1 (skS.0 7 a a_2) a_3)) False)))
% 12.33/12.49 Clause #318 (by clausification #[186]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.49 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.33/12.49 (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True))
% 12.33/12.49 Clause #319 (by eliminate duplicate literals #[318]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.49 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.33/12.49 Clause #322 (by clausification #[184]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.49 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.49 (Eq
% 12.33/12.49 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2)
% 12.33/12.49 (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.33/12.49 True))
% 12.33/12.49 Clause #323 (by eliminate duplicate literals #[322]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.49 (Eq
% 12.33/12.49 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.33/12.49 True)
% 12.33/12.49 Clause #326 (by clausification #[170]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.49 Or
% 12.33/12.49 (Eq
% 12.33/12.49 (And (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1))
% 12.33/12.49 (∀ (D : Iota),
% 12.33/12.49 element D (the_carrier (skS.0 6 a)) →
% 12.33/12.49 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D))
% 12.33/12.49 False)
% 12.33/12.49 (Eq
% 12.33/12.49 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.49 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.49 False)
% 12.33/12.49 Clause #358 (by clausification #[326]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.49 Or
% 12.33/12.49 (Eq
% 12.33/12.49 (And (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.49 (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.49 False)
% 12.33/12.49 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.49 (Eq
% 12.33/12.49 (∀ (D : Iota),
% 12.33/12.49 element D (the_carrier (skS.0 6 a)) →
% 12.33/12.49 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D)
% 12.33/12.49 False))
% 12.33/12.49 Clause #359 (by clausification #[358]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.49 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.49 (Or
% 12.33/12.49 (Eq
% 12.33/12.49 (∀ (D : Iota),
% 12.33/12.49 element D (the_carrier (skS.0 6 a)) →
% 12.33/12.49 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) D → related (skS.0 6 a) (skS.0 7 a a_1) D)
% 12.33/12.49 False)
% 12.33/12.49 (Or (Eq (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) False)
% 12.33/12.49 (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)))
% 12.33/12.49 Clause #360 (by clausification #[359]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.49 (Or (Eq (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) False)
% 12.33/12.49 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.49 (Eq
% 12.33/12.49 (Not
% 12.33/12.49 (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a)) →
% 12.33/12.49 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3) →
% 12.33/12.49 related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)))
% 12.33/12.49 True)))
% 12.33/12.49 Clause #361 (by clausification #[360]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.49 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.49 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.49 (Or
% 12.33/12.49 (Eq
% 12.33/12.49 (Not
% 12.33/12.49 (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a)) →
% 12.33/12.49 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3) →
% 12.33/12.49 related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)))
% 12.33/12.49 True)
% 12.33/12.49 (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.33/12.52 Clause #362 (by clausification #[361]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.52 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.52 (Eq
% 12.33/12.52 (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a)) →
% 12.33/12.52 relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3) →
% 12.33/12.52 related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3))
% 12.33/12.52 False)))
% 12.33/12.52 Clause #363 (by clausification #[362]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.52 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.52 (Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True)))
% 12.33/12.52 Clause #364 (by clausification #[362]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.52 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.52 (Eq
% 12.33/12.52 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3) →
% 12.33/12.52 related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3))
% 12.33/12.52 False)))
% 12.33/12.52 Clause #382 (by clausification #[364]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.52 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.52 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True)))
% 12.33/12.52 Clause #383 (by clausification #[364]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) False)
% 12.33/12.52 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.52 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False)))
% 12.33/12.52 Clause #434 (by clausification #[278]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.33/12.52 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_3 a_4)) True)
% 12.33/12.52 (Or
% 12.33/12.52 (Eq
% 12.33/12.52 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_3 a_4)
% 12.33/12.52 (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.33/12.52 False)
% 12.33/12.52 (Eq (related (skS.0 6 a) (skS.0 7 a a_3) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5)) True)))
% 12.33/12.52 Clause #435 (by superposition #[434, 323]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True) (Eq False True))))
% 12.33/12.52 Clause #436 (by clausification #[435]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.33/12.52 (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)))
% 12.33/12.52 Clause #437 (by eliminate duplicate literals #[436]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.52 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 4 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.33/12.52 Clause #438 (by superposition #[437, 319]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.52 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.52 (Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True) (Eq True False))
