TSTP Solution File: SEU217+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.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 : Tue Apr 30 15:24:32 EDT 2024
% Result : Theorem 0.10s 0.35s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 90
% Syntax : Number of formulae : 247 ( 74 unt; 0 def)
% Number of atoms : 581 ( 72 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 572 ( 238 ~; 200 |; 55 &)
% ( 53 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 58 ( 56 usr; 50 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-2 aty)
% Number of variables : 222 ( 194 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f405,plain,
$false,
inference(avatar_sat_refutation,[],[f134,f139,f144,f149,f154,f159,f164,f169,f174,f179,f184,f189,f194,f198,f202,f206,f210,f214,f218,f222,f226,f238,f242,f246,f251,f255,f259,f263,f277,f282,f286,f292,f296,f300,f304,f316,f326,f336,f346,f351,f356,f361,f369,f374,f380,f385,f391,f400,f402,f404]) ).
fof(f404,plain,
( ~ spl12_16
| spl12_49 ),
inference(avatar_contradiction_clause,[],[f403]) ).
fof(f403,plain,
( $false
| ~ spl12_16
| spl12_49 ),
inference(resolution,[],[f399,f205]) ).
fof(f205,plain,
( ! [X0] : function(identity_relation(X0))
| ~ spl12_16 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f204,plain,
( spl12_16
<=> ! [X0] : function(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).
fof(f399,plain,
( ~ function(identity_relation(sK0))
| spl12_49 ),
inference(avatar_component_clause,[],[f397]) ).
fof(f397,plain,
( spl12_49
<=> function(identity_relation(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_49])]) ).
fof(f402,plain,
( ~ spl12_15
| spl12_48 ),
inference(avatar_contradiction_clause,[],[f401]) ).
fof(f401,plain,
( $false
| ~ spl12_15
| spl12_48 ),
inference(resolution,[],[f395,f201]) ).
fof(f201,plain,
( ! [X0] : relation(identity_relation(X0))
| ~ spl12_15 ),
inference(avatar_component_clause,[],[f200]) ).
fof(f200,plain,
( spl12_15
<=> ! [X0] : relation(identity_relation(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).
fof(f395,plain,
( ~ relation(identity_relation(sK0))
| spl12_48 ),
inference(avatar_component_clause,[],[f393]) ).
fof(f393,plain,
( spl12_48
<=> relation(identity_relation(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_48])]) ).
fof(f400,plain,
( ~ spl12_48
| ~ spl12_49
| spl12_2
| ~ spl12_1
| ~ spl12_40 ),
inference(avatar_split_clause,[],[f357,f349,f131,f136,f397,f393]) ).
fof(f136,plain,
( spl12_2
<=> sK1 = apply(identity_relation(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).
fof(f131,plain,
( spl12_1
<=> in(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).
fof(f349,plain,
( spl12_40
<=> ! [X0,X3] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_40])]) ).
fof(f357,plain,
( sK1 = apply(identity_relation(sK0),sK1)
| ~ function(identity_relation(sK0))
| ~ relation(identity_relation(sK0))
| ~ spl12_1
| ~ spl12_40 ),
inference(resolution,[],[f350,f133]) ).
fof(f133,plain,
( in(sK1,sK0)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f350,plain,
( ! [X3,X0] :
( ~ in(X3,X0)
| apply(identity_relation(X0),X3) = X3
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) )
| ~ spl12_40 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f391,plain,
( spl12_47
| ~ spl12_6
| ~ spl12_20 ),
inference(avatar_split_clause,[],[f233,f220,f156,f388]) ).
fof(f388,plain,
( spl12_47
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_47])]) ).
fof(f156,plain,
( spl12_6
<=> empty(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).
fof(f220,plain,
( spl12_20
<=> ! [X0] :
( relation(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).
fof(f233,plain,
( relation(sK7)
| ~ spl12_6
| ~ spl12_20 ),
inference(resolution,[],[f221,f158]) ).
fof(f158,plain,
( empty(sK7)
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f156]) ).
fof(f221,plain,
( ! [X0] :
( ~ empty(X0)
| relation(X0) )
| ~ spl12_20 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f385,plain,
( spl12_46
| ~ spl12_12
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f230,f216,f186,f382]) ).
fof(f382,plain,
( spl12_46
<=> function(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_46])]) ).
