TSTP Solution File: SEU305+1 by Duper---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 16:41:21 EDT 2023
% Result : Theorem 70.35s 70.65s
% Output : Proof 70.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.14 % Command : duper %s
% 0.13/0.35 % Computer : n009.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 12:10:07 EDT 2023
% 0.13/0.35 % CPUTime :
% 70.35/70.65 SZS status Theorem for theBenchmark.p
% 70.35/70.65 SZS output start Proof for theBenchmark.p
% 70.35/70.65 Clause #3 (by assumption #[]): Eq
% 70.35/70.65 (∀ (A B C : Iota),
% 70.35/70.65 And (And (And (And (Not (empty_carrier A)) (join_commutative A)) (join_semilatt_str A)) (element B (the_carrier A)))
% 70.35/70.65 (element C (the_carrier A)) →
% 70.35/70.65 Eq (join_commut A B C) (join_commut A C B))
% 70.35/70.65 True
% 70.35/70.65 Clause #5 (by assumption #[]): Eq
% 70.35/70.65 (∀ (A : Iota),
% 70.35/70.65 And (Not (empty_carrier A)) (join_semilatt_str A) →
% 70.35/70.65 ∀ (B : Iota),
% 70.35/70.65 element B (the_carrier A) → ∀ (C : Iota), element C (the_carrier A) → Iff (below A B C) (Eq (join A B C) C))
% 70.35/70.65 True
% 70.35/70.65 Clause #23 (by assumption #[]): Eq
% 70.35/70.65 (∀ (A B C : Iota),
% 70.35/70.65 And (And (And (And (Not (empty_carrier A)) (join_commutative A)) (join_semilatt_str A)) (element B (the_carrier A)))
% 70.35/70.65 (element C (the_carrier A)) →
% 70.35/70.65 Eq (join_commut A B C) (join A B C))
% 70.35/70.65 True
% 70.35/70.65 Clause #27 (by assumption #[]): Eq
% 70.35/70.65 (Not
% 70.35/70.65 (∀ (A : Iota),
% 70.35/70.65 And (And (Not (empty_carrier A)) (join_commutative A)) (join_semilatt_str A) →
% 70.35/70.65 ∀ (B : Iota),
% 70.35/70.65 element B (the_carrier A) →
% 70.35/70.65 ∀ (C : Iota), element C (the_carrier A) → And (below A B C) (below A C B) → Eq B C))
% 70.35/70.65 True
% 70.35/70.65 Clause #85 (by clausification #[3]): ∀ (a : Iota),
% 70.35/70.65 Eq
% 70.35/70.65 (∀ (B C : Iota),
% 70.35/70.65 And
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.65 (element B (the_carrier a)))
% 70.35/70.65 (element C (the_carrier a)) →
% 70.35/70.65 Eq (join_commut a B C) (join_commut a C B))
% 70.35/70.65 True
% 70.35/70.65 Clause #86 (by clausification #[85]): ∀ (a a_1 : Iota),
% 70.35/70.65 Eq
% 70.35/70.65 (∀ (C : Iota),
% 70.35/70.65 And
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.65 (element a_1 (the_carrier a)))
% 70.35/70.65 (element C (the_carrier a)) →
% 70.35/70.65 Eq (join_commut a a_1 C) (join_commut a C a_1))
% 70.35/70.65 True
% 70.35/70.65 Clause #87 (by clausification #[86]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.65 Eq
% 70.35/70.65 (And
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.65 (element a_1 (the_carrier a)))
% 70.35/70.65 (element a_2 (the_carrier a)) →
% 70.35/70.65 Eq (join_commut a a_1 a_2) (join_commut a a_2 a_1))
% 70.35/70.65 True
% 70.35/70.65 Clause #88 (by clausification #[87]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.65 Or
% 70.35/70.65 (Eq
% 70.35/70.65 (And
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.65 (element a_1 (the_carrier a)))
% 70.35/70.65 (element a_2 (the_carrier a)))
% 70.35/70.65 False)
% 70.35/70.65 (Eq (Eq (join_commut a a_1 a_2) (join_commut a a_2 a_1)) True)
% 70.35/70.65 Clause #89 (by clausification #[88]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.65 Or (Eq (Eq (join_commut a a_1 a_2) (join_commut a a_2 a_1)) True)
% 70.35/70.65 (Or
% 70.35/70.65 (Eq
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.65 (element a_1 (the_carrier a)))
% 70.35/70.65 False)
% 70.35/70.65 (Eq (element a_2 (the_carrier a)) False))
% 70.35/70.65 Clause #90 (by clausification #[89]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.65 Or