% 12.33/12.55 Clause #440 (by clausification #[438]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.55 Or (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.55 (Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True)
% 12.33/12.55 Clause #441 (by eliminate duplicate literals #[440]): ∀ (a a_1 a_2 : Iota), Eq (ex_sup_of_relstr_set (skS.0 6 a) (skS.0 8 a a_1 a_2)) True
% 12.33/12.55 Clause #449 (by backward demodulation #[441, 363]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Or (Eq True False)
% 12.33/12.55 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.55 (Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True)))
% 12.33/12.55 Clause #450 (by backward demodulation #[441, 382]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Or (Eq True False)
% 12.33/12.55 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.55 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True)))
% 12.33/12.55 Clause #451 (by backward demodulation #[441, 383]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Or (Eq True False)
% 12.33/12.55 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.55 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False)))
% 12.33/12.55 Clause #461 (by superposition #[441, 109]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.55 Or (Eq True False)
% 12.33/12.55 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) True)
% 12.33/12.55 Clause #463 (by superposition #[441, 134]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq True False)
% 12.33/12.55 (Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.33/12.55 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) False)
% 12.33/12.55 (Eq (related (skS.0 6 a_1) (join_on_relstr (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3)) a) True)))
% 12.33/12.55 Clause #466 (by superposition #[441, 239]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.33/12.55 Or (Eq True False)
% 12.33/12.55 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.33/12.55 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Eq (element (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4) (the_carrier (skS.0 6 a))) True)))
% 12.33/12.55 Clause #467 (by superposition #[441, 241]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.33/12.55 Or (Eq True False)
% 12.33/12.55 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.33/12.55 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Eq
% 12.33/12.55 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3)
% 12.33/12.55 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4))
% 12.33/12.55 True)))
% 12.33/12.55 Clause #470 (by superposition #[441, 292]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.33/12.55 Or (Eq True False)
% 12.33/12.55 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.33/12.55 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4)) False)))
% 12.33/12.55 Clause #481 (by clausification #[461]): ∀ (a a_1 a_2 : Iota),
% 12.33/12.55 Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) True
% 12.33/12.55 Clause #491 (by clausification #[463]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.33/12.55 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) False)
% 12.33/12.55 (Eq (related (skS.0 6 a_1) (join_on_relstr (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3)) a) True))
% 12.33/12.55 Clause #522 (by clausification #[449]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.33/12.55 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.33/12.55 (Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True))
% 12.33/12.55 Clause #530 (by clausification #[451]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.33/12.55 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.42/12.57 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False))
% 12.42/12.57 Clause #533 (by clausification #[450]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.42/12.57 (Or (Ne (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True))
% 12.42/12.57 Clause #553 (by clausification #[466]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.42/12.57 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.42/12.57 (Eq (element (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4) (the_carrier (skS.0 6 a))) True))
% 12.42/12.57 Clause #554 (by superposition #[553, 228]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Or (Eq (element (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True)
% 12.42/12.57 (Or (Eq False True) (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.42/12.57 Clause #555 (by clausification #[554]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Or (Eq (element (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True)
% 12.42/12.57 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))))
% 12.42/12.57 Clause #556 (by eliminate duplicate literals #[555]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Eq (element (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3) (the_carrier (skS.0 6 a))) True)
% 12.42/12.57 Clause #563 (by superposition #[556, 221]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Or (Eq (skS.0 7 a a_3) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_3 a_4)))
% 12.42/12.57 (Or (Eq True False)
% 12.42/12.57 (Or
% 12.42/12.57 (Eq
% 12.42/12.57 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_3 a_4)
% 12.42/12.57 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.42/12.57 False)
% 12.42/12.57 (Eq (related (skS.0 6 a) (skS.0 7 a a_3) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.42/12.57 True))))
% 12.42/12.57 Clause #574 (by clausification #[470]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.42/12.57 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.42/12.57 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4)) False))
% 12.42/12.57 Clause #575 (by superposition #[574, 228]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.42/12.57 (Or (Eq False True) (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.42/12.57 Clause #576 (by clausification #[575]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.42/12.57 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))))
% 12.42/12.57 Clause #577 (by eliminate duplicate literals #[576]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.57 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) False)