fof(f186,plain,
( spl12_12
<=> empty(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).
fof(f216,plain,
( spl12_19
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).
fof(f230,plain,
( function(sK11)
| ~ spl12_12
| ~ spl12_19 ),
inference(resolution,[],[f217,f188]) ).
fof(f188,plain,
( empty(sK11)
| ~ spl12_12 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f217,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl12_19 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f380,plain,
( spl12_45
| ~ spl12_6
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f229,f216,f156,f377]) ).
fof(f377,plain,
( spl12_45
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_45])]) ).
fof(f229,plain,
( function(sK7)
| ~ spl12_6
| ~ spl12_19 ),
inference(resolution,[],[f217,f158]) ).
fof(f374,plain,
( spl12_44
| ~ spl12_1
| ~ spl12_31 ),
inference(avatar_split_clause,[],[f288,f284,f131,f371]) ).
fof(f371,plain,
( spl12_44
<=> element(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_44])]) ).
fof(f284,plain,
( spl12_31
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_31])]) ).
fof(f288,plain,
( element(sK1,sK0)
| ~ spl12_1
| ~ spl12_31 ),
inference(resolution,[],[f285,f133]) ).
fof(f285,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl12_31 ),
inference(avatar_component_clause,[],[f284]) ).
fof(f369,plain,
spl12_43,
inference(avatar_split_clause,[],[f126,f367]) ).
fof(f367,plain,
( spl12_43
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK5(relation_dom(X1),X1) != apply(X1,sK5(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_43])]) ).
fof(f126,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| sK5(relation_dom(X1),X1) != apply(X1,sK5(relation_dom(X1),X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f111]) ).
fof(f111,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| sK5(X0,X1) != apply(X1,sK5(X0,X1))
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ( sK5(X0,X1) != apply(X1,sK5(X0,X1))
& in(sK5(X0,X1),X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f67,f68]) ).
fof(f68,plain,
! [X0,X1] :
( ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
=> ( sK5(X0,X1) != apply(X1,sK5(X0,X1))
& in(sK5(X0,X1),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f67,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(rectify,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( ( ( identity_relation(X0) = X1
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| relation_dom(X1) != X0 )
& ( ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 )
| identity_relation(X0) != X1 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(nnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ( identity_relation(X0) = X1
<=> ( ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) )
& relation_dom(X1) = X0 ) )
| ~ function(X1)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1] :
( ( function(X1)
& relation(X1) )
=> ( identity_relation(X0) = X1
<=> ( ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 )
& relation_dom(X1) = X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f361,plain,
spl12_42,
inference(avatar_split_clause,[],[f127,f359]) ).
fof(f359,plain,
( spl12_42
<=> ! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK5(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_42])]) ).
fof(f127,plain,
! [X1] :
( identity_relation(relation_dom(X1)) = X1
| in(sK5(relation_dom(X1),X1),relation_dom(X1))
| ~ function(X1)
| ~ relation(X1) ),
inference(equality_resolution,[],[f110]) ).
fof(f110,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| in(sK5(X0,X1),X0)
| relation_dom(X1) != X0
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f356,plain,
( ~ spl12_41
| ~ spl12_1
| ~ spl12_29 ),
inference(avatar_split_clause,[],[f287,f275,f131,f353]) ).
fof(f353,plain,
( spl12_41
<=> in(sK0,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_41])]) ).
fof(f275,plain,
( spl12_29
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_29])]) ).
fof(f287,plain,
( ~ in(sK0,sK1)
| ~ spl12_1
| ~ spl12_29 ),
inference(resolution,[],[f276,f133]) ).
fof(f276,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl12_29 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f351,plain,
spl12_40,
inference(avatar_split_clause,[],[f128,f349]) ).
fof(f128,plain,
! [X3,X0] :
( apply(identity_relation(X0),X3) = X3
| ~ in(X3,X0)
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f109]) ).
fof(f109,plain,
! [X3,X0,X1] :
( apply(X1,X3) = X3
| ~ in(X3,X0)
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f346,plain,
spl12_39,
inference(avatar_split_clause,[],[f129,f344]) ).
fof(f344,plain,
( spl12_39
<=> ! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_39])]) ).
fof(f129,plain,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
| ~ function(identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f108]) ).
