%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU375+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 : Tue Sep 29 12:48:36 PM UTC 2026
% Result : Theorem 6.10s 2.51s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 12
% Syntax : Number of formulae : 94 ( 28 unt; 3 def)
% Number of atoms : 361 ( 27 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 437 ( 170 ~; 156 |; 68 &)
% ( 7 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 4 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 136 ( 0 sgn 122 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f181,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> ! [X2] :
( net_str(X2,X0)
=> ( subnetstr(X2,X0,X1)
<=> ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_yellow_6) ).
fof(f187,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> ! [X2] :
( subnetstr(X2,X0,X1)
=> ( full_subnetstr(X2,X0,X1)
<=> ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9_yellow_6) ).
fof(f269,axiom,
! [X0] :
( rel_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_orders_2) ).
fof(f272,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( net_str(X1,X0)
=> rel_str(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_waybel_0) ).
fof(f279,axiom,
! [X0,X1] :
( ( one_sorted_str(X0)
& net_str(X1,X0) )
=> ! [X2] :
( subnetstr(X2,X0,X1)
=> net_str(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_m1_yellow_6) ).
fof(f319,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f614,conjecture,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& full_subnetstr(X2,X0,X1)
& subnetstr(X2,X0,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X3 = X5
& X4 = X6
& related(X1,X3,X4) )
=> related(X2,X5,X6) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_yellow_6) ).
fof(f615,negated_conjecture,
~ ! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( ( ~ empty_carrier(X1)
& net_str(X1,X0) )
=> ! [X2] :
( ( ~ empty_carrier(X2)
& full_subnetstr(X2,X0,X1)
& subnetstr(X2,X0,X1) )
=> ! [X3] :
( element(X3,the_carrier(X1))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X2))
=> ! [X6] :
( element(X6,the_carrier(X2))
=> ( ( X3 = X5
& X4 = X6
& related(X1,X3,X4) )
=> related(X2,X5,X6) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f614]) ).
fof(f644,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( empty(X1)
| in(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f729,axiom,
! [X0] :
( rel_str(X0)
=> ! [X1] :
( ( full_subrelstr(X1,X0)
& subrelstr(X1,X0) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ! [X3] :
( element(X3,the_carrier(X0))
=> ! [X4] :
( element(X4,the_carrier(X1))
=> ! [X5] :
( element(X5,the_carrier(X1))
=> ( ( X4 = X2
& X5 = X3
& related(X0,X2,X3)
& in(X4,the_carrier(X1))
& in(X5,the_carrier(X1)) )
=> related(X1,X4,X5) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t61_yellow_0) ).
fof(f1049,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( subnetstr(X2,X0,X1)
<=> ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f181]) ).
fof(f1058,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( full_subnetstr(X2,X0,X1)
<=> ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) ) )
| ~ subnetstr(X2,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f187]) ).
fof(f1135,plain,
! [X0] :
( one_sorted_str(X0)
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f269]) ).
fof(f1137,plain,
! [X0] :
( ! [X1] :
( rel_str(X1)
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f272]) ).
fof(f1143,plain,
! [X0,X1] :
( ! [X2] :
( net_str(X2,X0)
| ~ subnetstr(X2,X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(ennf_transformation,[],[f279]) ).
fof(f1144,plain,
! [X0,X1] :
( ! [X2] :
( net_str(X2,X0)
| ~ subnetstr(X2,X0,X1) )
| ~ one_sorted_str(X0)
| ~ net_str(X1,X0) ),
inference(flattening,[],[f1143]) ).
fof(f1177,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(ennf_transformation,[],[f319]) ).
fof(f1178,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f1177]) ).
fof(f1526,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ~ related(X2,X5,X6)
& X3 = X5
& X4 = X6
& related(X1,X3,X4)
& element(X6,the_carrier(X2)) )
& element(X5,the_carrier(X2)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) )
& ~ empty_carrier(X2)
& full_subnetstr(X2,X0,X1)
& subnetstr(X2,X0,X1) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& one_sorted_str(X0) ),
inference(ennf_transformation,[],[f615]) ).
fof(f1527,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ? [X6] :
( ~ related(X2,X5,X6)
& X3 = X5
& X4 = X6
& related(X1,X3,X4)
& element(X6,the_carrier(X2)) )
& element(X5,the_carrier(X2)) )
& element(X4,the_carrier(X1)) )
& element(X3,the_carrier(X1)) )
& ~ empty_carrier(X2)
& full_subnetstr(X2,X0,X1)
& subnetstr(X2,X0,X1) )
& ~ empty_carrier(X1)
& net_str(X1,X0) )
& one_sorted_str(X0) ),
inference(flattening,[],[f1526]) ).
