TSTP Solution File: SYN349+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SYN349+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 : 600s
% DateTime : Thu Jul 21 09:01:38 EDT 2022
% Result : Theorem 0.19s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 165 ( 0 equ)
% Maximal formula atoms : 32 ( 3 avg)
% Number of connectives : 201 ( 81 ~; 68 |; 13 &)
% ( 36 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-2 aty)
% Number of variables : 80 ( 0 sgn 36 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(church_46_17_5,conjecture,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ) ).
fof(subgoal_0,plain,
? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(strip,[],[church_46_17_5]) ).
fof(negate_0_0,plain,
~ ? [X1] :
! [X2] :
? [X3] :
! [X4] :
( ( big_f(X1,X4)
<=> big_f(X2,X4) )
=> ( ( ( big_f(X1,X4)
<=> big_f(X4,X3) )
<=> big_f(X3,X4) )
<=> big_f(X4,X2) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ~ big_f(X1,X4)
<=> ~ big_f(X2,X4) )
& ( ~ big_f(X1,X4)
<=> ( ~ big_f(X3,X4)
<=> ( ~ big_f(X4,X2)
<=> big_f(X4,X3) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X1] :
? [X2] :
! [X3] :
? [X4] :
( ( ~ big_f(X1,X4)
<=> ~ big_f(X2,X4) )
& ( ~ big_f(X1,X4)
<=> ( ~ big_f(X3,X4)
<=> ( ~ big_f(X4,X2)
<=> big_f(X4,X3) ) ) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X1,X3] :
? [X4] :
( ( ~ big_f(X1,X4)
<=> ~ big_f(skolemFOFtoCNF_X2(X1),X4) )
& ( ~ big_f(X1,X4)
<=> ( ~ big_f(X3,X4)
<=> ( ~ big_f(X4,X3)
<=> big_f(X4,skolemFOFtoCNF_X2(X1)) ) ) ) ),
inference(skolemize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X1,X3] :
? [X4] :
( ( ~ big_f(X1,X4)
<=> ~ big_f(skolemFOFtoCNF_X2(X1),X4) )
& ( ~ big_f(X1,X4)
<=> ( ~ big_f(X3,X4)
<=> ( ~ big_f(X4,X3)
<=> big_f(X4,skolemFOFtoCNF_X2(X1)) ) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X1,X3] :
( ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
<=> ~ big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3)) )
& ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
<=> ( ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
<=> ( ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
<=> big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ) ) ) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X1,X3] :
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
<=> ( ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
<=> ( ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
<=> big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ) ) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X1,X3] :
( ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) )
& ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) )
& ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) )
& ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3) )
& ( ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) )
& ( ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3) )
& ( ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3)) )
& ( big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X1,X3] :
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X1,X3] :
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
<=> ~ big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_9,plain,
! [X1,X3] :
( ( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3)) )
& ( ~ big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X1,X3] :
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X1,X3] :
( ~ big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,plain,
! [X1,X3] :
( big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_13,plain,
! [X1,X3] :
( ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3)) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_14,plain,
! [X1,X3] :
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(conjunct,[],[normalize_0_6]) ).
cnf(refute_0_0,plain,
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_1,plain,
( ~ big_f(X_15,skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)))
| ~ big_f(skolemFOFtoCNF_X2(X_15),skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)))
| ~ big_f(skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)),skolemFOFtoCNF_X2(X_15)) ),
inference(subst,[],[refute_0_0:[bind(X1,$fot(X_15)),bind(X3,$fot(skolemFOFtoCNF_X2(X_15)))]]) ).
cnf(refute_0_2,plain,
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( ~ big_f(X_9,skolemFOFtoCNF_X4(X_9,skolemFOFtoCNF_X2(X_9)))
| big_f(skolemFOFtoCNF_X2(X_9),skolemFOFtoCNF_X4(X_9,skolemFOFtoCNF_X2(X_9))) ),
inference(subst,[],[refute_0_2:[bind(X1,$fot(X_9)),bind(X3,$fot(skolemFOFtoCNF_X2(X_9)))]]) ).
cnf(refute_0_4,plain,
( ~ big_f(skolemFOFtoCNF_X2(X1),skolemFOFtoCNF_X4(X1,X3))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_5,plain,
( ~ big_f(skolemFOFtoCNF_X2(X_8),skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8)))
| big_f(X_8,skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8))) ),
inference(subst,[],[refute_0_4:[bind(X1,$fot(X_8)),bind(X3,$fot(skolemFOFtoCNF_X2(X_8)))]]) ).
cnf(refute_0_6,plain,
( big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( big_f(X_7,skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)))
| big_f(skolemFOFtoCNF_X2(X_7),skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)))
| big_f(skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)),skolemFOFtoCNF_X2(X_7)) ),
inference(subst,[],[refute_0_6:[bind(X1,$fot(X_7)),bind(X3,$fot(skolemFOFtoCNF_X2(X_7)))]]) ).
