%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU253+1 : 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 : n004.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 12:48:01 PM UTC 2026
% Result : Theorem 2.61s 1.30s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 140 ( 25 unt; 15 def)
% Number of atoms : 407 ( 14 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 461 ( 194 ~; 199 |; 39 &)
% ( 20 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 15 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 117 ( 0 sgn 109 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f15,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f29,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
<=> ( in(X0,X2)
& in(X1,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t106_zfmisc_1) ).
fof(f36,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t16_wellord1) ).
fof(f37,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_field(relation_restriction(X2,X1)))
=> ( in(X0,relation_field(X2))
& in(X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f40,conjecture,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f41,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f40]) ).
fof(f57,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f60,plain,
! [X0] :
( ( connected(X0)
<=> ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(ennf_transformation,[],[f37]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f62]) ).
fof(f65,plain,
? [X0,X1] :
( ~ connected(relation_restriction(X1,X0))
& connected(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f41]) ).
fof(f66,plain,
? [X0,X1] :
( ~ connected(relation_restriction(X1,X0))
& connected(X1)
& relation(X1) ),
inference(flattening,[],[f65]) ).
fof(f73,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f60]) ).
fof(f74,plain,
! [X0] :
( ( ( connected(X0)
| ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ( ( connected(X0)
| ( in(sK1(X0),relation_field(X0))
& in(sK2(X0),relation_field(X0))
& sK1(X0) != sK2(X0)
& ~ in(ordered_pair(sK1(X0),sK2(X0)),X0)
& ~ in(ordered_pair(sK2(X0),sK1(X0)),X0) ) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f74]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(nnf_transformation,[],[f35]) ).
fof(f82,plain,
! [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) )
& ( ( in(X0,X2)
& in(X1,X3) )
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f61]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_restriction(X2,X1))
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1)) )
& ( ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) )
| ~ in(X0,relation_restriction(X2,X1)) ) )
| ~ relation(X2) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
( ~ connected(relation_restriction(sK9,sK8))
& connected(sK9)
& relation(sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X0,sK8),skolemize(X1,sK9)],[f66]) ).
fof(f93,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f96,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f104,plain,
! [X3,X0,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0)
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f105,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK2(X0),sK1(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f106,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK1(X0),sK2(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f107,plain,
! [X0] :
( connected(X0)
| sK1(X0) != sK2(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f108,plain,
! [X0] :
( connected(X0)
| in(sK2(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f109,plain,
! [X0] :
( connected(X0)
| in(sK1(X0),relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f82]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1))
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f84]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2)) ),
inference(cnf_transformation,[],[f63]) ).
fof(f129,plain,
relation(sK9),
inference(cnf_transformation,[],[f85]) ).
fof(f130,plain,
connected(sK9),
inference(cnf_transformation,[],[f85]) ).
fof(f131,plain,
~ connected(relation_restriction(sK9,sK8)),
inference(cnf_transformation,[],[f85]) ).
fof(f138,plain,
! [X0] :
( connected(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f106,f93]) ).
fof(f139,plain,
! [X0] :
( connected(X0)
| ~ in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f105,f93]) ).
fof(f140,plain,
! [X3,X0,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f104,f93,f93]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f121,f93]) ).
fof(f144,definition,
! [X0,X1] :
( sQ10_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ10_eqProxy])],[equality_proxy_definition]) ).
fof(f152,plain,
! [X0] :
( ~ sQ10_eqProxy(sK1(X0),sK2(X0))
| connected(X0)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f107,f144]) ).
fof(f153,plain,
! [X3,X0,X4] :
( sQ10_eqProxy(X3,X4)
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X0)
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),X0)
| ~ connected(X0)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f140,f144]) ).
fof(f171,plain,
( in(sK2(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8)))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(resolution,[],[f108,f131]) ).
fof(f173,definition,
( spl11_1
<=> relation(relation_restriction(sK9,sK8)) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f174,plain,
( ~ relation(relation_restriction(sK9,sK8))
| spl11_1 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f176,definition,
( spl11_2
<=> in(sK2(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8))) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f177,plain,
( in(sK2(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8)))
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f178,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f171,f176,f173]) ).
fof(f179,plain,
( ~ relation(sK9)
| spl11_1 ),
inference(resolution,[],[f174,f96]) ).