fof(f1573,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f644]) ).
fof(f1574,plain,
! [X0,X1] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f1573]) ).
fof(f1681,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( related(X1,X4,X5)
| X2 != X4
| X3 != X5
| ~ related(X0,X2,X3)
| ~ in(X4,the_carrier(X1))
| ~ in(X5,the_carrier(X1))
| ~ element(X5,the_carrier(X1)) )
| ~ element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ full_subrelstr(X1,X0)
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(ennf_transformation,[],[f729]) ).
fof(f1682,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( related(X1,X4,X5)
| X2 != X4
| X3 != X5
| ~ related(X0,X2,X3)
| ~ in(X4,the_carrier(X1))
| ~ in(X5,the_carrier(X1))
| ~ element(X5,the_carrier(X1)) )
| ~ element(X4,the_carrier(X1)) )
| ~ element(X3,the_carrier(X0)) )
| ~ element(X2,the_carrier(X0)) )
| ~ full_subrelstr(X1,X0)
| ~ subrelstr(X1,X0) )
| ~ rel_str(X0) ),
inference(flattening,[],[f1681]) ).
fof(f2054,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( subnetstr(X2,X0,X1)
| ~ subrelstr(X2,X1)
| the_mapping(X0,X2) != relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
& ( ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
| ~ subnetstr(X2,X0,X1) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f1049]) ).
fof(f2055,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( subnetstr(X2,X0,X1)
| ~ subrelstr(X2,X1)
| the_mapping(X0,X2) != relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
& ( ( subrelstr(X2,X1)
& the_mapping(X0,X2) = relation_dom_restr_as_relation_of(the_carrier(X1),the_carrier(X0),the_mapping(X0,X1),the_carrier(X2)) )
| ~ subnetstr(X2,X0,X1) ) )
| ~ net_str(X2,X0) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f2054]) ).
fof(f2065,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( full_subnetstr(X2,X0,X1)
| ~ full_subrelstr(X2,X1)
| ~ subrelstr(X2,X1) )
& ( ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) )
| ~ full_subnetstr(X2,X0,X1) ) )
| ~ subnetstr(X2,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(nnf_transformation,[],[f1058]) ).
fof(f2066,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( full_subnetstr(X2,X0,X1)
| ~ full_subrelstr(X2,X1)
| ~ subrelstr(X2,X1) )
& ( ( full_subrelstr(X2,X1)
& subrelstr(X2,X1) )
| ~ full_subnetstr(X2,X0,X1) ) )
| ~ subnetstr(X2,X0,X1) )
| ~ net_str(X1,X0) )
| ~ one_sorted_str(X0) ),
inference(flattening,[],[f2065]) ).
fof(f2409,plain,
( ~ related(sK515,sK518,sK519)
& sK516 = sK518
& sK517 = sK519
& related(sK514,sK516,sK517)
& element(sK519,the_carrier(sK515))
& element(sK518,the_carrier(sK515))
& element(sK517,the_carrier(sK514))
& element(sK516,the_carrier(sK514))
& ~ empty_carrier(sK515)
& full_subnetstr(sK515,sK513,sK514)
& subnetstr(sK515,sK513,sK514)
& ~ empty_carrier(sK514)
& net_str(sK514,sK513)
& one_sorted_str(sK513) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK513,sK514,sK515,sK516,sK517,sK518,sK519]),skolemize(X0,sK513),skolemize(X1,sK514),skolemize(X2,sK515),skolemize(X3,sK516),skolemize(X4,sK517),skolemize(X5,sK518),skolemize(X6,sK519)],[f1527]) ).
fof(f3154,plain,
! [X2,X0,X1] :
( subrelstr(X2,X1)
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X2,X0)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f2055]) ).
fof(f3171,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ full_subnetstr(X2,X0,X1)
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X1,X0)
| full_subrelstr(X2,X1) ),
inference(cnf_transformation,[],[f2066]) ).
fof(f3252,plain,
! [X0] :
( ~ rel_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1135]) ).
fof(f3254,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ net_str(X1,X0)
| rel_str(X1) ),
inference(cnf_transformation,[],[f1137]) ).
