%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU449+1 : TPTP v9.3.1. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:52:10 PM UTC 2026
% Result : Theorem 210.18s 27.13s
% Output : Proof 210.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 77 ( 36 unt; 0 def)
% Number of atoms : 161 ( 23 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 160 ( 76 ~; 50 |; 19 &)
% ( 2 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 156 ( 5 sgn 93 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f46_nnf,plain,
! [A,B,C] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(nnf_transformation,[status(thm)],[f46]) ).
fof(f46_sk,plain,
! [C,A,B] :
( ( ~ m1_relset_1(C,A,B)
| m2_relset_1(C,A,B) )
& ( m1_relset_1(C,A,B)
| ~ m2_relset_1(C,A,B) ) ),
inference(skolemisation,[status(esa)],[f46_nnf]) ).
cnf(c63,plain,
( m1_relset_1(X2,X0,X1)
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f46_sk]) ).
cnf(hi53,axiom,
ifeq(m2_relset_1(X0,X1,X2),true,m1_relset_1(X0,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
fof(f0,conjecture,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t63_relset_2) ).
fof(f0_neg,negated_conjecture,
~ ! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
& r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f0]) ).
fof(f0_nnf,plain,
? [A,B,C] :
( ? [D] :
( ? [E] :
( ( ~ r1_tarski(D,k8_relset_2(A,B,k8_relset_2(B,A,D,k6_relset_1(A,B,E)),E))
| ~ r1_tarski(C,k8_relset_2(B,A,k8_relset_2(A,B,C,E),k6_relset_1(A,B,E))) )
& m2_relset_1(E,A,B) )
& m1_subset_1(D,k1_zfmisc_1(B)) )
& m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(nnf_transformation,[status(thm)],[f0_neg]) ).
fof(f0_sk,plain,
( ( ~ r1_tarski(sk3,k8_relset_2(sk0,sk1,k8_relset_2(sk1,sk0,sk3,k6_relset_1(sk0,sk1,sk4)),sk4))
| ~ r1_tarski(sk2,k8_relset_2(sk1,sk0,k8_relset_2(sk0,sk1,sk2,sk4),k6_relset_1(sk0,sk1,sk4))) )
& m2_relset_1(sk4,sk0,sk1)
& m1_subset_1(sk3,k1_zfmisc_1(sk1))
& m1_subset_1(sk2,k1_zfmisc_1(sk0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1,sk2,sk3,sk4])],[f0_nnf]) ).
cnf(c2,plain,
m2_relset_1(sk4,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi2,negated_conjecture,
m2_relset_1(sk4,sk0,sk1) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h59,plain,
m1_relset_1(sk4,sk0,sk1) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi2]) ).
fof(f48,axiom,
! [A,B,C] :
( m1_relset_1(C,A,B)
=> m2_relset_1(k6_relset_1(A,B,C),B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relset_1) ).
fof(f48_nnf,plain,
! [A,B,C] :
( m2_relset_1(k6_relset_1(A,B,C),B,A)
| ~ m1_relset_1(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [C,A,B] :
( m2_relset_1(k6_relset_1(A,B,C),B,A)
| ~ m1_relset_1(C,A,B) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c66,plain,
( m2_relset_1(k6_relset_1(X0,X1,X2),X1,X0)
| ~ m1_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(hi55,axiom,
ifeq(m1_relset_1(X0,X1,X2),true,m2_relset_1(k6_relset_1(X1,X2,X0),X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(h168,plain,
m2_relset_1(k6_relset_1(sk0,sk1,sk4),sk1,sk0) = true,
inference(hyper_resolution,[status(thm)],[hi55,h59]) ).
fof(f51,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f51_nnf,plain,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(nnf_transformation,[status(thm)],[f51]) ).
fof(f51_sk,plain,
! [C,A,B] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m2_relset_1(C,A,B) ),
inference(skolemisation,[status(esa)],[f51_nnf]) ).
cnf(c69,plain,
( m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m2_relset_1(X2,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f51_sk]) ).
cnf(hi57,axiom,
ifeq(m2_relset_1(X0,X1,X2),true,m1_subset_1(X0,k1_zfmisc_1(k2_zfmisc_1(X1,X2))),true) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(h601,plain,
m1_subset_1(k6_relset_1(sk0,sk1,sk4),k1_zfmisc_1(k2_zfmisc_1(sk1,sk0))) = true,
inference(hyper_resolution,[status(thm)],[hi57,h168]) ).