fof(f180,plain,
( $false
| spl11_1 ),
inference(resolution,[],[f179,f129]) ).
fof(f181,plain,
spl11_1,
inference(avatar_contradiction_clause,[],[f180]) ).
fof(f186,plain,
( in(sK1(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8)))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(resolution,[],[f109,f131]) ).
fof(f188,definition,
( spl11_3
<=> in(sK1(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8))) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f189,plain,
( in(sK1(relation_restriction(sK9,sK8)),relation_field(relation_restriction(sK9,sK8)))
| ~ spl11_3 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( ~ spl11_1
| spl11_3 ),
inference(avatar_split_clause,[],[f186,f188,f173]) ).
fof(f210,plain,
! [X0,X1] :
( ~ in(X0,relation_field(relation_restriction(sK9,X1)))
| in(X0,X1) ),
inference(resolution,[],[f125,f129]) ).
fof(f211,plain,
( in(sK2(relation_restriction(sK9,sK8)),sK8)
| ~ spl11_2 ),
inference(resolution,[],[f210,f177]) ).
fof(f213,plain,
( in(sK1(relation_restriction(sK9,sK8)),sK8)
| ~ spl11_3 ),
inference(resolution,[],[f210,f189]) ).
fof(f232,plain,
! [X0,X1] :
( ~ in(X0,relation_field(relation_restriction(sK9,X1)))
| in(X0,relation_field(sK9)) ),
inference(resolution,[],[f126,f129]) ).
fof(f235,plain,
( in(sK1(relation_restriction(sK9,sK8)),relation_field(sK9))
| ~ spl11_3 ),
inference(resolution,[],[f232,f189]) ).
fof(f236,plain,
( in(sK2(relation_restriction(sK9,sK8)),relation_field(sK9))
| ~ spl11_2 ),
inference(resolution,[],[f232,f177]) ).
fof(f248,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sK9)
| in(X0,relation_restriction(sK9,X1)) ),
inference(resolution,[],[f124,f129]) ).
fof(f249,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(resolution,[],[f138,f131]) ).
fof(f251,definition,
( spl11_4
<=> in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8)) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f252,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8))
| spl11_4 ),
inference(avatar_component_clause,[],[f251]) ).
fof(f253,plain,
( ~ spl11_1
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f249,f251,f173]) ).
fof(f255,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8))
| ~ relation(relation_restriction(sK9,sK8)) ),
inference(resolution,[],[f139,f131]) ).
fof(f257,definition,
( spl11_5
<=> in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8)) ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f258,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),relation_restriction(sK9,sK8))
| spl11_5 ),
inference(avatar_component_clause,[],[f257]) ).
fof(f259,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f255,f257,f173]) ).
fof(f265,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),relation_restriction(sK9,X2))
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK9)
| ~ in(X0,X2)
| ~ in(X1,X2) ),
inference(resolution,[],[f248,f141]) ).
fof(f267,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK2(X0),sK1(X0)),singleton(sK2(X0))),X1)
| ~ in(sK1(X0),relation_field(X1))
| in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X1)
| ~ in(sK2(X0),relation_field(X1))
| ~ connected(X1)
| ~ relation(X1)
| connected(X0)
| ~ relation(X0) ),
inference(resolution,[],[f153,f152]) ).
fof(f366,definition,
( spl11_9
<=> in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),sK9) ),
introduced(definition,[new_symbols(definition,[spl11_9])],[avatar_definition]) ).
fof(f367,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),sK9)
| spl11_9 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f373,definition,
( spl11_11
<=> in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),sK9) ),
introduced(definition,[new_symbols(definition,[spl11_11])],[avatar_definition]) ).
fof(f612,definition,
( spl11_48
<=> connected(relation_restriction(sK9,sK8)) ),
introduced(definition,[new_symbols(definition,[spl11_48])],[avatar_definition]) ).
fof(f613,plain,
( connected(relation_restriction(sK9,sK8))
| ~ spl11_48 ),
inference(avatar_component_clause,[],[f612]) ).
fof(f832,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),sK9)
| ~ in(sK1(relation_restriction(sK9,sK8)),sK8)
| ~ in(sK2(relation_restriction(sK9,sK8)),sK8)
| spl11_4 ),
inference(resolution,[],[f265,f252]) ).