fof(f3260,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ subnetstr(X2,X0,X1)
| net_str(X2,X0)
| ~ net_str(X1,X0) ),
inference(cnf_transformation,[],[f1144]) ).
fof(f3341,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| empty_carrier(X0)
| ~ one_sorted_str(X0) ),
inference(cnf_transformation,[],[f1178]) ).
fof(f4548,plain,
one_sorted_str(sK513),
inference(cnf_transformation,[],[f2409]) ).
fof(f4549,plain,
net_str(sK514,sK513),
inference(cnf_transformation,[],[f2409]) ).
fof(f4551,plain,
subnetstr(sK515,sK513,sK514),
inference(cnf_transformation,[],[f2409]) ).
fof(f4552,plain,
full_subnetstr(sK515,sK513,sK514),
inference(cnf_transformation,[],[f2409]) ).
fof(f4553,plain,
~ empty_carrier(sK515),
inference(cnf_transformation,[],[f2409]) ).
fof(f4554,plain,
element(sK516,the_carrier(sK514)),
inference(cnf_transformation,[],[f2409]) ).
fof(f4555,plain,
element(sK517,the_carrier(sK514)),
inference(cnf_transformation,[],[f2409]) ).
fof(f4556,plain,
element(sK518,the_carrier(sK515)),
inference(cnf_transformation,[],[f2409]) ).
fof(f4557,plain,
element(sK519,the_carrier(sK515)),
inference(cnf_transformation,[],[f2409]) ).
fof(f4558,plain,
related(sK514,sK516,sK517),
inference(cnf_transformation,[],[f2409]) ).
fof(f4559,plain,
sK517 = sK519,
inference(cnf_transformation,[],[f2409]) ).
fof(f4560,plain,
sK516 = sK518,
inference(cnf_transformation,[],[f2409]) ).
fof(f4561,plain,
~ related(sK515,sK518,sK519),
inference(cnf_transformation,[],[f2409]) ).
fof(f4609,plain,
! [X0,X1] :
( ~ element(X0,X1)
| in(X0,X1)
| empty(X1) ),
inference(cnf_transformation,[],[f1574]) ).
fof(f4779,plain,
! [X2,X3,X0,X1,X4,X5] :
( related(X1,X4,X5)
| X2 != X4
| X3 != X5
| ~ related(X0,X2,X3)
| ~ in(X4,the_carrier(X1))
| ~ in(X5,the_carrier(X1))
| ~ element(X5,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ full_subrelstr(X1,X0)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[],[f1682]) ).
fof(f5565,plain,
related(sK514,sK518,sK519),
inference(definition_unfolding,[],[f4558,f4560,f4559]) ).
fof(f5566,plain,
element(sK519,the_carrier(sK514)),
inference(definition_unfolding,[],[f4555,f4559]) ).
fof(f5567,plain,
element(sK518,the_carrier(sK514)),
inference(definition_unfolding,[],[f4554,f4560]) ).
fof(f5968,plain,
! [X3,X0,X1,X4,X5] :
( related(X1,X4,X5)
| X3 != X5
| ~ related(X0,X4,X3)
| ~ in(X4,the_carrier(X1))
| ~ in(X5,the_carrier(X1))
| ~ element(X5,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ element(X3,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| ~ full_subrelstr(X1,X0)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(equality_resolution,[],[f4779]) ).
fof(f5969,plain,
! [X0,X1,X4,X5] :
( ~ full_subrelstr(X1,X0)
| ~ related(X0,X4,X5)
| ~ in(X4,the_carrier(X1))
| ~ in(X5,the_carrier(X1))
| ~ element(X5,the_carrier(X1))
| ~ element(X4,the_carrier(X1))
| ~ element(X5,the_carrier(X0))
| ~ element(X4,the_carrier(X0))
| related(X1,X4,X5)
| ~ subrelstr(X1,X0)
| ~ rel_str(X0) ),
inference(equality_resolution,[],[f5968]) ).
fof(f6334,plain,
! [X2,X0,X1] :
( ~ one_sorted_str(X0)
| ~ subnetstr(X2,X0,X1)
| ~ net_str(X1,X0)
| subrelstr(X2,X1) ),
inference(forward_subsumption_resolution,[],[f3154,f3260]) ).
fof(f6417,plain,
! [X0,X1] :
( ~ net_str(X1,sK513)
| ~ subnetstr(X0,sK513,X1)
| subrelstr(X0,X1) ),
inference(resolution,[],[f4548,f6334]) ).