% 70.35/70.65 (Eq
% 70.35/70.65 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a)) (element a_1 (the_carrier a)))
% 70.35/70.66 False)
% 70.35/70.66 (Or (Eq (element a_2 (the_carrier a)) False) (Eq (join_commut a a_1 a_2) (join_commut a a_2 a_1)))
% 70.35/70.66 Clause #91 (by clausification #[90]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.66 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.66 (Or (Eq (join_commut a_1 a_2 a) (join_commut a_1 a a_2))
% 70.35/70.66 (Or (Eq (And (And (Not (empty_carrier a_1)) (join_commutative a_1)) (join_semilatt_str a_1)) False)
% 70.35/70.66 (Eq (element a_2 (the_carrier a_1)) False)))
% 70.35/70.66 Clause #92 (by clausification #[91]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.66 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.66 (Or (Eq (join_commut a_1 a_2 a) (join_commut a_1 a a_2))
% 70.35/70.66 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.66 (Or (Eq (And (Not (empty_carrier a_1)) (join_commutative a_1)) False) (Eq (join_semilatt_str a_1) False))))
% 70.35/70.66 Clause #93 (by clausification #[92]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.66 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.66 (Or (Eq (join_commut a_1 a_2 a) (join_commut a_1 a a_2))
% 70.35/70.66 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.66 (Or (Eq (join_semilatt_str a_1) False)
% 70.35/70.68 (Or (Eq (Not (empty_carrier a_1)) False) (Eq (join_commutative a_1) False)))))
% 70.35/70.68 Clause #94 (by clausification #[93]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.68 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.68 (Or (Eq (join_commut a_1 a_2 a) (join_commut a_1 a a_2))
% 70.35/70.68 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.68 (Or (Eq (join_semilatt_str a_1) False) (Or (Eq (join_commutative a_1) False) (Eq (empty_carrier a_1) True)))))
% 70.35/70.68 Clause #137 (by clausification #[5]): ∀ (a : Iota),
% 70.35/70.68 Eq
% 70.35/70.68 (And (Not (empty_carrier a)) (join_semilatt_str a) →
% 70.35/70.68 ∀ (B : Iota),
% 70.35/70.68 element B (the_carrier a) → ∀ (C : Iota), element C (the_carrier a) → Iff (below a B C) (Eq (join a B C) C))
% 70.35/70.68 True
% 70.35/70.68 Clause #138 (by clausification #[137]): ∀ (a : Iota),
% 70.35/70.68 Or (Eq (And (Not (empty_carrier a)) (join_semilatt_str a)) False)
% 70.35/70.68 (Eq
% 70.35/70.68 (∀ (B : Iota),
% 70.35/70.68 element B (the_carrier a) → ∀ (C : Iota), element C (the_carrier a) → Iff (below a B C) (Eq (join a B C) C))
% 70.35/70.68 True)
% 70.35/70.68 Clause #139 (by clausification #[138]): ∀ (a : Iota),
% 70.35/70.68 Or
% 70.35/70.68 (Eq
% 70.35/70.68 (∀ (B : Iota),
% 70.35/70.68 element B (the_carrier a) → ∀ (C : Iota), element C (the_carrier a) → Iff (below a B C) (Eq (join a B C) C))
% 70.35/70.68 True)
% 70.35/70.68 (Or (Eq (Not (empty_carrier a)) False) (Eq (join_semilatt_str a) False))
% 70.35/70.68 Clause #140 (by clausification #[139]): ∀ (a a_1 : Iota),
% 70.35/70.68 Or (Eq (Not (empty_carrier a)) False)
% 70.35/70.68 (Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Eq
% 70.35/70.68 (element a_1 (the_carrier a) →
% 70.35/70.68 ∀ (C : Iota), element C (the_carrier a) → Iff (below a a_1 C) (Eq (join a a_1 C) C))
% 70.35/70.68 True))
% 70.35/70.68 Clause #141 (by clausification #[140]): ∀ (a a_1 : Iota),
% 70.35/70.68 Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Or
% 70.35/70.68 (Eq
% 70.35/70.68 (element a_1 (the_carrier a) →
% 70.35/70.68 ∀ (C : Iota), element C (the_carrier a) → Iff (below a a_1 C) (Eq (join a a_1 C) C))
% 70.35/70.68 True)
% 70.35/70.68 (Eq (empty_carrier a) True))
% 70.35/70.68 Clause #142 (by clausification #[141]): ∀ (a a_1 : Iota),
