TSTP Solution File: SEU361+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n031.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 5.23s 5.45s
% Output : Proof 5.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SEU361+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : duper %s
% 0.14/0.35 % Computer : n031.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 19:33:50 EDT 2023
% 0.14/0.35 % CPUTime :
% 5.23/5.45 SZS status Theorem for theBenchmark.p
% 5.23/5.45 SZS output start Proof for theBenchmark.p
% 5.23/5.45 Clause #2 (by assumption #[]): Eq (∀ (A : Iota), rel_str A → Eq (bottom_of_relstr A) (join_on_relstr A empty_set)) True
% 5.23/5.45 Clause #4 (by assumption #[]): Eq (∀ (A B : Iota), rel_str A → element (join_on_relstr A B) (the_carrier A)) True
% 5.23/5.45 Clause #18 (by assumption #[]): Eq
% 5.23/5.45 (∀ (A : Iota),
% 5.23/5.45 And (antisymmetric_relstr A) (rel_str A) →
% 5.23/5.45 ∀ (B : Iota),
% 5.23/5.45 element B (the_carrier A) →
% 5.23/5.45 ∀ (C : Iota),
% 5.23/5.45 And
% 5.23/5.45 (And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C) →
% 5.23/5.45 And (relstr_set_smaller A C B)
% 5.23/5.45 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D))
% 5.23/5.45 (And (relstr_set_smaller A C B)
% 5.23/5.45 (∀ (D : Iota), element D (the_carrier A) → relstr_set_smaller A C D → related A B D) →
% 5.23/5.45 And (Eq B (join_on_relstr A C)) (ex_sup_of_relstr_set A C)))
% 5.23/5.45 True
% 5.23/5.45 Clause #19 (by assumption #[]): Eq
% 5.23/5.45 (∀ (A : Iota),
% 5.23/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) →
% 5.23/5.45 And (ex_sup_of_relstr_set A empty_set) (ex_inf_of_relstr_set A (the_carrier A)))
% 5.23/5.45 True
% 5.23/5.45 Clause #20 (by assumption #[]): Eq
% 5.23/5.45 (Not
% 5.23/5.45 (∀ (A : Iota),
% 5.23/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) →
% 5.23/5.45 ∀ (B : Iota), element B (the_carrier A) → related A (bottom_of_relstr A) B))
% 5.23/5.45 True
% 5.23/5.45 Clause #22 (by assumption #[]): Eq
% 5.23/5.45 (∀ (A : Iota),
% 5.23/5.45 rel_str A →
% 5.23/5.45 ∀ (B : Iota),
% 5.23/5.45 element B (the_carrier A) → And (relstr_set_smaller A empty_set B) (relstr_element_smaller A empty_set B))
% 5.23/5.45 True
% 5.23/5.45 Clause #49 (by clausification #[2]): ∀ (a : Iota), Eq (rel_str a → Eq (bottom_of_relstr a) (join_on_relstr a empty_set)) True
% 5.23/5.45 Clause #50 (by clausification #[49]): ∀ (a : Iota), Or (Eq (rel_str a) False) (Eq (Eq (bottom_of_relstr a) (join_on_relstr a empty_set)) True)
% 5.23/5.45 Clause #51 (by clausification #[50]): ∀ (a : Iota), Or (Eq (rel_str a) False) (Eq (bottom_of_relstr a) (join_on_relstr a empty_set))
% 5.23/5.45 Clause #69 (by clausification #[4]): ∀ (a : Iota), Eq (∀ (B : Iota), rel_str a → element (join_on_relstr a B) (the_carrier a)) True
% 5.23/5.45 Clause #70 (by clausification #[69]): ∀ (a a_1 : Iota), Eq (rel_str a → element (join_on_relstr a a_1) (the_carrier a)) True
% 5.23/5.45 Clause #71 (by clausification #[70]): ∀ (a a_1 : Iota), Or (Eq (rel_str a) False) (Eq (element (join_on_relstr a a_1) (the_carrier a)) True)
% 5.23/5.45 Clause #95 (by clausification #[19]): ∀ (a : Iota),
% 5.23/5.45 Eq
% 5.23/5.45 (And (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) (rel_str a) →
% 5.23/5.45 And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a)))
% 5.23/5.45 True
% 5.23/5.45 Clause #96 (by clausification #[95]): ∀ (a : Iota),
% 5.23/5.45 Or (Eq (And (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) (rel_str a)) False)
% 5.23/5.45 (Eq (And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a))) True)
% 5.23/5.45 Clause #97 (by clausification #[96]): ∀ (a : Iota),
% 5.23/5.45 Or (Eq (And (ex_sup_of_relstr_set a empty_set) (ex_inf_of_relstr_set a (the_carrier a))) True)
% 5.23/5.45 (Or (Eq (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) False)
% 5.23/5.45 (Eq (rel_str a) False))
% 5.23/5.45 Clause #99 (by clausification #[97]): ∀ (a : Iota),
