TSTP Solution File: SEV258^5 by Duper---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Duper---1.0
% Problem : SEV258^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : duper %s
% Computer : n023.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 19:24:36 EDT 2023
% Result : Theorem 4.58s 4.78s
% Output : Proof 4.65s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12 % Problem : SEV258^5 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.13 % Command : duper %s
% 0.14/0.35 % Computer : n023.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 : Thu Aug 24 02:09:57 EDT 2023
% 0.14/0.35 % CPUTime :
% 4.58/4.78 SZS status Theorem for theBenchmark.p
% 4.58/4.78 SZS output start Proof for theBenchmark.p
% 4.58/4.78 Clause #0 (by assumption #[]): Eq
% 4.58/4.78 (Not
% 4.58/4.78 (And
% 4.58/4.78 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True))
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True))
% 4.58/4.78 (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True)))
% 4.58/4.78 True
% 4.58/4.78 Clause #1 (by clausification #[0]): Eq
% 4.58/4.78 (And
% 4.58/4.78 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True))
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True))
% 4.58/4.78 (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True))
% 4.58/4.78 False
% 4.58/4.78 Clause #2 (by clausification #[1]): Or
% 4.58/4.78 (Eq
% 4.58/4.78 (And (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True))
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True))
% 4.58/4.78 False)
% 4.58/4.78 (Eq (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True) False)
% 4.58/4.78 Clause #3 (by clausification #[2]): Or (Eq (∀ (Y Z S : a → Prop), And (And True True) (Eq S fun Xx => And (Y Xx) (Z Xx)) → True) False)
% 4.58/4.78 (Or
% 4.58/4.78 (Eq (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True))
% 4.58/4.78 False)
% 4.58/4.78 (Eq
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)
% 4.58/4.78 False))
% 4.58/4.78 Clause #4 (by clausification #[3]): ∀ (a_1 : a → Prop),
% 4.58/4.78 Or
% 4.58/4.78 (Eq (And (∀ (R : a → Prop), (Eq R fun Xx => False) → True) (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True))
% 4.58/4.78 False)
% 4.58/4.78 (Or
% 4.58/4.78 (Eq
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)
% 4.58/4.78 False)
% 4.58/4.78 (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True))
% 4.58/4.78 Clause #5 (by clausification #[4]): ∀ (a_1 : a → Prop),
% 4.58/4.78 Or
% 4.58/4.78 (Eq
% 4.58/4.78 (∀ (K : (a → Prop) → Prop) (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), K Xx → True) (Eq R fun Xx => Exists fun S => And (K S) (S Xx)) → True)
% 4.58/4.78 False)
% 4.58/4.78 (Or (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True)
% 4.58/4.78 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False)
% 4.58/4.78 (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False)))
% 4.58/4.78 Clause #6 (by clausification #[5]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop),
% 4.58/4.78 Or (Eq (Not (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True)) True)
% 4.58/4.78 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False)
% 4.58/4.78 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False)
% 4.58/4.78 (Eq
% 4.58/4.78 (Not
% 4.58/4.78 (∀ (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True)
% 4.58/4.78 (Eq R fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) →
% 4.58/4.78 True))
% 4.58/4.78 True)))
% 4.58/4.78 Clause #7 (by clausification #[6]): ∀ (a_1 : (a → Prop) → Prop) (a_2 : a → Prop),
% 4.58/4.78 Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => False) → True) False)
% 4.58/4.78 (Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False)
% 4.58/4.78 (Or
% 4.58/4.78 (Eq
% 4.58/4.78 (Not
% 4.58/4.78 (∀ (R : a → Prop),
% 4.58/4.78 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True)
% 4.58/4.78 (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.58/4.78 True))
% 4.65/4.81 True)