% 70.35/70.68 Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Or (Eq (empty_carrier a) True)
% 70.35/70.68 (Or (Eq (element a_1 (the_carrier a)) False)
% 70.35/70.68 (Eq (∀ (C : Iota), element C (the_carrier a) → Iff (below a a_1 C) (Eq (join a a_1 C) C)) True)))
% 70.35/70.68 Clause #143 (by clausification #[142]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.68 Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Or (Eq (empty_carrier a) True)
% 70.35/70.68 (Or (Eq (element a_1 (the_carrier a)) False)
% 70.35/70.68 (Eq (element a_2 (the_carrier a) → Iff (below a a_1 a_2) (Eq (join a a_1 a_2) a_2)) True)))
% 70.35/70.68 Clause #144 (by clausification #[143]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.68 Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Or (Eq (empty_carrier a) True)
% 70.35/70.68 (Or (Eq (element a_1 (the_carrier a)) False)
% 70.35/70.68 (Or (Eq (element a_2 (the_carrier a)) False) (Eq (Iff (below a a_1 a_2) (Eq (join a a_1 a_2) a_2)) True))))
% 70.35/70.68 Clause #146 (by clausification #[144]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.68 Or (Eq (join_semilatt_str a) False)
% 70.35/70.68 (Or (Eq (empty_carrier a) True)
% 70.35/70.68 (Or (Eq (element a_1 (the_carrier a)) False)
% 70.35/70.68 (Or (Eq (element a_2 (the_carrier a)) False)
% 70.35/70.68 (Or (Eq (below a a_1 a_2) False) (Eq (Eq (join a a_1 a_2) a_2) True)))))
% 70.35/70.68 Clause #188 (by clausification #[27]): Eq
% 70.35/70.68 (∀ (A : Iota),
% 70.35/70.68 And (And (Not (empty_carrier A)) (join_commutative A)) (join_semilatt_str A) →
% 70.35/70.68 ∀ (B : Iota),
% 70.35/70.68 element B (the_carrier A) → ∀ (C : Iota), element C (the_carrier A) → And (below A B C) (below A C B) → Eq B C)
% 70.35/70.68 False
% 70.35/70.68 Clause #189 (by clausification #[188]): ∀ (a : Iota),
% 70.35/70.68 Eq
% 70.35/70.68 (Not
% 70.35/70.68 (And (And (Not (empty_carrier (skS.0 6 a))) (join_commutative (skS.0 6 a))) (join_semilatt_str (skS.0 6 a)) →
% 70.35/70.68 ∀ (B : Iota),
% 70.35/70.68 element B (the_carrier (skS.0 6 a)) →
% 70.35/70.68 ∀ (C : Iota),
% 70.35/70.68 element C (the_carrier (skS.0 6 a)) → And (below (skS.0 6 a) B C) (below (skS.0 6 a) C B) → Eq B C))
% 70.35/70.68 True
% 70.35/70.68 Clause #190 (by clausification #[189]): ∀ (a : Iota),
% 70.35/70.68 Eq
% 70.35/70.68 (And (And (Not (empty_carrier (skS.0 6 a))) (join_commutative (skS.0 6 a))) (join_semilatt_str (skS.0 6 a)) →
% 70.35/70.68 ∀ (B : Iota),
% 70.35/70.68 element B (the_carrier (skS.0 6 a)) →
% 70.35/70.71 ∀ (C : Iota),
% 70.35/70.71 element C (the_carrier (skS.0 6 a)) → And (below (skS.0 6 a) B C) (below (skS.0 6 a) C B) → Eq B C)
% 70.35/70.71 False
% 70.35/70.71 Clause #191 (by clausification #[190]): ∀ (a : Iota),
% 70.35/70.71 Eq (And (And (Not (empty_carrier (skS.0 6 a))) (join_commutative (skS.0 6 a))) (join_semilatt_str (skS.0 6 a))) True
% 70.35/70.71 Clause #192 (by clausification #[190]): ∀ (a : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (∀ (B : Iota),
% 70.35/70.71 element B (the_carrier (skS.0 6 a)) →
% 70.35/70.71 ∀ (C : Iota),
% 70.35/70.71 element C (the_carrier (skS.0 6 a)) → And (below (skS.0 6 a) B C) (below (skS.0 6 a) C B) → Eq B C)
% 70.35/70.71 False
% 70.35/70.71 Clause #193 (by clausification #[191]): ∀ (a : Iota), Eq (join_semilatt_str (skS.0 6 a)) True
% 70.35/70.71 Clause #194 (by clausification #[191]): ∀ (a : Iota), Eq (And (Not (empty_carrier (skS.0 6 a))) (join_commutative (skS.0 6 a))) True
% 70.35/70.71 Clause #200 (by clausification #[192]): ∀ (a a_1 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (Not
% 70.35/70.71 (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a)) →