fof(f108,plain,
! [X0,X1] :
( relation_dom(X1) = X0
| identity_relation(X0) != X1
| ~ function(X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f336,plain,
spl12_38,
inference(avatar_split_clause,[],[f115,f334]) ).
fof(f334,plain,
( spl12_38
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_38])]) ).
fof(f115,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).
fof(f326,plain,
spl12_37,
inference(avatar_split_clause,[],[f116,f324]) ).
fof(f324,plain,
( spl12_37
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_37])]) ).
fof(f116,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f316,plain,
spl12_36,
inference(avatar_split_clause,[],[f107,f314]) ).
fof(f314,plain,
( spl12_36
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_36])]) ).
fof(f107,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).
fof(f304,plain,
spl12_35,
inference(avatar_split_clause,[],[f113,f302]) ).
fof(f302,plain,
( spl12_35
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_35])]) ).
fof(f113,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8_boole) ).
fof(f300,plain,
spl12_34,
inference(avatar_split_clause,[],[f112,f298]) ).
fof(f298,plain,
( spl12_34
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_34])]) ).
fof(f112,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f12]) ).
fof(f12,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f296,plain,
spl12_33,
inference(avatar_split_clause,[],[f100,f294]) ).
fof(f294,plain,
( spl12_33
<=> ! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_33])]) ).
fof(f100,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(flattening,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ~ empty(relation_dom(X0))
| ~ relation(X0)
| empty(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ( relation(X0)
& ~ empty(X0) )
=> ~ empty(relation_dom(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc5_relat_1) ).
fof(f292,plain,
spl12_32,
inference(avatar_split_clause,[],[f93,f290]) ).
fof(f290,plain,
( spl12_32
<=> ! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_32])]) ).
fof(f93,plain,
! [X0] :
( element(sK2(X0),powerset(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0] :
( ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) )
| empty(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f38,f59]) ).
fof(f59,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
=> ( ~ empty(sK2(X0))
& element(sK2(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f38,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) )
| empty(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ~ empty(X0)
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).
fof(f286,plain,
spl12_31,
inference(avatar_split_clause,[],[f106,f284]) ).
fof(f106,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).
fof(f282,plain,
( ~ spl12_30
| ~ spl12_1
| ~ spl12_28 ),
inference(avatar_split_clause,[],[f273,f261,f131,f279]) ).
fof(f279,plain,
( spl12_30
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_30])]) ).
fof(f261,plain,
( spl12_28
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_28])]) ).
fof(f273,plain,
( ~ empty(sK0)
| ~ spl12_1
| ~ spl12_28 ),
inference(resolution,[],[f262,f133]) ).
fof(f262,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl12_28 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f277,plain,
spl12_29,
inference(avatar_split_clause,[],[f105,f275]) ).
fof(f105,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f263,plain,
spl12_28,
inference(avatar_split_clause,[],[f114,f261]) ).
fof(f114,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f259,plain,
spl12_27,
inference(avatar_split_clause,[],[f102,f257]) ).
fof(f257,plain,
( spl12_27
<=> ! [X0] : element(sK4(X0),powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_27])]) ).
fof(f102,plain,
! [X0] : element(sK4(X0),powerset(X0)),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0] :
( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f22,f63]) ).
fof(f63,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK4(X0))
& element(sK4(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f255,plain,
spl12_26,
inference(avatar_split_clause,[],[f99,f253]) ).
fof(f253,plain,
( spl12_26
<=> ! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_26])]) ).
fof(f99,plain,
! [X0] :
( relation(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( ( relation(relation_dom(X0))
& empty(relation_dom(X0)) )
| ~ empty(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( empty(X0)
=> ( relation(relation_dom(X0))
& empty(relation_dom(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc7_relat_1) ).
fof(f251,plain,
( spl12_25
| ~ spl12_3
| ~ spl12_19 ),
inference(avatar_split_clause,[],[f227,f216,f141,f248]) ).
fof(f248,plain,
( spl12_25
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).
fof(f141,plain,
( spl12_3
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).
fof(f227,plain,
( function(empty_set)
| ~ spl12_3
| ~ spl12_19 ),
inference(resolution,[],[f217,f143]) ).
fof(f143,plain,
( empty(empty_set)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f246,plain,
spl12_24,
inference(avatar_split_clause,[],[f98,f244]) ).