fof(f49,axiom,
! [A,B,C,D] :
( ( m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k8_relset_2) ).
fof(f49_nnf,plain,
! [A,B,C,D] :
( m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B))
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(nnf_transformation,[status(thm)],[f49]) ).
fof(f49_sk,plain,
! [C,A,D,B] :
( m1_subset_1(k8_relset_2(A,B,C,D),k1_zfmisc_1(B))
| ~ m1_subset_1(D,k1_zfmisc_1(k2_zfmisc_1(A,B)))
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(skolemisation,[status(esa)],[f49_nnf]) ).
cnf(c67,plain,
( m1_subset_1(k8_relset_2(X0,X1,X2,X3),k1_zfmisc_1(X1))
| ~ m1_subset_1(X3,k1_zfmisc_1(k2_zfmisc_1(X0,X1)))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f49_sk]) ).
cnf(hi56,axiom,
ifeq(m1_subset_1(X0,k1_zfmisc_1(X1)),true,ifeq(m1_subset_1(X2,k1_zfmisc_1(k2_zfmisc_1(X1,X3))),true,m1_subset_1(k8_relset_2(X1,X3,X0,X2),k1_zfmisc_1(X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(c1,plain,
m1_subset_1(sk3,k1_zfmisc_1(sk1)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi1,negated_conjecture,
m1_subset_1(sk3,k1_zfmisc_1(sk1)) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1860,plain,
m1_subset_1(k8_relset_2(sk1,sk0,sk3,k6_relset_1(sk0,sk1,sk4)),k1_zfmisc_1(sk0)) = true,
inference(hyper_resolution,[status(thm)],[hi56,hi1,h601]) ).
fof(f54,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(B))
=> ! [E] :
( m2_relset_1(E,A,B)
=> ( r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E)))
<=> r1_tarski(D,k8_relset_2(A,B,C,E)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_relset_2) ).
fof(f54_nnf,plain,
! [A,B,C] :
( ! [D] :
( ! [E] :
( ( ( ~ r1_tarski(D,k8_relset_2(A,B,C,E))
| r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E))) )
& ( r1_tarski(D,k8_relset_2(A,B,C,E))
| ~ r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E))) ) )
| ~ m2_relset_1(E,A,B) )
| ~ m1_subset_1(D,k1_zfmisc_1(B)) )
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [C,A,D,B,E] :
( ( ( ~ r1_tarski(D,k8_relset_2(A,B,C,E))
| r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E))) )
& ( r1_tarski(D,k8_relset_2(A,B,C,E))
| ~ r1_tarski(C,k8_relset_2(B,A,D,k6_relset_1(A,B,E))) ) )
| ~ m2_relset_1(E,A,B)
| ~ m1_subset_1(D,k1_zfmisc_1(B))
| ~ m1_subset_1(C,k1_zfmisc_1(A)) ),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c73,plain,
( r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| ~ r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| ~ m2_relset_1(X4,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi60,axiom,
ifeq(m1_subset_1(X0,k1_zfmisc_1(X1)),true,ifeq(m1_subset_1(X2,k1_zfmisc_1(X3)),true,ifeq(m2_relset_1(X4,X1,X3),true,ifeq(r1_tarski(X0,k8_relset_2(X3,X1,X2,k6_relset_1(X1,X3,X4))),true,r1_tarski(X2,k8_relset_2(X1,X3,X0,X4)),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
fof(f41,axiom,
! [A,B] : r1_tarski(A,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f41_nnf,plain,
! [A,B] : r1_tarski(A,A),
inference(nnf_transformation,[status(thm)],[f41]) ).
fof(f41_sk,plain,
! [A] : r1_tarski(A,A),
inference(skolemisation,[status(esa)],[f41_nnf]) ).
cnf(c58,plain,
r1_tarski(X0,X0),
inference(cnf_transformation,[status(esa)],[f41_sk]) ).
cnf(hi48,axiom,
r1_tarski(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(h6460,plain,
r1_tarski(sk3,k8_relset_2(sk0,sk1,k8_relset_2(sk1,sk0,sk3,k6_relset_1(sk0,sk1,sk4)),sk4)) = true,
inference(hyper_resolution,[status(thm)],[hi60,h1860,hi1,hi2,hi48]) ).
cnf(h58,plain,
m1_subset_1(sk4,k1_zfmisc_1(k2_zfmisc_1(sk0,sk1))) = true,
inference(hyper_resolution,[status(thm)],[hi57,hi2]) ).