% 70.35/70.71 ∀ (C : Iota),
% 70.35/70.71 element C (the_carrier (skS.0 6 a)) →
% 70.35/70.71 And (below (skS.0 6 a) (skS.0 7 a a_1) C) (below (skS.0 6 a) C (skS.0 7 a a_1)) → Eq (skS.0 7 a a_1) C))
% 70.35/70.71 True
% 70.35/70.71 Clause #201 (by clausification #[200]): ∀ (a a_1 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a)) →
% 70.35/70.71 ∀ (C : Iota),
% 70.35/70.71 element C (the_carrier (skS.0 6 a)) →
% 70.35/70.71 And (below (skS.0 6 a) (skS.0 7 a a_1) C) (below (skS.0 6 a) C (skS.0 7 a a_1)) → Eq (skS.0 7 a a_1) C)
% 70.35/70.71 False
% 70.35/70.71 Clause #202 (by clausification #[201]): ∀ (a a_1 : Iota), Eq (element (skS.0 7 a a_1) (the_carrier (skS.0 6 a))) True
% 70.35/70.71 Clause #203 (by clausification #[201]): ∀ (a a_1 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (∀ (C : Iota),
% 70.35/70.71 element C (the_carrier (skS.0 6 a)) →
% 70.35/70.71 And (below (skS.0 6 a) (skS.0 7 a a_1) C) (below (skS.0 6 a) C (skS.0 7 a a_1)) → Eq (skS.0 7 a a_1) C)
% 70.35/70.71 False
% 70.35/70.71 Clause #204 (by superposition #[202, 94]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.71 Or (Eq True False)
% 70.35/70.71 (Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.35/70.71 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.35/70.71 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.35/70.71 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True)))))
% 70.35/70.71 Clause #230 (by clausification #[203]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (Not
% 70.35/70.71 (element (skS.0 8 a a_1 a_2) (the_carrier (skS.0 6 a)) →
% 70.35/70.71 And (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.71 (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) →
% 70.35/70.71 Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)))
% 70.35/70.71 True
% 70.35/70.71 Clause #231 (by clausification #[230]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (element (skS.0 8 a a_1 a_2) (the_carrier (skS.0 6 a)) →
% 70.35/70.71 And (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.71 (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) →
% 70.35/70.71 Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.71 False
% 70.35/70.71 Clause #232 (by clausification #[231]): ∀ (a a_1 a_2 : Iota), Eq (element (skS.0 8 a a_1 a_2) (the_carrier (skS.0 6 a))) True
% 70.35/70.71 Clause #233 (by clausification #[231]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (And (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.71 (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) →
% 70.35/70.71 Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.71 False
% 70.35/70.71 Clause #293 (by clausification #[23]): ∀ (a : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (∀ (B C : Iota),
% 70.35/70.71 And
% 70.35/70.71 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.71 (element B (the_carrier a)))
% 70.35/70.71 (element C (the_carrier a)) →
% 70.35/70.71 Eq (join_commut a B C) (join a B C))
% 70.35/70.71 True
% 70.35/70.71 Clause #294 (by clausification #[293]): ∀ (a a_1 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (∀ (C : Iota),
% 70.35/70.71 And
% 70.35/70.71 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.71 (element a_1 (the_carrier a)))
% 70.35/70.71 (element C (the_carrier a)) →
% 70.35/70.71 Eq (join_commut a a_1 C) (join a a_1 C))
% 70.35/70.71 True
% 70.35/70.71 Clause #295 (by clausification #[294]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.71 Eq
% 70.35/70.71 (And
% 70.35/70.71 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.73 (element a_1 (the_carrier a)))
% 70.35/70.73 (element a_2 (the_carrier a)) →
% 70.35/70.73 Eq (join_commut a a_1 a_2) (join a a_1 a_2))