fof(f244,plain,
( spl12_24
<=> ! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_24])]) ).
fof(f98,plain,
! [X0] :
( empty(relation_dom(X0))
| ~ empty(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f242,plain,
spl12_23,
inference(avatar_split_clause,[],[f97,f240]) ).
fof(f240,plain,
( spl12_23
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_23])]) ).
fof(f97,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f238,plain,
spl12_22,
inference(avatar_split_clause,[],[f94,f236]) ).
fof(f236,plain,
( spl12_22
<=> ! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).
fof(f94,plain,
! [X0] :
( ~ empty(sK2(X0))
| empty(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f226,plain,
spl12_21,
inference(avatar_split_clause,[],[f101,f224]) ).
fof(f224,plain,
( spl12_21
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_21])]) ).
fof(f101,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f5,f61]) ).
fof(f61,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f5,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f222,plain,
spl12_20,
inference(avatar_split_clause,[],[f96,f220]) ).
fof(f96,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( relation(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( empty(X0)
=> relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_relat_1) ).
fof(f218,plain,
spl12_19,
inference(avatar_split_clause,[],[f95,f216]) ).
fof(f95,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f214,plain,
spl12_18,
inference(avatar_split_clause,[],[f104,f212]) ).
fof(f212,plain,
( spl12_18
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).
fof(f104,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f210,plain,
spl12_17,
inference(avatar_split_clause,[],[f103,f208]) ).
fof(f208,plain,
( spl12_17
<=> ! [X0] : empty(sK4(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).
fof(f103,plain,
! [X0] : empty(sK4(X0)),
inference(cnf_transformation,[],[f64]) ).
fof(f206,plain,
spl12_16,
inference(avatar_split_clause,[],[f92,f204]) ).
fof(f92,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] :
( function(identity_relation(X0))
& relation(identity_relation(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f202,plain,
spl12_15,
inference(avatar_split_clause,[],[f90,f200]) ).
fof(f90,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f198,plain,
spl12_14,
inference(avatar_split_clause,[],[f89,f196]) ).
fof(f196,plain,
( spl12_14
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).
fof(f89,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f194,plain,
spl12_13,
inference(avatar_split_clause,[],[f125,f191]) ).
fof(f191,plain,
( spl12_13
<=> relation(sK11) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).
fof(f125,plain,
relation(sK11),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
( relation(sK11)
& empty(sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f23,f80]) ).
fof(f80,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK11)
& empty(sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f189,plain,
spl12_12,
inference(avatar_split_clause,[],[f124,f186]) ).
fof(f124,plain,
empty(sK11),
inference(cnf_transformation,[],[f81]) ).
fof(f184,plain,
spl12_11,
inference(avatar_split_clause,[],[f123,f181]) ).
fof(f181,plain,
( spl12_11
<=> function(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).
fof(f123,plain,
function(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( function(sK10)
& relation(sK10) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f20,f78]) ).
fof(f78,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK10)
& relation(sK10) ) ),
introduced(choice_axiom,[]) ).
fof(f20,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f179,plain,
spl12_10,
inference(avatar_split_clause,[],[f122,f176]) ).
fof(f176,plain,
( spl12_10
<=> relation(sK10) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).
fof(f122,plain,
relation(sK10),
inference(cnf_transformation,[],[f79]) ).
fof(f174,plain,
spl12_9,
inference(avatar_split_clause,[],[f121,f171]) ).
fof(f171,plain,
( spl12_9
<=> relation(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).
fof(f121,plain,
relation(sK9),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
relation(sK9),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f36,f76]) ).
fof(f76,plain,
( ? [X0] : relation(X0)
=> relation(sK9) ),
introduced(choice_axiom,[]) ).
fof(f36,plain,
? [X0] : relation(X0),
inference(pure_predicate_removal,[],[f25]) ).
fof(f25,axiom,
? [X0] :
( relation_empty_yielding(X0)
& relation(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc3_relat_1) ).
fof(f169,plain,
spl12_8,
inference(avatar_split_clause,[],[f120,f166]) ).
fof(f166,plain,
( spl12_8
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).
fof(f120,plain,
relation(sK8),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( relation(sK8)
& ~ empty(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f24,f74]) ).