% 5.23/5.45 Or (Eq (And (And (Not (empty_carrier a)) (antisymmetric_relstr a)) (lower_bounded_relstr a)) False)
% 5.23/5.45 (Or (Eq (rel_str a) False) (Eq (ex_sup_of_relstr_set a empty_set) True))
% 5.23/5.45 Clause #104 (by clausification #[20]): Eq
% 5.23/5.45 (∀ (A : Iota),
% 5.23/5.45 And (And (And (Not (empty_carrier A)) (antisymmetric_relstr A)) (lower_bounded_relstr A)) (rel_str A) →
% 5.23/5.45 ∀ (B : Iota), element B (the_carrier A) → related A (bottom_of_relstr A) B)
% 5.23/5.45 False
% 5.23/5.45 Clause #105 (by clausification #[104]): ∀ (a : Iota),
% 5.23/5.45 Eq
% 5.23/5.45 (Not
% 5.23/5.45 (And
% 5.23/5.45 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a)))
% 5.23/5.45 (lower_bounded_relstr (skS.0 7 a)))
% 5.31/5.47 (rel_str (skS.0 7 a)) →
% 5.31/5.47 ∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B))
% 5.31/5.47 True
% 5.31/5.47 Clause #106 (by clausification #[105]): ∀ (a : Iota),
% 5.31/5.47 Eq
% 5.31/5.47 (And
% 5.31/5.47 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a)))
% 5.31/5.47 (lower_bounded_relstr (skS.0 7 a)))
% 5.31/5.47 (rel_str (skS.0 7 a)) →
% 5.31/5.47 ∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B)
% 5.31/5.47 False
% 5.31/5.47 Clause #107 (by clausification #[106]): ∀ (a : Iota),
% 5.31/5.47 Eq
% 5.31/5.47 (And
% 5.31/5.47 (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a)))
% 5.31/5.47 (lower_bounded_relstr (skS.0 7 a)))
% 5.31/5.47 (rel_str (skS.0 7 a)))
% 5.31/5.47 True
% 5.31/5.47 Clause #108 (by clausification #[106]): ∀ (a : Iota),
% 5.31/5.47 Eq (∀ (B : Iota), element B (the_carrier (skS.0 7 a)) → related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) B) False
% 5.31/5.47 Clause #109 (by clausification #[107]): ∀ (a : Iota), Eq (rel_str (skS.0 7 a)) True
% 5.31/5.47 Clause #110 (by clausification #[107]): ∀ (a : Iota),
% 5.31/5.47 Eq (And (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) (lower_bounded_relstr (skS.0 7 a)))
% 5.31/5.47 True
% 5.31/5.47 Clause #112 (by superposition #[109, 51]): ∀ (a : Iota), Or (Eq True False) (Eq (bottom_of_relstr (skS.0 7 a)) (join_on_relstr (skS.0 7 a) empty_set))
% 5.31/5.47 Clause #114 (by superposition #[109, 71]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) True)
% 5.31/5.47 Clause #116 (by clausification #[18]): ∀ (a : Iota),
% 5.31/5.47 Eq
% 5.31/5.47 (And (antisymmetric_relstr a) (rel_str a) →
% 5.31/5.47 ∀ (B : Iota),
% 5.31/5.47 element B (the_carrier a) →
% 5.31/5.47 ∀ (C : Iota),
% 5.31/5.47 And
% 5.31/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) →
% 5.31/5.47 And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D))
% 5.31/5.47 (And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) →
% 5.31/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C)))
% 5.31/5.47 True
% 5.31/5.47 Clause #117 (by clausification #[116]): ∀ (a : Iota),
% 5.31/5.47 Or (Eq (And (antisymmetric_relstr a) (rel_str a)) False)
% 5.31/5.47 (Eq
% 5.31/5.47 (∀ (B : Iota),
% 5.31/5.47 element B (the_carrier a) →
% 5.31/5.47 ∀ (C : Iota),
% 5.31/5.47 And
% 5.31/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) →
% 5.31/5.47 And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D))
% 5.31/5.47 (And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) →
% 5.31/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C)))
% 5.31/5.47 True)
% 5.31/5.47 Clause #118 (by clausification #[117]): ∀ (a : Iota),
% 5.31/5.47 Or
% 5.31/5.47 (Eq
% 5.31/5.47 (∀ (B : Iota),
% 5.31/5.47 element B (the_carrier a) →
% 5.31/5.47 ∀ (C : Iota),
% 5.31/5.47 And
% 5.31/5.47 (And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C) →
% 5.31/5.47 And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D))
% 5.31/5.47 (And (relstr_set_smaller a C B)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a B D) →
% 5.31/5.47 And (Eq B (join_on_relstr a C)) (ex_sup_of_relstr_set a C)))
% 5.31/5.47 True)
% 5.31/5.47 (Or (Eq (antisymmetric_relstr a) False) (Eq (rel_str a) False))
% 5.31/5.47 Clause #119 (by clausification #[118]): ∀ (a a_1 : Iota),