fof(f833,plain,
( ~ in(unordered_pair(unordered_pair(sK2(relation_restriction(sK9,sK8)),sK1(relation_restriction(sK9,sK8))),singleton(sK2(relation_restriction(sK9,sK8)))),sK9)
| ~ in(sK2(relation_restriction(sK9,sK8)),sK8)
| ~ in(sK1(relation_restriction(sK9,sK8)),sK8)
| spl11_5 ),
inference(resolution,[],[f265,f258]) ).
fof(f843,definition,
( spl11_89
<=> in(sK1(relation_restriction(sK9,sK8)),sK8) ),
introduced(definition,[new_symbols(definition,[spl11_89])],[avatar_definition]) ).
fof(f844,plain,
( ~ in(sK1(relation_restriction(sK9,sK8)),sK8)
| spl11_89 ),
inference(avatar_component_clause,[],[f843]) ).
fof(f846,definition,
( spl11_90
<=> in(sK2(relation_restriction(sK9,sK8)),sK8) ),
introduced(definition,[new_symbols(definition,[spl11_90])],[avatar_definition]) ).
fof(f847,plain,
( ~ in(sK2(relation_restriction(sK9,sK8)),sK8)
| spl11_90 ),
inference(avatar_component_clause,[],[f846]) ).
fof(f848,plain,
( ~ spl11_89
| ~ spl11_90
| ~ spl11_9
| spl11_5 ),
inference(avatar_split_clause,[],[f833,f257,f366,f846,f843]) ).
fof(f849,plain,
( ~ in(sK1(relation_restriction(sK9,sK8)),relation_field(sK9))
| in(unordered_pair(unordered_pair(sK1(relation_restriction(sK9,sK8)),sK2(relation_restriction(sK9,sK8))),singleton(sK1(relation_restriction(sK9,sK8)))),sK9)
| ~ in(sK2(relation_restriction(sK9,sK8)),relation_field(sK9))
| ~ connected(sK9)
| ~ relation(sK9)
| connected(relation_restriction(sK9,sK8))
| ~ relation(relation_restriction(sK9,sK8))
| spl11_9 ),
inference(resolution,[],[f367,f267]) ).
fof(f851,definition,
( spl11_91
<=> relation(sK9) ),
introduced(definition,[new_symbols(definition,[spl11_91])],[avatar_definition]) ).
fof(f852,plain,
( ~ relation(sK9)
| spl11_91 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f854,definition,
( spl11_92
<=> connected(sK9) ),
introduced(definition,[new_symbols(definition,[spl11_92])],[avatar_definition]) ).
fof(f855,plain,
( ~ connected(sK9)
| spl11_92 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f857,definition,
( spl11_93
<=> in(sK2(relation_restriction(sK9,sK8)),relation_field(sK9)) ),
introduced(definition,[new_symbols(definition,[spl11_93])],[avatar_definition]) ).
fof(f858,plain,
( ~ in(sK2(relation_restriction(sK9,sK8)),relation_field(sK9))
| spl11_93 ),
inference(avatar_component_clause,[],[f857]) ).
fof(f861,definition,
( spl11_94
<=> in(sK1(relation_restriction(sK9,sK8)),relation_field(sK9)) ),
introduced(definition,[new_symbols(definition,[spl11_94])],[avatar_definition]) ).
fof(f862,plain,
( ~ in(sK1(relation_restriction(sK9,sK8)),relation_field(sK9))
| spl11_94 ),
inference(avatar_component_clause,[],[f861]) ).
fof(f863,plain,
( ~ spl11_1
| spl11_48
| ~ spl11_91
| ~ spl11_92
| ~ spl11_93
| spl11_11
| ~ spl11_94
| spl11_9 ),
inference(avatar_split_clause,[],[f849,f366,f861,f373,f857,f854,f851,f612,f173]) ).
fof(f864,plain,
( $false
| spl11_91 ),
inference(resolution,[],[f852,f129]) ).
fof(f865,plain,
spl11_91,
inference(avatar_contradiction_clause,[],[f864]) ).
fof(f866,plain,
( $false
| spl11_92 ),
inference(resolution,[],[f855,f130]) ).