% 4.65/4.81 (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False)))
% 4.65/4.81 Clause #8 (by clausification #[7]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 : a → Prop),
% 4.65/4.81 Or (Eq (∀ (R : a → Prop), (Eq R fun Xx => Not False) → True) False)
% 4.65/4.81 (Or
% 4.65/4.81 (Eq
% 4.65/4.81 (Not
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.81 True))
% 4.65/4.81 True)
% 4.65/4.81 (Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False)
% 4.65/4.81 (Eq (Not ((Eq (skS.0 2 a_3) fun Xx => False) → True)) True)))
% 4.65/4.81 Clause #9 (by clausification #[8]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 : a → Prop),
% 4.65/4.81 Or
% 4.65/4.81 (Eq
% 4.65/4.81 (Not
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.81 True))
% 4.65/4.81 True)
% 4.65/4.81 (Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (Z Xx)) → True) False)
% 4.65/4.81 (Or (Eq (Not ((Eq (skS.0 2 a_3) fun Xx => False) → True)) True)
% 4.65/4.81 (Eq (Not ((Eq (skS.0 3 a_4) fun Xx => Not False) → True)) True)))
% 4.65/4.81 Clause #10 (by clausification #[9]): ∀ (a_1 a_2 a_3 : a → Prop) (a_4 : (a → Prop) → Prop),
% 4.65/4.81 Or (Eq (∀ (Z S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (Z Xx)) → True) False)
% 4.65/4.81 (Or (Eq (Not ((Eq (skS.0 2 a_2) fun Xx => False) → True)) True)
% 4.65/4.81 (Or (Eq (Not ((Eq (skS.0 3 a_3) fun Xx => Not False) → True)) True)
% 4.65/4.81 (Eq
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_4 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_4 S) (S Xx)) →
% 4.65/4.81 True)
% 4.65/4.81 False)))
% 4.65/4.81 Clause #11 (by clausification #[10]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 a_5 : a → Prop),
% 4.65/4.81 Or (Eq (Not ((Eq (skS.0 2 a_1) fun Xx => False) → True)) True)
% 4.65/4.81 (Or (Eq (Not ((Eq (skS.0 3 a_2) fun Xx => Not False) → True)) True)
% 4.65/4.81 (Or
% 4.65/4.81 (Eq
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) →
% 4.65/4.81 True)
% 4.65/4.81 False)
% 4.65/4.81 (Eq
% 4.65/4.81 (Not
% 4.65/4.81 (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_4 Xx) (skS.0 4 a_4 a_5 Xx)) → True))
% 4.65/4.81 True)))
% 4.65/4.81 Clause #12 (by clausification #[11]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop) (a_3 a_4 a_5 : a → Prop),
% 4.65/4.81 Or (Eq (Not ((Eq (skS.0 3 a_1) fun Xx => Not False) → True)) True)
% 4.65/4.81 (Or
% 4.65/4.81 (Eq
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) →
% 4.65/4.81 True)
% 4.65/4.81 False)
% 4.65/4.81 (Or
% 4.65/4.81 (Eq
% 4.65/4.81 (Not
% 4.65/4.81 (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True))
% 4.65/4.81 True)
% 4.65/4.81 (Eq ((Eq (skS.0 2 a_5) fun Xx => False) → True) False)))
% 4.65/4.81 Clause #13 (by clausification #[12]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop),
% 4.65/4.81 Or
% 4.65/4.81 (Eq
% 4.65/4.81 (∀ (R : a → Prop),
% 4.65/4.81 And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True) (Eq R fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.81 True)
% 4.65/4.81 False)
% 4.65/4.81 (Or
% 4.65/4.81 (Eq
% 4.65/4.81 (Not (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_2 Xx) (skS.0 4 a_2 a_3 Xx)) → True))
% 4.65/4.81 True)
% 4.65/4.81 (Or (Eq ((Eq (skS.0 2 a_4) fun Xx => False) → True) False)
% 4.65/4.81 (Eq ((Eq (skS.0 3 a_5) fun Xx => Not False) → True) False)))
% 4.65/4.81 Clause #14 (by clausification #[13]): ∀ (a_1 a_2 a_3 a_4 : a → Prop) (a_5 : (a → Prop) → Prop) (a_6 : a → Prop),
% 4.65/4.81 Or
% 4.65/4.81 (Eq (Not (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True))
% 4.65/4.81 True)
% 4.65/4.81 (Or (Eq ((Eq (skS.0 2 a_3) fun Xx => False) → True) False)
% 4.65/4.83 (Or (Eq ((Eq (skS.0 3 a_4) fun Xx => Not False) → True) False)
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_5 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_5 a_6) fun Xx => Exists fun S => And (skS.0 1 a_5 S) (S Xx)) →
% 4.65/4.83 True))
% 4.65/4.83 True)))
% 4.65/4.83 Clause #15 (by clausification #[14]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 a_5 a_6 : a → Prop),