% 5.31/5.47 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.47 (Or (Eq (rel_str a) False)
% 5.31/5.47 (Eq
% 5.31/5.47 (element a_1 (the_carrier a) →
% 5.31/5.47 ∀ (C : Iota),
% 5.31/5.47 And
% 5.31/5.47 (And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C) →
% 5.31/5.47 And (relstr_set_smaller a C a_1)
% 5.31/5.47 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D))
% 5.31/5.48 (And (relstr_set_smaller a C a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D) →
% 5.31/5.48 And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C)))
% 5.31/5.48 True))
% 5.31/5.48 Clause #120 (by clausification #[119]): ∀ (a a_1 : Iota),
% 5.31/5.48 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.48 (Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.48 (Eq
% 5.31/5.48 (∀ (C : Iota),
% 5.31/5.48 And
% 5.31/5.48 (And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C) →
% 5.31/5.48 And (relstr_set_smaller a C a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D))
% 5.31/5.48 (And (relstr_set_smaller a C a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a C D → related a a_1 D) →
% 5.31/5.48 And (Eq a_1 (join_on_relstr a C)) (ex_sup_of_relstr_set a C)))
% 5.31/5.48 True)))
% 5.31/5.48 Clause #121 (by clausification #[120]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.48 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.48 (Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.48 (Eq
% 5.31/5.48 (And
% 5.31/5.48 (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2) →
% 5.31/5.48 And (relstr_set_smaller a a_2 a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 5.31/5.48 (And (relstr_set_smaller a a_2 a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) →
% 5.31/5.48 And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2)))
% 5.31/5.48 True)))
% 5.31/5.48 Clause #123 (by clausification #[121]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.48 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.48 (Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.48 (Eq
% 5.31/5.48 (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2) →
% 5.31/5.48 And (relstr_set_smaller a a_2 a_1)
% 5.31/5.48 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 5.31/5.48 True)))
% 5.31/5.48 Clause #141 (by clausification #[22]): ∀ (a : Iota),
% 5.31/5.48 Eq
% 5.31/5.48 (rel_str a →
% 5.31/5.48 ∀ (B : Iota),
% 5.31/5.48 element B (the_carrier a) → And (relstr_set_smaller a empty_set B) (relstr_element_smaller a empty_set B))
% 5.31/5.48 True
% 5.31/5.48 Clause #142 (by clausification #[141]): ∀ (a : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False)
% 5.31/5.48 (Eq
% 5.31/5.48 (∀ (B : Iota),
% 5.31/5.48 element B (the_carrier a) → And (relstr_set_smaller a empty_set B) (relstr_element_smaller a empty_set B))
% 5.31/5.48 True)
% 5.31/5.48 Clause #143 (by clausification #[142]): ∀ (a a_1 : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False)
% 5.31/5.48 (Eq
% 5.31/5.48 (element a_1 (the_carrier a) → And (relstr_set_smaller a empty_set a_1) (relstr_element_smaller a empty_set a_1))
% 5.31/5.48 True)
% 5.31/5.48 Clause #144 (by clausification #[143]): ∀ (a a_1 : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.48 (Eq (And (relstr_set_smaller a empty_set a_1) (relstr_element_smaller a empty_set a_1)) True))
% 5.31/5.48 Clause #146 (by clausification #[144]): ∀ (a a_1 : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False) (Or (Eq (element a_1 (the_carrier a)) False) (Eq (relstr_set_smaller a empty_set a_1) True))
% 5.31/5.48 Clause #150 (by superposition #[146, 109]): ∀ (a a_1 : Iota),
% 5.31/5.48 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 5.31/5.48 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) True) (Eq False True))
% 5.31/5.48 Clause #159 (by clausification #[112]): ∀ (a : Iota), Eq (bottom_of_relstr (skS.0 7 a)) (join_on_relstr (skS.0 7 a) empty_set)
% 5.31/5.48 Clause #161 (by clausification #[99]): ∀ (a : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (ex_sup_of_relstr_set a empty_set) True)