cnf(c0,plain,
m1_subset_1(sk2,k1_zfmisc_1(sk0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
m1_subset_1(sk2,k1_zfmisc_1(sk0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h308,plain,
m1_subset_1(k8_relset_2(sk0,sk1,sk2,sk4),k1_zfmisc_1(sk1)) = true,
inference(hyper_resolution,[status(thm)],[hi56,hi0,h58]) ).
cnf(c74,plain,
( ~ r1_tarski(X3,k8_relset_2(X0,X1,X2,X4))
| r1_tarski(X2,k8_relset_2(X1,X0,X3,k6_relset_1(X0,X1,X4)))
| ~ m2_relset_1(X4,X0,X1)
| ~ m1_subset_1(X3,k1_zfmisc_1(X1))
| ~ m1_subset_1(X2,k1_zfmisc_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi61,axiom,
ifeq(m1_subset_1(X0,k1_zfmisc_1(X1)),true,ifeq(m1_subset_1(X2,k1_zfmisc_1(X3)),true,ifeq(m2_relset_1(X4,X1,X3),true,ifeq(r1_tarski(X2,k8_relset_2(X1,X3,X0,X4)),true,r1_tarski(X0,k8_relset_2(X3,X1,X2,k6_relset_1(X1,X3,X4))),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c74]) ).
cnf(h1121,plain,
r1_tarski(sk2,k8_relset_2(sk1,sk0,k8_relset_2(sk0,sk1,sk2,sk4),k6_relset_1(sk0,sk1,sk4))) = true,
inference(hyper_resolution,[status(thm)],[hi61,hi0,h308,hi2,hi48]) ).
cnf(c3,plain,
( ~ r1_tarski(sk3,k8_relset_2(sk0,sk1,k8_relset_2(sk1,sk0,sk3,k6_relset_1(sk0,sk1,sk4)),sk4))
| ~ r1_tarski(sk2,k8_relset_2(sk1,sk0,k8_relset_2(sk0,sk1,sk2,sk4),k6_relset_1(sk0,sk1,sk4))) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi62,negated_conjecture,
ifeq(r1_tarski(sk2,k8_relset_2(sk1,sk0,k8_relset_2(sk0,sk1,sk2,sk4),k6_relset_1(sk0,sk1,sk4))),true,ifeq(r1_tarski(sk3,k8_relset_2(sk0,sk1,k8_relset_2(sk1,sk0,sk3,k6_relset_1(sk0,sk1,sk4)),sk4)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t1,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi62,h1121,h6460]) ).
cnf(t1007,plain,
false = true,
inference(orient,[status(thm)],[t1]) ).
fof(f7,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f7_nnf,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B] :
( ~ r2_hidden(B,A)
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c14,plain,
( ~ r2_hidden(X1,X0)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
fof(f18,axiom,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f18_nnf,plain,
? [A] :
( v1_relat_1(A)
& ~ v1_xboole_0(A) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( v1_relat_1(sk9)
& ~ v1_xboole_0(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9])],[f18_nnf]) ).
cnf(c31,plain,
~ v1_xboole_0(sk9),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f21,axiom,
! [A,B,C] :
~ ( v1_xboole_0(C)
& m1_subset_1(B,k1_zfmisc_1(C))
& r2_hidden(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f21_nnf,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C] :
( ~ v1_xboole_0(C)
| ~ m1_subset_1(B,k1_zfmisc_1(C))
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c35,plain,
( ~ v1_xboole_0(X2)
| ~ m1_subset_1(X1,k1_zfmisc_1(X2))
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
fof(f37,axiom,
! [A,B] :
~ ( v1_xboole_0(B)
& r2_hidden(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f37_nnf,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A,B] :
( ~ v1_xboole_0(B)
| ~ r2_hidden(A,B) ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c54,plain,
( ~ v1_xboole_0(X1)
| ~ r2_hidden(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
fof(f52,axiom,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f52_nnf,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(nnf_transformation,[status(thm)],[f52]) ).
fof(f52_sk,plain,
! [A] : ~ v1_xboole_0(k1_zfmisc_1(A)),
inference(skolemisation,[status(esa)],[f52_nnf]) ).
cnf(c70,plain,
~ v1_xboole_0(k1_zfmisc_1(X0)),
inference(cnf_transformation,[status(esa)],[f52_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3,c14,c31,c35,c54,c70]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1007]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU449+1 : TPTP v9.3.1. Released v3.4.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 14:21:50 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 210.18/27.13 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 210.18/27.13 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------