% 4.65/4.83 Or (Eq ((Eq (skS.0 2 a_1) fun Xx => False) → True) False)
% 4.65/4.83 (Or (Eq ((Eq (skS.0 3 a_2) fun Xx => Not False) → True) False)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_3 a_4) fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) →
% 4.65/4.83 True))
% 4.65/4.83 True)
% 4.65/4.83 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_5 Xx) (skS.0 4 a_5 a_6 Xx)) → True)
% 4.65/4.83 False)))
% 4.65/4.83 Clause #17 (by clausification #[15]): ∀ (a_1 : a → Prop) (a_2 : (a → Prop) → Prop) (a_3 a_4 a_5 : a → Prop),
% 4.65/4.83 Or (Eq ((Eq (skS.0 3 a_1) fun Xx => Not False) → True) False)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_2 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_2 a_3) fun Xx => Exists fun S => And (skS.0 1 a_2 S) (S Xx)) →
% 4.65/4.83 True))
% 4.65/4.83 True)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_4 Xx) (skS.0 4 a_4 a_5 Xx)) → True)
% 4.65/4.83 False)
% 4.65/4.83 (Eq True False)))
% 4.65/4.83 Clause #58 (by clausification #[17]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 : a → Prop),
% 4.65/4.83 Or
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.83 True))
% 4.65/4.83 True)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True)
% 4.65/4.83 False)
% 4.65/4.83 (Or (Eq True False) (Eq True False)))
% 4.65/4.83 Clause #125 (by clausification #[58]): ∀ (a_1 a_2 : a → Prop) (a_3 : (a → Prop) → Prop) (a_4 : a → Prop),
% 4.65/4.83 Or
% 4.65/4.83 (Eq (∀ (S : a → Prop), And (And True True) (Eq S fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True) False)
% 4.65/4.83 (Or (Eq True False)
% 4.65/4.83 (Or (Eq True False)
% 4.65/4.83 (Eq
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_3 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_3 a_4) fun Xx => Exists fun S => And (skS.0 1 a_3 S) (S Xx)) →
% 4.65/4.83 True)
% 4.65/4.83 False)))
% 4.65/4.83 Clause #126 (by clausification #[125]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop),
% 4.65/4.83 Or (Eq True False)
% 4.65/4.83 (Or (Eq True False)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.83 True)
% 4.65/4.83 False)
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True))
% 4.65/4.83 True)))
% 4.65/4.83 Clause #127 (by clausification #[126]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop),
% 4.65/4.83 Or (Eq True False)
% 4.65/4.83 (Or
% 4.65/4.83 (Eq
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.83 True)
% 4.65/4.83 False)
% 4.65/4.83 (Eq
% 4.65/4.83 (Not
% 4.65/4.83 (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True))
% 4.65/4.83 True))
% 4.65/4.83 Clause #128 (by clausification #[127]): ∀ (a_1 : (a → Prop) → Prop) (a_2 a_3 a_4 a_5 : a → Prop),
% 4.65/4.83 Or
% 4.65/4.83 (Eq
% 4.65/4.83 (And (∀ (Xx : a → Prop), skS.0 1 a_1 Xx → True)
% 4.65/4.83 (Eq (skS.0 5 a_1 a_2) fun Xx => Exists fun S => And (skS.0 1 a_1 S) (S Xx)) →
% 4.65/4.83 True)
% 4.65/4.83 False)
% 4.65/4.83 (Eq
% 4.65/4.83 (Not (And (And True True) (Eq (skS.0 8 a_3 a_4 a_5) fun Xx => And (skS.0 0 a_3 Xx) (skS.0 4 a_3 a_4 Xx)) → True))
% 4.65/4.83 True)
% 4.65/4.83 Clause #130 (by clausification #[128]): ∀ (a_1 a_2 a_3 : a → Prop),
% 4.65/4.83 Or
% 4.65/4.83 (Eq
% 4.65/4.83 (Not (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True))
% 4.65/4.84 True)
% 4.65/4.84 (Eq True False)
% 4.65/4.84 Clause #211 (by clausification #[130]): ∀ (a_1 a_2 a_3 : a → Prop),
% 4.65/4.84 Or (Eq True False)
% 4.65/4.84 (Eq (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True)
% 4.65/4.84 False)
% 4.65/4.84 Clause #212 (by clausification #[211]): ∀ (a_1 a_2 a_3 : a → Prop),
% 4.65/4.84 Eq (And (And True True) (Eq (skS.0 8 a_1 a_2 a_3) fun Xx => And (skS.0 0 a_1 Xx) (skS.0 4 a_1 a_2 Xx)) → True) False
% 4.65/4.84 Clause #214 (by clausification #[212]): Eq True False
% 4.65/4.84 Clause #257 (by clausification #[214]): False
% 4.65/4.84 SZS output end Proof for theBenchmark.p
%------------------------------------------------------------------------------