fof(f873,plain,
spl11_92,
inference(avatar_contradiction_clause,[],[f866]) ).
fof(f907,plain,
( $false
| ~ spl11_2
| spl11_93 ),
inference(resolution,[],[f858,f236]) ).
fof(f908,plain,
( ~ spl11_2
| spl11_93 ),
inference(avatar_contradiction_clause,[],[f907]) ).
fof(f909,plain,
( $false
| ~ spl11_3
| spl11_94 ),
inference(resolution,[],[f862,f235]) ).
fof(f910,plain,
( ~ spl11_3
| spl11_94 ),
inference(avatar_contradiction_clause,[],[f909]) ).
fof(f911,plain,
( $false
| ~ spl11_2
| spl11_90 ),
inference(resolution,[],[f847,f211]) ).
fof(f912,plain,
( ~ spl11_2
| spl11_90 ),
inference(avatar_contradiction_clause,[],[f911]) ).
fof(f913,plain,
( $false
| ~ spl11_3
| spl11_89 ),
inference(resolution,[],[f844,f213]) ).
fof(f914,plain,
( ~ spl11_3
| spl11_89 ),
inference(avatar_contradiction_clause,[],[f913]) ).
fof(f915,plain,
( ~ spl11_90
| ~ spl11_89
| ~ spl11_11
| spl11_4 ),
inference(avatar_split_clause,[],[f832,f251,f373,f843,f846]) ).
fof(f916,plain,
( $false
| ~ spl11_48 ),
inference(resolution,[],[f613,f131]) ).
fof(f917,plain,
~ spl11_48,
inference(avatar_contradiction_clause,[],[f916]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f178]) ).
cnf(s2,plain,
spl11_1,
inference(sat_conversion,[],[f181]) ).
cnf(s3,plain,
( ~ spl11_1
| spl11_3 ),
inference(sat_conversion,[],[f190]) ).
cnf(s4,plain,
( ~ spl11_1
| ~ spl11_4 ),
inference(sat_conversion,[],[f253]) ).
cnf(s5,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(sat_conversion,[],[f259]) ).
cnf(s45,plain,
( spl11_5
| ~ spl11_9
| ~ spl11_89
| ~ spl11_90 ),
inference(sat_conversion,[],[f848]) ).
cnf(s46,plain,
( ~ spl11_1
| spl11_9
| spl11_11
| spl11_48
| ~ spl11_91
| ~ spl11_92
| ~ spl11_93
| ~ spl11_94 ),
inference(sat_conversion,[],[f863]) ).
cnf(s47,plain,
spl11_91,
inference(sat_conversion,[],[f865]) ).
cnf(s48,plain,
spl11_92,
inference(sat_conversion,[],[f873]) ).
cnf(s55,plain,
( ~ spl11_2
| spl11_93 ),
inference(sat_conversion,[],[f908]) ).
cnf(s56,plain,
( ~ spl11_3
| spl11_94 ),
inference(sat_conversion,[],[f910]) ).
cnf(s57,plain,
( ~ spl11_2
| spl11_90 ),
inference(sat_conversion,[],[f912]) ).
cnf(s58,plain,
( ~ spl11_3
| spl11_89 ),
inference(sat_conversion,[],[f914]) ).
cnf(s59,plain,
( spl11_4
| ~ spl11_11
| ~ spl11_89
| ~ spl11_90 ),
inference(sat_conversion,[],[f915]) ).
cnf(s60,plain,
~ spl11_48,
inference(sat_conversion,[],[f917]) ).
cnf(s61,plain,
( ~ spl11_1
| spl11_9
| spl11_11
| ~ spl11_93
| ~ spl11_94 ),
inference(rat,[],[s46,s48,s47,s60]) ).
cnf(s64,plain,
~ spl11_5,
inference(rat,[],[s5,s2]) ).
cnf(s65,plain,
~ spl11_4,
inference(rat,[],[s4,s2]) ).
cnf(s66,plain,
spl11_3,
inference(rat,[],[s3,s2]) ).
cnf(s67,plain,
spl11_89,
inference(rat,[],[s58,s66]) ).
cnf(s68,plain,
spl11_94,
inference(rat,[],[s56,s66]) ).
cnf(s69,plain,
spl11_2,
inference(rat,[],[s1,s2]) ).