% 70.35/70.73 True
% 70.35/70.73 Clause #296 (by clausification #[295]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or
% 70.35/70.73 (Eq
% 70.35/70.73 (And
% 70.35/70.73 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.73 (element a_1 (the_carrier a)))
% 70.35/70.73 (element a_2 (the_carrier a)))
% 70.35/70.73 False)
% 70.35/70.73 (Eq (Eq (join_commut a a_1 a_2) (join a a_1 a_2)) True)
% 70.35/70.73 Clause #297 (by clausification #[296]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (Eq (join_commut a a_1 a_2) (join a a_1 a_2)) True)
% 70.35/70.73 (Or
% 70.35/70.73 (Eq
% 70.35/70.73 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a))
% 70.35/70.73 (element a_1 (the_carrier a)))
% 70.35/70.73 False)
% 70.35/70.73 (Eq (element a_2 (the_carrier a)) False))
% 70.35/70.73 Clause #298 (by clausification #[297]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or
% 70.35/70.73 (Eq
% 70.35/70.73 (And (And (And (Not (empty_carrier a)) (join_commutative a)) (join_semilatt_str a)) (element a_1 (the_carrier a)))
% 70.35/70.73 False)
% 70.35/70.73 (Or (Eq (element a_2 (the_carrier a)) False) (Eq (join_commut a a_1 a_2) (join a a_1 a_2)))
% 70.35/70.73 Clause #299 (by clausification #[298]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_commut a_1 a_2 a) (join a_1 a_2 a))
% 70.35/70.73 (Or (Eq (And (And (Not (empty_carrier a_1)) (join_commutative a_1)) (join_semilatt_str a_1)) False)
% 70.35/70.73 (Eq (element a_2 (the_carrier a_1)) False)))
% 70.35/70.73 Clause #300 (by clausification #[299]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_commut a_1 a_2 a) (join a_1 a_2 a))
% 70.35/70.73 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (And (Not (empty_carrier a_1)) (join_commutative a_1)) False) (Eq (join_semilatt_str a_1) False))))
% 70.35/70.73 Clause #301 (by clausification #[300]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_commut a_1 a_2 a) (join a_1 a_2 a))
% 70.35/70.73 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_semilatt_str a_1) False)
% 70.35/70.73 (Or (Eq (Not (empty_carrier a_1)) False) (Eq (join_commutative a_1) False)))))
% 70.35/70.73 Clause #302 (by clausification #[301]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (element a (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_commut a_1 a_2 a) (join a_1 a_2 a))
% 70.35/70.73 (Or (Eq (element a_2 (the_carrier a_1)) False)
% 70.35/70.73 (Or (Eq (join_semilatt_str a_1) False) (Or (Eq (join_commutative a_1) False) (Eq (empty_carrier a_1) True)))))
% 70.35/70.73 Clause #303 (by superposition #[302, 202]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.35/70.73 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.35/70.73 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.35/70.73 (Or (Eq (join_commutative (skS.0 6 a)) False) (Or (Eq (empty_carrier (skS.0 6 a)) True) (Eq False True)))))
% 70.35/70.73 Clause #304 (by superposition #[302, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.35/70.73 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.35/70.73 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.35/70.73 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.35/70.73 (Or (Eq (join_commutative (skS.0 6 a)) False) (Or (Eq (empty_carrier (skS.0 6 a)) True) (Eq False True)))))
% 70.35/70.73 Clause #329 (by clausification #[194]): ∀ (a : Iota), Eq (join_commutative (skS.0 6 a)) True
% 70.35/70.73 Clause #330 (by clausification #[194]): ∀ (a : Iota), Eq (Not (empty_carrier (skS.0 6 a))) True
% 70.35/70.73 Clause #331 (by clausification #[330]): ∀ (a : Iota), Eq (empty_carrier (skS.0 6 a)) False
% 70.35/70.73 Clause #374 (by clausification #[233]): ∀ (a a_1 a_2 : Iota),
% 70.35/70.73 Eq