fof(f74,plain,
( ? [X0] :
( relation(X0)
& ~ empty(X0) )
=> ( relation(sK8)
& ~ empty(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
? [X0] :
( relation(X0)
& ~ empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f164,plain,
~ spl12_7,
inference(avatar_split_clause,[],[f119,f161]) ).
fof(f161,plain,
( spl12_7
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).
fof(f119,plain,
~ empty(sK8),
inference(cnf_transformation,[],[f75]) ).
fof(f159,plain,
spl12_6,
inference(avatar_split_clause,[],[f118,f156]) ).
fof(f118,plain,
empty(sK7),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
empty(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f26,f72]) ).
fof(f72,plain,
( ? [X0] : empty(X0)
=> empty(sK7) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f154,plain,
~ spl12_5,
inference(avatar_split_clause,[],[f117,f151]) ).
fof(f151,plain,
( spl12_5
<=> empty(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).
fof(f117,plain,
~ empty(sK6),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
~ empty(sK6),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f70]) ).
fof(f70,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK6) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f149,plain,
spl12_4,
inference(avatar_split_clause,[],[f86,f146]) ).
fof(f146,plain,
( spl12_4
<=> relation(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).
fof(f86,plain,
relation(empty_set),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
( relation(empty_set)
& empty(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_relat_1) ).
fof(f144,plain,
spl12_3,
inference(avatar_split_clause,[],[f84,f141]) ).
fof(f84,plain,
empty(empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f139,plain,
~ spl12_2,
inference(avatar_split_clause,[],[f83,f136]) ).
fof(f83,plain,
sK1 != apply(identity_relation(sK0),sK1),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
( sK1 != apply(identity_relation(sK0),sK1)
& in(sK1,sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f37,f57]) ).
fof(f57,plain,
( ? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) )
=> ( sK1 != apply(identity_relation(sK0),sK1)
& in(sK1,sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f37,plain,
? [X0,X1] :
( apply(identity_relation(X0),X1) != X1
& in(X1,X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
inference(negated_conjecture,[],[f30]) ).
fof(f30,conjecture,
! [X0,X1] :
( in(X1,X0)
=> apply(identity_relation(X0),X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t35_funct_1) ).
fof(f134,plain,
spl12_1,
inference(avatar_split_clause,[],[f82,f131]) ).
fof(f82,plain,
in(sK1,sK0),
inference(cnf_transformation,[],[f58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.11 % Problem : SEU217+3 : TPTP v8.1.2. Released v3.2.0.
% 0.02/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.32 % Computer : n003.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Mon Apr 29 20:49:33 EDT 2024
% 0.10/0.32 % CPUTime :
% 0.10/0.33 % (25211)Running in auto input_syntax mode. Trying TPTP
% 0.10/0.34 % (25214)WARNING: value z3 for option sas not known
% 0.10/0.34 % (25212)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.10/0.34 % (25216)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.10/0.34 % (25215)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.10/0.34 % (25213)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.10/0.34 % (25218)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.10/0.34 % (25217)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.10/0.34 % (25214)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.10/0.34 TRYING [1]
% 0.10/0.34 TRYING [2]
% 0.10/0.35 TRYING [3]
% 0.10/0.35 % (25216)First to succeed.
% 0.10/0.35 TRYING [1]
% 0.10/0.35 TRYING [2]
% 0.10/0.35 TRYING [4]
% 0.10/0.35 TRYING [1]
% 0.10/0.35 TRYING [2]
% 0.10/0.35 % (25214)Also succeeded, but the first one will report.
% 0.10/0.35 TRYING [3]
% 0.10/0.35 % (25216)Refutation found. Thanks to Tanya!
% 0.10/0.35 % SZS status Theorem for theBenchmark
% 0.10/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.35 % (25216)------------------------------
% 0.10/0.35 % (25216)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.10/0.35 % (25216)Termination reason: Refutation
% 0.10/0.35
% 0.10/0.35 % (25216)Memory used [KB]: 966
% 0.10/0.35 % (25216)Time elapsed: 0.009 s
% 0.10/0.35 % (25216)Instructions burned: 12 (million)
% 0.10/0.35 % (25216)------------------------------
% 0.10/0.35 % (25216)------------------------------
% 0.10/0.35 % (25211)Success in time 0.023 s
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