cnf(s70,plain,
spl11_90,
inference(rat,[],[s57,s69]) ).
cnf(s71,plain,
spl11_93,
inference(rat,[],[s55,s69]) ).
cnf(s72,plain,
~ spl11_9,
inference(rat,[],[s45,s67,s64,s70]) ).
cnf(s73,plain,
~ spl11_11,
inference(rat,[],[s59,s67,s65,s70]) ).
cnf(s74,plain,
$false,
inference(rat,[],[s61,s68,s71,s2,s73,s72]) ).
fof(f918,plain,
$false,
inference(avatar_sat_refutation,[],[s74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU253+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n004.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:20:22 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 2.61/1.30 % (4143500)Detected formulas, will run a generic FOF schedule.
% 2.61/1.30 % (4143508)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2400613267:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.61/1.30 % (4143508)Refutation not found, incomplete strategy
% 2.61/1.30 % (4143508)------------------------------
% 2.61/1.30 % (4143508)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.30 % (4143508)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.30 % (4143508)CaDiCaL version: 2.1.3
% 2.61/1.30 % (4143508)Termination reason: Refutation not found, incomplete strategy
% 2.61/1.30 % (4143508)Time elapsed: 0.001 s
% 2.61/1.30 % (4143508)Peak memory usage: 88 MB
% 2.61/1.30 % (4143505)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=1711953925:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.61/1.30 % (4143506)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=2138209081:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.61/1.30 % (4143507)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=3593253129:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.61/1.30 % (4143510)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2035566909:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.61/1.30 % (4143511)dis-21_1_sil=8000:lcm=predicate:random_seed=3584402826: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)
% 2.61/1.30 % (4143509)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=518560514:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.61/1.30 % (4143511)First to succeed.
% 2.61/1.30 % (4143511)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4143500"
% 2.61/1.30 % (4143509)Instruction limit reached!
% 2.61/1.30 % (4143509)------------------------------
% 2.61/1.30 % (4143509)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.30 % (4143509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.30 % (4143509)CaDiCaL version: 2.1.3
% 2.61/1.30 % (4143509)Termination reason: Instruction limit
% 2.61/1.30 % (4143509)Termination phase: Saturation
% 2.61/1.30 % (4143509)Time elapsed: 0.066 s
% 2.61/1.30 % (4143509)Peak memory usage: 88 MB
% 2.61/1.30 % (4143509)Instructions burned: 120 (million)
% 2.61/1.30 % (4143510)Instruction limit reached!
% 2.61/1.30 % (4143510)------------------------------
% 2.61/1.30 % (4143510)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.30 % (4143510)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.30 % (4143510)CaDiCaL version: 2.1.3
% 2.61/1.30 % (4143510)Termination reason: Instruction limit
% 2.61/1.30 % (4143510)Termination phase: Saturation
% 2.61/1.30 % (4143510)Time elapsed: 0.088 s
% 2.61/1.30 % (4143510)Peak memory usage: 90 MB
% 2.61/1.30 % (4143510)Instructions burned: 140 (million)
% 2.61/1.30 % (4143508)------------------------------
% 2.61/1.30 % (4143508)------------------------------
% 2.61/1.30 % (4143521)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2107603151:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.61/1.30 % (4143519)lrs+10_1_sil=8000:sp=occurrence:random_seed=2447287018:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.61/1.30 % (4143520)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2456982485:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.61/1.30 % (4143511)Refutation found. Thanks to Tanya!
% 2.61/1.30 % SZS status Theorem for theBenchmark
% 2.61/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.49 % (4143511)------------------------------
% 3.68/1.49 % (4143511)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (4143511)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (4143511)CaDiCaL version: 2.1.3
% 3.68/1.49 % (4143511)Termination reason: Refutation
% 3.68/1.49 % (4143511)Time elapsed: 0.015 s
% 3.68/1.49 % (4143511)Peak memory usage: 89 MB
% 3.68/1.49 % (4143511)Instructions burned: 21 (million)
% 3.68/1.49 % (4143511)------------------------------
% 3.68/1.49 % (4143511)------------------------------
% 3.68/1.49 % (4143500)Success in time 0.447 s
% 3.68/1.49 % Vampire exiting
%------------------------------------------------------------------------------