fof(f6427,plain,
! [X0] :
( ~ subnetstr(X0,sK513,sK514)
| subrelstr(X0,sK514) ),
inference(resolution,[],[f6417,f4549]) ).
fof(f6428,plain,
subrelstr(sK515,sK514),
inference(resolution,[],[f6427,f4551]) ).
fof(f6432,plain,
! [X0,X1] :
( ~ net_str(X1,sK513)
| net_str(X0,sK513)
| ~ subnetstr(X0,sK513,X1) ),
inference(resolution,[],[f3260,f4548]) ).
fof(f6434,plain,
! [X0] :
( ~ net_str(X0,sK513)
| rel_str(X0) ),
inference(resolution,[],[f3254,f4548]) ).
fof(f6435,plain,
! [X0] :
( ~ subnetstr(X0,sK513,sK514)
| net_str(X0,sK513) ),
inference(resolution,[],[f6432,f4549]) ).
fof(f6436,plain,
net_str(sK515,sK513),
inference(resolution,[],[f6435,f4551]) ).
fof(f6440,plain,
rel_str(sK514),
inference(resolution,[],[f6434,f4549]) ).
fof(f6441,plain,
rel_str(sK515),
inference(resolution,[],[f6434,f6436]) ).
fof(f6446,plain,
! [X0,X1] :
( ~ full_subnetstr(X0,sK513,X1)
| ~ subnetstr(X0,sK513,X1)
| ~ net_str(X1,sK513)
| full_subrelstr(X0,X1) ),
inference(resolution,[],[f3171,f4548]) ).
fof(f6550,plain,
( ~ subnetstr(sK515,sK513,sK514)
| ~ net_str(sK514,sK513)
| full_subrelstr(sK515,sK514) ),
inference(resolution,[],[f6446,f4552]) ).
fof(f6551,plain,
( ~ net_str(sK514,sK513)
| full_subrelstr(sK515,sK514) ),
inference(forward_subsumption_resolution,[],[f6550,f4551]) ).
fof(f6552,plain,
full_subrelstr(sK515,sK514),
inference(forward_subsumption_resolution,[],[f6551,f4549]) ).
fof(f6618,plain,
( in(sK518,the_carrier(sK515))
| empty(the_carrier(sK515)) ),
inference(resolution,[],[f4609,f4556]) ).
fof(f6619,plain,
( in(sK519,the_carrier(sK515))
| empty(the_carrier(sK515)) ),
inference(resolution,[],[f4609,f4557]) ).
fof(f6638,definition,
( spl549_97
<=> empty(the_carrier(sK515)) ),
introduced(definition,[new_symbols(definition,[spl549_97])],[avatar_definition]) ).
fof(f6639,plain,
( empty(the_carrier(sK515))
| ~ spl549_97 ),
inference(avatar_component_clause,[],[f6638]) ).
fof(f6641,definition,
( spl549_98
<=> in(sK519,the_carrier(sK515)) ),
introduced(definition,[new_symbols(definition,[spl549_98])],[avatar_definition]) ).
fof(f6642,plain,
( in(sK519,the_carrier(sK515))
| ~ spl549_98 ),
inference(avatar_component_clause,[],[f6641]) ).
fof(f6643,plain,
( spl549_97
| spl549_98 ),
inference(avatar_split_clause,[],[f6619,f6641,f6638]) ).
fof(f6645,definition,
( spl549_99
<=> in(sK518,the_carrier(sK515)) ),
introduced(definition,[new_symbols(definition,[spl549_99])],[avatar_definition]) ).
fof(f6646,plain,
( in(sK518,the_carrier(sK515))
| ~ spl549_99 ),
inference(avatar_component_clause,[],[f6645]) ).
fof(f6647,plain,
( spl549_97
| spl549_99 ),
inference(avatar_split_clause,[],[f6618,f6645,f6638]) ).
fof(f6649,plain,
( empty_carrier(sK515)
| ~ one_sorted_str(sK515)
| ~ spl549_97 ),
inference(resolution,[],[f6639,f3341]) ).
fof(f6657,plain,
one_sorted_str(sK515),
inference(resolution,[],[f3252,f6441]) ).
fof(f6673,plain,
( ~ one_sorted_str(sK515)
| ~ spl549_97 ),
inference(forward_subsumption_resolution,[],[f6649,f4553]) ).