cnf(refute_0_8,plain,
( ~ big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| ~ big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1))
| big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| big_f(X3,skolemFOFtoCNF_X4(X1,X3)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ big_f(skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)),skolemFOFtoCNF_X2(X_7))
| big_f(X_7,skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)))
| big_f(skolemFOFtoCNF_X2(X_7),skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7))) ),
inference(subst,[],[refute_0_8:[bind(X1,$fot(X_7)),bind(X3,$fot(skolemFOFtoCNF_X2(X_7)))]]) ).
cnf(refute_0_10,plain,
( big_f(X_7,skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)))
| big_f(skolemFOFtoCNF_X2(X_7),skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7))) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X4(X_7,skolemFOFtoCNF_X2(X_7)),skolemFOFtoCNF_X2(X_7)) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( big_f(X_8,skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8)))
| big_f(skolemFOFtoCNF_X2(X_8),skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8))) ),
inference(subst,[],[refute_0_10:[bind(X_7,$fot(X_8))]]) ).
cnf(refute_0_12,plain,
big_f(X_8,skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8))),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X2(X_8),skolemFOFtoCNF_X4(X_8,skolemFOFtoCNF_X2(X_8))) )],[refute_0_11,refute_0_5]) ).
cnf(refute_0_13,plain,
big_f(X_9,skolemFOFtoCNF_X4(X_9,skolemFOFtoCNF_X2(X_9))),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(X_9))]]) ).
cnf(refute_0_14,plain,
big_f(skolemFOFtoCNF_X2(X_9),skolemFOFtoCNF_X4(X_9,skolemFOFtoCNF_X2(X_9))),
inference(resolve,[$cnf( big_f(X_9,skolemFOFtoCNF_X4(X_9,skolemFOFtoCNF_X2(X_9))) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
big_f(skolemFOFtoCNF_X2(X_13),skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13))),
inference(subst,[],[refute_0_14:[bind(X_9,$fot(X_13))]]) ).
cnf(refute_0_16,plain,
( ~ big_f(X1,skolemFOFtoCNF_X4(X1,X3))
| ~ big_f(X3,skolemFOFtoCNF_X4(X1,X3))
| big_f(skolemFOFtoCNF_X4(X1,X3),X3)
| big_f(skolemFOFtoCNF_X4(X1,X3),skolemFOFtoCNF_X2(X1)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
( ~ big_f(X_13,skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)))
| ~ big_f(skolemFOFtoCNF_X2(X_13),skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)))
| big_f(skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)),skolemFOFtoCNF_X2(X_13)) ),
inference(subst,[],[refute_0_16:[bind(X1,$fot(X_13)),bind(X3,$fot(skolemFOFtoCNF_X2(X_13)))]]) ).
cnf(refute_0_18,plain,
( ~ big_f(X_13,skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)))
| big_f(skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)),skolemFOFtoCNF_X2(X_13)) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X2(X_13),skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13))) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
big_f(X_13,skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13))),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(X_13))]]) ).
cnf(refute_0_20,plain,
big_f(skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13)),skolemFOFtoCNF_X2(X_13)),
inference(resolve,[$cnf( big_f(X_13,skolemFOFtoCNF_X4(X_13,skolemFOFtoCNF_X2(X_13))) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
big_f(skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)),skolemFOFtoCNF_X2(X_15)),
inference(subst,[],[refute_0_20:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_22,plain,
( ~ big_f(X_15,skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)))
| ~ big_f(skolemFOFtoCNF_X2(X_15),skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))) ),
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15)),skolemFOFtoCNF_X2(X_15)) )],[refute_0_21,refute_0_1]) ).
cnf(refute_0_23,plain,
big_f(X_15,skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))),
inference(subst,[],[refute_0_12:[bind(X_8,$fot(X_15))]]) ).
cnf(refute_0_24,plain,
~ big_f(skolemFOFtoCNF_X2(X_15),skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))),
inference(resolve,[$cnf( big_f(X_15,skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))) )],[refute_0_23,refute_0_22]) ).
cnf(refute_0_25,plain,
big_f(skolemFOFtoCNF_X2(X_15),skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))),
inference(subst,[],[refute_0_14:[bind(X_9,$fot(X_15))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( big_f(skolemFOFtoCNF_X2(X_15),skolemFOFtoCNF_X4(X_15,skolemFOFtoCNF_X2(X_15))) )],[refute_0_25,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN349+1 : TPTP v8.1.0. Released v2.0.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 20:16:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.35 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.35
% 0.19/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.36
%------------------------------------------------------------------------------