% 70.35/70.73 (And (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.35/70.73 (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)))
% 70.35/70.73 True
% 70.35/70.73 Clause #375 (by clausification #[233]): ∀ (a a_1 a_2 : Iota), Eq (Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) False
% 70.35/70.73 Clause #376 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), Eq (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) True
% 70.35/70.73 Clause #377 (by clausification #[374]): ∀ (a a_1 a_2 : Iota), Eq (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) True
% 70.45/70.76 Clause #378 (by clausification #[375]): ∀ (a a_1 a_2 : Iota), Ne (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)
% 70.45/70.76 Clause #397 (by clausification #[146]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_semilatt_str a) False)
% 70.45/70.76 (Or (Eq (empty_carrier a) True)
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier a)) False)
% 70.45/70.76 (Or (Eq (element a_2 (the_carrier a)) False) (Or (Eq (below a a_1 a_2) False) (Eq (join a a_1 a_2) a_2)))))
% 70.45/70.76 Clause #399 (by superposition #[397, 193]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (empty_carrier (skS.0 6 a)) True)
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq (below (skS.0 6 a) a_1 a_2) False) (Or (Eq (join (skS.0 6 a) a_1 a_2) a_2) (Eq False True)))))
% 70.45/70.76 Clause #523 (by clausification #[204]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.45/70.76 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.76 Clause #524 (by forward demodulation #[523, 193]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq True False) (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.76 Clause #525 (by clausification #[524]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.76 Clause #526 (by forward demodulation #[525, 329]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Or (Eq True False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.76 Clause #527 (by clausification #[526]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq (empty_carrier (skS.0 6 a)) True))
% 70.45/70.76 Clause #528 (by forward demodulation #[527, 331]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq False True))
% 70.45/70.76 Clause #529 (by clausification #[528]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join_commut (skS.0 6 a) (skS.0 7 a a_2) a_1))
% 70.45/70.76 (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 Clause #531 (by superposition #[529, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.76 Or
% 70.45/70.76 (Eq (join_commut (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.76 (join_commut (skS.0 6 a) (skS.0 7 a a_3) (skS.0 8 a a_1 a_2)))
% 70.45/70.76 (Eq False True)
% 70.45/70.76 Clause #1163 (by clausification #[303]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.45/70.76 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.76 Clause #1164 (by forward demodulation #[1163, 193]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.76 (Or (Eq True False) (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.76 Clause #1165 (by clausification #[1164]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.76 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.76 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.79 Clause #1166 (by forward demodulation #[1165, 329]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Or (Eq True False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.79 Clause #1167 (by clausification #[1166]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq (empty_carrier (skS.0 6 a)) True))
% 70.45/70.79 Clause #1168 (by forward demodulation #[1167, 331]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq False True))