% 5.31/5.48 (Or (Eq (And (Not (empty_carrier a)) (antisymmetric_relstr a)) False) (Eq (lower_bounded_relstr a) False)))
% 5.31/5.48 Clause #162 (by clausification #[161]): ∀ (a : Iota),
% 5.31/5.48 Or (Eq (rel_str a) False)
% 5.31/5.48 (Or (Eq (ex_sup_of_relstr_set a empty_set) True)
% 5.31/5.48 (Or (Eq (lower_bounded_relstr a) False)
% 5.31/5.48 (Or (Eq (Not (empty_carrier a)) False) (Eq (antisymmetric_relstr a) False))))
% 5.31/5.50 Clause #163 (by clausification #[162]): ∀ (a : Iota),
% 5.31/5.50 Or (Eq (rel_str a) False)
% 5.31/5.50 (Or (Eq (ex_sup_of_relstr_set a empty_set) True)
% 5.31/5.50 (Or (Eq (lower_bounded_relstr a) False) (Or (Eq (antisymmetric_relstr a) False) (Eq (empty_carrier a) True))))
% 5.31/5.50 Clause #165 (by superposition #[163, 109]): ∀ (a : Iota),
% 5.31/5.50 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True)
% 5.31/5.50 (Or (Eq (lower_bounded_relstr (skS.0 7 a)) False)
% 5.31/5.50 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Or (Eq (empty_carrier (skS.0 7 a)) True) (Eq False True))))
% 5.31/5.50 Clause #166 (by clausification #[108]): ∀ (a a_1 : Iota),
% 5.31/5.50 Eq
% 5.31/5.50 (Not
% 5.31/5.50 (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a)) →
% 5.31/5.50 related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)))
% 5.31/5.50 True
% 5.31/5.50 Clause #167 (by clausification #[166]): ∀ (a a_1 : Iota),
% 5.31/5.50 Eq
% 5.31/5.50 (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a)) →
% 5.31/5.50 related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1))
% 5.31/5.51 False
% 5.31/5.51 Clause #168 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (element (skS.0 9 a a_1) (the_carrier (skS.0 7 a))) True
% 5.31/5.51 Clause #169 (by clausification #[167]): ∀ (a a_1 : Iota), Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) False
% 5.31/5.51 Clause #181 (by clausification #[114]): ∀ (a a_1 : Iota), Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) True
% 5.31/5.51 Clause #199 (by clausification #[110]): ∀ (a : Iota), Eq (lower_bounded_relstr (skS.0 7 a)) True
% 5.31/5.51 Clause #200 (by clausification #[110]): ∀ (a : Iota), Eq (And (Not (empty_carrier (skS.0 7 a))) (antisymmetric_relstr (skS.0 7 a))) True
% 5.31/5.51 Clause #201 (by clausification #[200]): ∀ (a : Iota), Eq (antisymmetric_relstr (skS.0 7 a)) True
% 5.31/5.51 Clause #202 (by clausification #[200]): ∀ (a : Iota), Eq (Not (empty_carrier (skS.0 7 a))) True
% 5.31/5.51 Clause #204 (by clausification #[202]): ∀ (a : Iota), Eq (empty_carrier (skS.0 7 a)) False
% 5.31/5.51 Clause #207 (by clausification #[150]): ∀ (a a_1 : Iota),
% 5.31/5.51 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False) (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) True)
% 5.31/5.51 Clause #208 (by superposition #[207, 168]): ∀ (a a_1 : Iota), Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) True) (Eq False True)
% 5.31/5.51 Clause #220 (by clausification #[208]): ∀ (a a_1 : Iota), Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) True
% 5.31/5.51 Clause #228 (by clausification #[123]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.51 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.51 (Or (Eq (rel_str a) False)
% 5.31/5.51 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.51 (Or (Eq (And (Eq a_1 (join_on_relstr a a_2)) (ex_sup_of_relstr_set a a_2)) False)
% 5.31/5.51 (Eq
% 5.31/5.51 (And (relstr_set_smaller a a_2 a_1)
% 5.31/5.51 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 5.31/5.51 True))))
% 5.31/5.51 Clause #229 (by clausification #[228]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.51 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.51 (Or (Eq (rel_str a) False)
% 5.31/5.51 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.51 (Or
% 5.31/5.51 (Eq
% 5.31/5.51 (And (relstr_set_smaller a a_2 a_1)
% 5.31/5.51 (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D))
% 5.31/5.51 True)