fof(f6684,plain,
( $false
| ~ spl549_97 ),
inference(forward_subsumption_resolution,[],[f6673,f6657]) ).
fof(f6685,plain,
~ spl549_97,
inference(avatar_contradiction_clause,[],[f6684]) ).
fof(f6831,plain,
( $false
| ~ spl549_98
| ~ spl549_99 ),
inference(unit_resulting_resolution,[],[f5969,f6440,f6428,f6552,f5565,f5567,f5566,f4561,f4556,f6646,f4557,f6642]) ).
fof(f6835,plain,
( ~ spl549_98
| ~ spl549_99 ),
inference(avatar_contradiction_clause,[],[f6831]) ).
cnf(s80,plain,
( spl549_97
| spl549_98 ),
inference(sat_conversion,[],[f6643]) ).
cnf(s81,plain,
( spl549_97
| spl549_99 ),
inference(sat_conversion,[],[f6647]) ).
cnf(s87,plain,
~ spl549_97,
inference(sat_conversion,[],[f6685]) ).
cnf(s92,plain,
( ~ spl549_98
| ~ spl549_99 ),
inference(sat_conversion,[],[f6835]) ).
cnf(s93,plain,
spl549_99,
inference(rat,[],[s81,s87]) ).
cnf(s94,plain,
~ spl549_98,
inference(rat,[],[s92,s93]) ).
cnf(s96,plain,
$false,
inference(rat,[],[s80,s94,s87]) ).
fof(f6839,plain,
$false,
inference(avatar_sat_refutation,[],[s96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU375+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.39 % Computer : n008.cluster.edu
% 0.10/0.39 % Model : x86_64 x86_64
% 0.10/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.39 % Memory : 8046.5625MB
% 0.10/0.39 % OS : Linux 6.8.0-71-generic
% 0.10/0.39 % CPULimit : 300
% 0.10/0.39 % WCLimit : 300
% 0.10/0.39 % DateTime : Mon Sep 28 05:00:09 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.43 Running first-order theorem proving
% 0.10/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.10/2.51 % (1889880)Detected formulas, will run a generic FOF schedule.
% 6.10/2.51 % (1889891)dis-21_1_sil=8000:lcm=predicate:random_seed=1871131545:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 6.10/2.51 % (1889891)Instruction limit reached!
% 6.10/2.51 % (1889891)------------------------------
% 6.10/2.51 % (1889891)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889891)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889891)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889891)Termination reason: Instruction limit
% 6.10/2.51 % (1889891)Termination phase: Saturation
% 6.10/2.51 % (1889891)Time elapsed: 0.039 s
% 6.10/2.51 % (1889891)Peak memory usage: 92 MB
% 6.10/2.51 % (1889891)Instructions burned: 132 (million)
% 6.10/2.51 % (1889888)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=152751308:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.10/2.51 % (1889887)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=4142329254:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.10/2.51 % (1889889)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4002450625:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.10/2.51 % (1889886)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=393086264:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.10/2.51 % (1889885)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2191109332:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.10/2.51 % (1889890)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3110121880:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.10/2.51 % (1889888)Instruction limit reached!
% 6.10/2.51 % (1889888)------------------------------
% 6.10/2.51 % (1889888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889888)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889888)Termination reason: Instruction limit
% 6.10/2.51 % (1889888)Termination phase: Property scanning
% 6.10/2.51 % (1889888)Time elapsed: 0.062 s
% 6.10/2.51 % (1889888)Peak memory usage: 90 MB
% 6.10/2.51 % (1889888)Instructions burned: 111 (million)
% 6.10/2.51 % (1889889)Instruction limit reached!
% 6.10/2.51 % (1889889)------------------------------
% 6.10/2.51 % (1889889)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889889)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889889)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889889)Termination reason: Instruction limit
% 6.10/2.51 % (1889889)Termination phase: Saturation
% 6.10/2.51 % (1889889)Time elapsed: 0.073 s
% 6.10/2.51 % (1889889)Peak memory usage: 91 MB
% 6.10/2.51 % (1889889)Instructions burned: 119 (million)
% 6.10/2.51 % (1889890)Instruction limit reached!