% 70.45/70.79 Clause #1169 (by clausification #[1168]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 7 a a_2)) (join (skS.0 6 a) a_1 (skS.0 7 a a_2)))
% 70.45/70.79 (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 Clause #1171 (by superposition #[1169, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or
% 70.45/70.79 (Eq (join_commut (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.79 (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)))
% 70.45/70.79 (Eq False True)
% 70.45/70.79 Clause #1201 (by clausification #[304]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq (join_semilatt_str (skS.0 6 a)) False)
% 70.45/70.79 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.79 Clause #1202 (by forward demodulation #[1201, 193]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq True False) (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True))))
% 70.45/70.79 Clause #1203 (by clausification #[1202]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq (join_commutative (skS.0 6 a)) False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.79 Clause #1204 (by forward demodulation #[1203, 329]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Or (Eq True False) (Eq (empty_carrier (skS.0 6 a)) True)))
% 70.45/70.79 Clause #1205 (by clausification #[1204]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq (empty_carrier (skS.0 6 a)) True))
% 70.45/70.79 Clause #1206 (by forward demodulation #[1205, 331]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False) (Eq False True))
% 70.45/70.79 Clause #1207 (by clausification #[1206]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or (Eq (join_commut (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)) (join (skS.0 6 a) a_1 (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 Clause #1208 (by superposition #[1207, 202]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.79 Or
% 70.45/70.79 (Eq (join_commut (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3))
% 70.45/70.79 (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)))
% 70.45/70.79 (Eq False True)
% 70.45/70.79 Clause #1666 (by clausification #[399]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq (empty_carrier (skS.0 6 a)) True)
% 70.45/70.79 (Or (Eq (element a_1 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq (element a_2 (the_carrier (skS.0 6 a))) False)
% 70.45/70.79 (Or (Eq (below (skS.0 6 a) a_1 a_2) False) (Eq (join (skS.0 6 a) a_1 a_2) a_2))))
% 70.45/70.79 Clause #1667 (by forward demodulation #[1666, 331]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.79 Or (Eq False True)
% 70.45/70.81 (Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (element a_2 (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) a a_2) False) (Eq (join (skS.0 6 a_1) a a_2) a_2))))
% 70.45/70.81 Clause #1668 (by clausification #[1667]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.81 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (element a_2 (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) a a_2) False) (Eq (join (skS.0 6 a_1) a a_2) a_2)))
% 70.45/70.81 Clause #1669 (by superposition #[1668, 202]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.81 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) (skS.0 7 a_1 a_2) a) False)
% 70.45/70.81 (Or (Eq (join (skS.0 6 a_1) (skS.0 7 a_1 a_2) a) a) (Eq False True)))
% 70.45/70.81 Clause #1670 (by superposition #[1668, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) False)
% 70.45/70.81 (Or (Eq (join (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) a) (Eq False True)))
% 70.45/70.81 Clause #1690 (by clausification #[1669]): ∀ (a a_1 a_2 : Iota),