% 5.31/5.51 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) False) (Eq (ex_sup_of_relstr_set a a_2) False)))))
% 5.31/5.51 Clause #230 (by clausification #[229]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.51 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.51 (Or (Eq (rel_str a) False)
% 5.31/5.51 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.51 (Or (Eq (Eq a_1 (join_on_relstr a a_2)) False)
% 5.31/5.51 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 5.31/5.51 (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) True)))))
% 5.31/5.51 Clause #232 (by clausification #[230]): ∀ (a a_1 a_2 : Iota),
% 5.31/5.51 Or (Eq (antisymmetric_relstr a) False)
% 5.31/5.51 (Or (Eq (rel_str a) False)
% 5.31/5.51 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.31/5.51 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 5.31/5.51 (Or (Eq (∀ (D : Iota), element D (the_carrier a) → relstr_set_smaller a a_2 D → related a a_1 D) True)
% 5.36/5.53 (Ne a_1 (join_on_relstr a a_2))))))
% 5.36/5.53 Clause #233 (by clausification #[232]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.53 Or (Eq (antisymmetric_relstr a) False)
% 5.36/5.53 (Or (Eq (rel_str a) False)
% 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2))
% 5.36/5.53 (Eq (element a_3 (the_carrier a) → relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True)))))
% 5.36/5.53 Clause #234 (by clausification #[233]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.53 Or (Eq (antisymmetric_relstr a) False)
% 5.36/5.53 (Or (Eq (rel_str a) False)
% 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2))
% 5.36/5.53 (Or (Eq (element a_3 (the_carrier a)) False)
% 5.36/5.53 (Eq (relstr_set_smaller a a_2 a_3 → related a a_1 a_3) True))))))
% 5.36/5.53 Clause #235 (by clausification #[234]): ∀ (a a_1 a_2 a_3 : Iota),
% 5.36/5.53 Or (Eq (antisymmetric_relstr a) False)
% 5.36/5.53 (Or (Eq (rel_str a) False)
% 5.36/5.53 (Or (Eq (element a_1 (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_2) False)
% 5.36/5.53 (Or (Ne a_1 (join_on_relstr a a_2))
% 5.36/5.53 (Or (Eq (element a_3 (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (relstr_set_smaller a a_2 a_3) False) (Eq (related a a_1 a_3) True)))))))
% 5.36/5.53 Clause #236 (by destructive equality resolution #[235]): ∀ (a a_1 a_2 : Iota),
% 5.36/5.53 Or (Eq (antisymmetric_relstr a) False)
% 5.36/5.53 (Or (Eq (rel_str a) False)
% 5.36/5.53 (Or (Eq (element (join_on_relstr a a_1) (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set a a_1) False)
% 5.36/5.53 (Or (Eq (element a_2 (the_carrier a)) False)
% 5.36/5.53 (Or (Eq (relstr_set_smaller a a_1 a_2) False) (Eq (related a (join_on_relstr a a_1) a_2) True))))))
% 5.36/5.53 Clause #237 (by superposition #[236, 201]): ∀ (a a_1 a_2 : Iota),
% 5.36/5.53 Or (Eq (rel_str (skS.0 7 a)) False)
% 5.36/5.53 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.36/5.53 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.36/5.53 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.36/5.53 (Or (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True) (Eq False True))))))
% 5.36/5.53 Clause #283 (by clausification #[165]): ∀ (a : Iota),
% 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True)
% 5.36/5.53 (Or (Eq (lower_bounded_relstr (skS.0 7 a)) False)
% 5.36/5.53 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True)))
% 5.36/5.53 Clause #284 (by forward demodulation #[283, 199]): ∀ (a : Iota),
% 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True)
% 5.36/5.53 (Or (Eq True False) (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True)))
% 5.36/5.53 Clause #285 (by clausification #[284]): ∀ (a : Iota),
% 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True)
% 5.36/5.53 (Or (Eq (antisymmetric_relstr (skS.0 7 a)) False) (Eq (empty_carrier (skS.0 7 a)) True))
% 5.36/5.53 Clause #286 (by forward demodulation #[285, 201]): ∀ (a : Iota),