% 6.10/2.51 % (1889890)------------------------------
% 6.10/2.51 % (1889890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889890)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889890)Termination reason: Instruction limit
% 6.10/2.51 % (1889890)Termination phase: Saturation
% 6.10/2.51 % (1889890)Time elapsed: 0.084 s
% 6.10/2.51 % (1889890)Peak memory usage: 92 MB
% 6.10/2.51 % (1889890)Instructions burned: 140 (million)
% 6.10/2.51 % (1889899)lrs+10_1_sil=8000:sp=occurrence:random_seed=2225973353:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 6.10/2.51 % (1889899)Instruction limit reached!
% 6.10/2.51 % (1889899)------------------------------
% 6.10/2.51 % (1889899)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889899)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889899)Termination reason: Instruction limit
% 6.10/2.51 % (1889899)Termination phase: Saturation
% 6.10/2.51 % (1889899)Time elapsed: 0.098 s
% 6.10/2.51 % (1889899)Peak memory usage: 95 MB
% 6.10/2.51 % (1889899)Instructions burned: 286 (million)
% 6.10/2.51 % (1889900)lrs+10_1_sil=32000:urr=on:br=off:random_seed=978178834:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.10/2.51 % (1889901)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2126707402:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.10/2.51 % (1889902)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=1945169565:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.10/2.51 % (1889900)Instruction limit reached!
% 6.10/2.51 % (1889900)------------------------------
% 6.10/2.51 % (1889900)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889900)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889900)Termination reason: Instruction limit
% 6.10/2.51 % (1889900)Termination phase: Saturation
% 6.10/2.51 % (1889900)Time elapsed: 0.096 s
% 6.10/2.51 % (1889900)Peak memory usage: 90 MB
% 6.10/2.51 % (1889900)Instructions burned: 157 (million)
% 6.10/2.51 % (1889906)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2393084697:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 6.10/2.51 % (1889902)Instruction limit reached!
% 6.10/2.51 % (1889902)------------------------------
% 6.10/2.51 % (1889902)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889902)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889902)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889902)Termination reason: Instruction limit
% 6.10/2.51 % (1889902)Termination phase: Saturation
% 6.10/2.51 % (1889902)Time elapsed: 0.150 s
% 6.10/2.51 % (1889902)Peak memory usage: 94 MB
% 6.10/2.51 % (1889902)Instructions burned: 249 (million)
% 6.10/2.51 % (1889906)Instruction limit reached!
% 6.10/2.51 % (1889906)------------------------------
% 6.10/2.51 % (1889906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889906)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889906)Termination reason: Instruction limit
% 6.10/2.51 % (1889906)Termination phase: Saturation
% 6.10/2.51 % (1889906)Time elapsed: 0.096 s
% 6.10/2.51 % (1889906)Peak memory usage: 94 MB
% 6.10/2.51 % (1889906)Instructions burned: 294 (million)
% 6.10/2.51 % (1889901)Instruction limit reached!
% 6.10/2.51 % (1889901)------------------------------
% 6.10/2.51 % (1889901)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889901)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889901)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889901)Termination reason: Instruction limit
% 6.10/2.51 % (1889901)Termination phase: Saturation
% 6.10/2.51 % (1889901)Time elapsed: 0.218 s
% 6.10/2.51 % (1889901)Peak memory usage: 95 MB
% 6.10/2.51 % (1889901)Instructions burned: 326 (million)
% 6.10/2.51 % (1889908)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3980291408:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.10/2.51 % (1889910)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=284578937:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.10/2.51 % (1889912)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=204060851:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 6.10/2.51 % (1889911)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=271430367:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.10/2.51 % (1889912)Instruction limit reached!
% 6.10/2.51 % (1889912)------------------------------
% 6.10/2.51 % (1889912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889912)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889912)Termination reason: Instruction limit
% 6.10/2.51 % (1889912)Termination phase: Saturation
% 6.10/2.51 % (1889912)Time elapsed: 0.040 s
% 6.10/2.51 % (1889912)Peak memory usage: 90 MB
% 6.10/2.51 % (1889912)Instructions burned: 117 (million)
% 6.10/2.51 % (1889910)Instruction limit reached!
% 6.10/2.51 % (1889910)------------------------------
% 6.10/2.51 % (1889910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889910)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889910)Termination reason: Instruction limit
% 6.10/2.51 % (1889910)Termination phase: Saturation
% 6.10/2.51 % (1889910)Time elapsed: 0.064 s
% 6.10/2.51 % (1889910)Peak memory usage: 92 MB
% 6.10/2.51 % (1889910)Instructions burned: 113 (million)
% 6.10/2.51 % (1889911)Instruction limit reached!