% 70.45/70.81 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) (skS.0 7 a_1 a_2) a) False) (Eq (join (skS.0 6 a_1) (skS.0 7 a_1 a_2) a) a))
% 70.45/70.81 Clause #1692 (by superposition #[1690, 232]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) False)
% 70.45/70.81 (Or (Eq (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) (skS.0 8 a a_2 a_3)) (Eq False True))
% 70.45/70.81 Clause #2128 (by clausification #[1670]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (element a (the_carrier (skS.0 6 a_1))) False)
% 70.45/70.81 (Or (Eq (below (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) False) (Eq (join (skS.0 6 a_1) (skS.0 8 a_1 a_2 a_3) a) a))
% 70.45/70.81 Clause #2129 (by superposition #[2128, 202]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)) False)
% 70.45/70.81 (Or (Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)) (skS.0 7 a a_3)) (Eq False True))
% 70.45/70.81 Clause #2690 (by clausification #[1208]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Eq (join_commut (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3))
% 70.45/70.81 (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3))
% 70.45/70.81 Clause #2691 (by clausification #[1171]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Eq (join_commut (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.81 (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.81 Clause #2692 (by clausification #[531]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Eq (join_commut (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.81 (join_commut (skS.0 6 a) (skS.0 7 a a_3) (skS.0 8 a a_1 a_2))
% 70.45/70.81 Clause #2693 (by forward demodulation #[2692, 2691]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3))
% 70.45/70.81 (join_commut (skS.0 6 a) (skS.0 7 a a_3) (skS.0 8 a a_1 a_2))
% 70.45/70.81 Clause #2694 (by superposition #[2693, 2690]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)) (join (skS.0 6 a) (skS.0 7 a a_3) (skS.0 8 a a_1 a_2))
% 70.45/70.81 Clause #6771 (by clausification #[2129]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (below (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)) False)
% 70.45/70.81 (Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_3)) (skS.0 7 a a_3))
% 70.45/70.81 Clause #6772 (by superposition #[6771, 376]): ∀ (a a_1 a_2 : Iota), Or (Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) (skS.0 7 a a_1)) (Eq False True)
% 70.45/70.81 Clause #6778 (by clausification #[6772]): ∀ (a a_1 a_2 : Iota), Eq (join (skS.0 6 a) (skS.0 8 a a_1 a_2) (skS.0 7 a a_1)) (skS.0 7 a a_1)
% 70.45/70.81 Clause #6779 (by superposition #[6778, 2694]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 7 a a_1) (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2))
% 70.45/70.81 Clause #8850 (by clausification #[1692]): ∀ (a a_1 a_2 a_3 : Iota),
% 70.45/70.81 Or (Eq (below (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) False)
% 70.45/70.81 (Eq (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_2 a_3)) (skS.0 8 a a_2 a_3))
% 70.45/70.81 Clause #8851 (by superposition #[8850, 377]): ∀ (a a_1 a_2 : Iota), Or (Eq (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) (skS.0 8 a a_1 a_2)) (Eq False True)
% 70.45/70.81 Clause #8852 (by clausification #[8851]): ∀ (a a_1 a_2 : Iota), Eq (join (skS.0 6 a) (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)) (skS.0 8 a a_1 a_2)
% 70.68/70.90 Clause #8854 (by superposition #[8852, 6779]): ∀ (a a_1 a_2 : Iota), Eq (skS.0 7 a a_1) (skS.0 8 a a_1 a_2)
% 70.68/70.90 Clause #8855 (by forward contextual literal cutting #[8854, 378]): False
% 70.68/70.90 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------