% 12.42/12.57 Clause #583 (by clausification #[467]): ∀ (a a_1 a_2 a_3 a_4 : Iota),
% 12.42/12.57 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_2 a_3)))
% 12.42/12.57 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1)) False)
% 12.42/12.57 (Eq
% 12.42/12.57 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_2 a_3)
% 12.42/12.57 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_2 a_3) (skS.0 7 a a_1) a_4))
% 12.42/12.60 True))
% 12.42/12.60 Clause #584 (by superposition #[583, 228]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or
% 12.42/12.60 (Eq
% 12.42/12.60 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2)
% 12.42/12.60 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.42/12.60 True)
% 12.42/12.60 (Or (Eq False True) (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.42/12.60 Clause #585 (by clausification #[584]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or
% 12.42/12.60 (Eq
% 12.42/12.60 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2)
% 12.42/12.60 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.42/12.60 True)
% 12.42/12.60 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))))
% 12.42/12.60 Clause #586 (by eliminate duplicate literals #[585]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Eq
% 12.42/12.60 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3))
% 12.42/12.60 True)
% 12.42/12.60 Clause #646 (by clausification #[563]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (skS.0 7 a a_3) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_3 a_4)))
% 12.42/12.60 (Or
% 12.42/12.60 (Eq
% 12.42/12.60 (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_3 a_4)
% 12.42/12.60 (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5))
% 12.42/12.60 False)
% 12.42/12.60 (Eq (related (skS.0 6 a) (skS.0 7 a a_3) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_5)) True)))
% 12.42/12.60 Clause #647 (by superposition #[646, 586]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.42/12.60 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) (Eq False True))))
% 12.42/12.60 Clause #648 (by clausification #[647]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.42/12.60 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))))
% 12.42/12.60 Clause #649 (by eliminate duplicate literals #[648]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 3 (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1) a_3)) True)
% 12.42/12.60 Clause #650 (by superposition #[649, 577]): ∀ (a a_1 a_2 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))) (Eq True False))
% 12.42/12.60 Clause #651 (by clausification #[650]): ∀ (a a_1 a_2 : Iota),
% 12.42/12.60 Or (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 (Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2)))
% 12.42/12.60 Clause #652 (by eliminate duplicate literals #[651]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 7 a a_1) (join_on_relstr (skS.0 6 a) (skS.0 8 a a_1 a_2))
% 12.42/12.60 Clause #658 (by backward demodulation #[652, 481]): ∀ (a a_1 a_2 : Iota), Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True
% 12.42/12.60 Clause #659 (by backward demodulation #[652, 491]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 12.42/12.60 (Or (Eq (relstr_set_smaller (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) False)
% 12.42/12.60 (Eq (related (skS.0 6 a_1) (skS.0 7 a_1 a_2) a) True))
% 12.42/12.60 Clause #696 (by backward contextual literal cutting #[652, 522]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.42/12.60 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.42/12.60 (Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True)
% 12.42/12.60 Clause #697 (by backward contextual literal cutting #[652, 530]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.45/12.62 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.45/12.62 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False)
% 12.45/12.62 Clause #698 (by backward contextual literal cutting #[652, 533]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.45/12.62 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) False)
% 12.45/12.62 (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True)
% 12.45/12.62 Clause #712 (by superposition #[696, 658]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True) (Eq False True)
% 12.45/12.62 Clause #715 (by clausification #[712]): ∀ (a a_1 a_2 a_3 : Iota), Eq (element (skS.0 11 a a_1 a_2 a_3) (the_carrier (skS.0 6 a))) True
% 12.45/12.62 Clause #723 (by superposition #[715, 659]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.45/12.62 Or (Eq True False)
% 12.45/12.62 (Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_3 a_4 a_5)) False)
% 12.45/12.62 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_3 a_4 a_5)) True))
% 12.45/12.62 Clause #727 (by forward demodulation #[697, 658]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq True False) (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False)
% 12.45/12.62 Clause #728 (by clausification #[727]): ∀ (a a_1 a_2 a_3 : Iota), Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) False
% 12.45/12.62 Clause #729 (by forward demodulation #[698, 658]): ∀ (a a_1 a_2 a_3 : Iota),
% 12.45/12.62 Or (Eq True False) (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True)
% 12.45/12.62 Clause #730 (by clausification #[729]): ∀ (a a_1 a_2 a_3 : Iota), Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_1 a_2 a_3)) True
% 12.45/12.62 Clause #733 (by clausification #[723]): ∀ (a a_1 a_2 a_3 a_4 a_5 : Iota),
% 12.45/12.62 Or (Eq (relstr_set_smaller (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 11 a a_3 a_4 a_5)) False)
% 12.45/12.62 (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_3 a_4 a_5)) True)
% 12.45/12.62 Clause #734 (by superposition #[733, 730]): ∀ (a a_1 a_2 a_3 : Iota), Or (Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) True) (Eq False True)
% 12.45/12.62 Clause #735 (by clausification #[734]): ∀ (a a_1 a_2 a_3 : Iota), Eq (related (skS.0 6 a) (skS.0 7 a a_1) (skS.0 11 a a_1 a_2 a_3)) True
% 12.45/12.62 Clause #736 (by superposition #[735, 728]): Eq True False
% 12.45/12.62 Clause #737 (by clausification #[736]): False
% 12.45/12.62 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------