% 6.10/2.51 % (1889911)------------------------------
% 6.10/2.51 % (1889911)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889911)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889911)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889911)Termination reason: Instruction limit
% 6.10/2.51 % (1889911)Termination phase: Property scanning
% 6.10/2.51 % (1889911)Time elapsed: 0.075 s
% 6.10/2.51 % (1889911)Peak memory usage: 91 MB
% 6.10/2.51 % (1889911)Instructions burned: 127 (million)
% 6.10/2.51 % (1889917)lrs+10_1_sil=8000:sp=occurrence:random_seed=4069296572:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 6.10/2.51 % (1889918)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=590392085:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.10/2.51 % (1889919)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2583073810:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 6.10/2.51 % (1889917)Instruction limit reached!
% 6.10/2.51 % (1889917)------------------------------
% 6.10/2.51 % (1889917)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889917)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889917)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889917)Termination reason: Instruction limit
% 6.10/2.51 % (1889917)Termination phase: Saturation
% 6.10/2.51 % (1889917)Time elapsed: 0.312 s
% 6.10/2.51 % (1889917)Peak memory usage: 105 MB
% 6.10/2.51 % (1889917)Instructions burned: 907 (million)
% 6.10/2.51 % (1889918)Instruction limit reached!
% 6.10/2.51 % (1889918)------------------------------
% 6.10/2.51 % (1889918)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889918)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889918)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889918)Termination reason: Instruction limit
% 6.10/2.51 % (1889918)Termination phase: Saturation
% 6.10/2.51 % (1889918)Time elapsed: 0.263 s
% 6.10/2.51 % (1889918)Peak memory usage: 96 MB
% 6.10/2.51 % (1889918)Instructions burned: 438 (million)
% 6.10/2.51 % (1889923)dis+10_3:1_sil=8000:acc=on:urr=on:br=off:sac=on:newcnf=on:random_seed=2127883614:i=134:sd=2:doe=on:nm=16:sup=off:ss=included_2987 on theBenchmark for (2987ds/134Mi)
% 6.10/2.51 % (1889886)First to succeed.
% 6.10/2.51 % (1889886)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1889880"
% 6.10/2.51 % (1889923)Instruction limit reached!
% 6.10/2.51 % (1889923)------------------------------
% 6.10/2.51 % (1889923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.10/2.51 % (1889923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.10/2.51 % (1889923)CaDiCaL version: 2.1.3
% 6.10/2.51 % (1889923)Termination reason: Instruction limit
% 6.10/2.51 % (1889923)Termination phase: Saturation
% 6.10/2.51 % (1889923)Time elapsed: 0.038 s
% 6.10/2.51 % (1889923)Peak memory usage: 91 MB
% 6.10/2.51 % (1889923)Instructions burned: 137 (million)
% 6.10/2.51 % (1889924)lrs+1002_8_sil=8000:sp=occurrence:sos=on:sac=on:random_seed=3318552162:st=8:i=592:sd=3:ep=RST:ss=axioms_2987 on theBenchmark for (2987ds/592Mi)
% 6.10/2.51 % (1889885)Also succeeded, but the first one will report.
% 6.10/2.51 % (1889926)lrs+10_1_ncem=casc2026/models/loop6.pt:sil=32000:npcc=on:random_seed=1445702427:st=3:i=13193:sd=3:ss=axioms_2986 on theBenchmark for (2986ds/13193Mi)
% 6.10/2.51 % (1889886)Refutation found. Thanks to Tanya!
% 6.10/2.51 % SZS status Theorem for theBenchmark
% 6.10/2.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.71 % (1889886)------------------------------
% 0.16/2.71 % (1889886)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.71 % (1889886)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.71 % (1889886)CaDiCaL version: 2.1.3
% 0.16/2.71 % (1889886)Termination reason: Refutation
% 0.16/2.71 % (1889886)Time elapsed: 1.164 s
% 0.16/2.71 % (1889886)Peak memory usage: 149 MB
% 0.16/2.71 % (1889886)Instructions burned: 1913 (million)
% 0.16/2.71 % (1889886)------------------------------
% 0.16/2.71 % (1889886)------------------------------
% 0.16/2.71 % (1889880)Success in time 1.639 s
% 0.16/2.71 % Vampire exiting
%------------------------------------------------------------------------------