% 5.36/5.53 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Or (Eq True False) (Eq (empty_carrier (skS.0 7 a)) True))
% 5.36/5.53 Clause #287 (by clausification #[286]): ∀ (a : Iota), Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Eq (empty_carrier (skS.0 7 a)) True)
% 5.36/5.53 Clause #288 (by forward demodulation #[287, 204]): ∀ (a : Iota), Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True) (Eq False True)
% 5.36/5.53 Clause #289 (by clausification #[288]): ∀ (a : Iota), Eq (ex_sup_of_relstr_set (skS.0 7 a) empty_set) True
% 5.36/5.53 Clause #318 (by clausification #[237]): ∀ (a a_1 a_2 : Iota),
% 5.36/5.53 Or (Eq (rel_str (skS.0 7 a)) False)
% 5.36/5.53 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False)
% 5.36/5.53 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.36/5.53 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.36/5.53 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.36/5.53 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True)))))
% 5.36/5.53 Clause #319 (by forward demodulation #[318, 109]): ∀ (a a_1 a_2 : Iota),
% 5.40/5.55 Or (Eq True False)
% 5.40/5.55 (Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.40/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.40/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True)))))
% 5.40/5.55 Clause #320 (by clausification #[319]): ∀ (a a_1 a_2 : Iota),
% 5.40/5.55 Or (Eq (element (join_on_relstr (skS.0 7 a) a_1) (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.40/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.40/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True))))
% 5.40/5.55 Clause #321 (by forward demodulation #[320, 181]): ∀ (a a_1 a_2 : Iota),
% 5.40/5.55 Or (Eq True False)
% 5.40/5.55 (Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.40/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.40/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True))))
% 5.40/5.55 Clause #322 (by clausification #[321]): ∀ (a a_1 a_2 : Iota),
% 5.40/5.55 Or (Eq (ex_sup_of_relstr_set (skS.0 7 a) a_1) False)
% 5.40/5.55 (Or (Eq (element a_2 (the_carrier (skS.0 7 a))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a) a_1 a_2) False)
% 5.40/5.55 (Eq (related (skS.0 7 a) (join_on_relstr (skS.0 7 a) a_1) a_2) True)))
% 5.40/5.55 Clause #323 (by superposition #[322, 289]): ∀ (a a_1 : Iota),
% 5.40/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False)
% 5.40/5.55 (Or (Eq (related (skS.0 7 a_1) (join_on_relstr (skS.0 7 a_1) empty_set) a) True) (Eq False True)))
% 5.40/5.55 Clause #324 (by clausification #[323]): ∀ (a a_1 : Iota),
% 5.40/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False)
% 5.40/5.55 (Eq (related (skS.0 7 a_1) (join_on_relstr (skS.0 7 a_1) empty_set) a) True))
% 5.40/5.55 Clause #325 (by forward demodulation #[324, 159]): ∀ (a a_1 : Iota),
% 5.40/5.55 Or (Eq (element a (the_carrier (skS.0 7 a_1))) False)
% 5.40/5.55 (Or (Eq (relstr_set_smaller (skS.0 7 a_1) empty_set a) False)
% 5.40/5.55 (Eq (related (skS.0 7 a_1) (bottom_of_relstr (skS.0 7 a_1)) a) True))
% 5.40/5.55 Clause #326 (by superposition #[325, 168]): ∀ (a a_1 : Iota),
% 5.40/5.55 Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) False)
% 5.40/5.55 (Or (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True) (Eq False True))
% 5.40/5.55 Clause #333 (by clausification #[326]): ∀ (a a_1 : Iota),
% 5.40/5.55 Or (Eq (relstr_set_smaller (skS.0 7 a) empty_set (skS.0 9 a a_1)) False)
% 5.40/5.55 (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True)
% 5.40/5.55 Clause #334 (by forward demodulation #[333, 220]): ∀ (a a_1 : Iota), Or (Eq True False) (Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True)
% 5.40/5.55 Clause #335 (by clausification #[334]): ∀ (a a_1 : Iota), Eq (related (skS.0 7 a) (bottom_of_relstr (skS.0 7 a)) (skS.0 9 a a_1)) True
% 5.40/5.55 Clause #336 (by superposition #[335, 169]): Eq True False
% 5.40/5.55 Clause #337 (by clausification #[336]): False
% 5.40/5.55 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------