%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU191+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 : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:47:39 PM UTC 2026
% Result : Theorem 3.06s 1.35s
% Output : Refutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 87 ( 8 unt; 3 def)
% Number of atoms : 368 ( 48 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 477 ( 196 ~; 207 |; 53 &)
% ( 13 <=>; 7 =>; 0 <=; 1 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 0 sgn 149 !; 28 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f30,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f50,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f52,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f167,conjecture,
! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t74_relat_1) ).
fof(f168,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( relation(X3)
=> ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<=> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f167]) ).
fof(f193,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f7]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f209,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f210,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f209]) ).
fof(f311,plain,
? [X0,X1,X2,X3] :
( ( in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3))
<~> ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) ) )
& relation(X3) ),
inference(ennf_transformation,[],[f168]) ).
fof(f321,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f193]) ).
fof(f322,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f321]) ).
fof(f323,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f322]) ).
fof(f324,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( in(sK0(X0,X1),X0)
& sK0(X0,X1) = sK1(X0,X1) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f323]) ).
fof(f378,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f379,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f378]) ).
fof(f380,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK32(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK33(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK32(X0,X1,X2),sK33(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK32(X0,X1,X2),sK34(X0,X1,X2)),X0)
& in(ordered_pair(sK34(X0,X1,X2),sK33(X0,X1,X2)),X1) )
| in(ordered_pair(sK32(X0,X1,X2),sK33(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK35(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK35(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK32,sK33,sK34,sK35]),skolemize(X3,sK32(X0,X1,X2)),skolemize(X4,sK33(X0,X1,X2)),skolemize(X6,sK34(X0,X1,X2)),skolemize(X10,sK35(X0,X1,X7,X8))],[f379]) ).
fof(f417,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& ( ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) )
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& relation(X3) ),
inference(nnf_transformation,[],[f311]) ).
fof(f418,plain,
? [X0,X1,X2,X3] :
( ( ~ in(X0,X2)
| ~ in(ordered_pair(X0,X1),X3)
| ~ in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& ( ( in(X0,X2)
& in(ordered_pair(X0,X1),X3) )
| in(ordered_pair(X0,X1),relation_composition(identity_relation(X2),X3)) )
& relation(X3) ),
inference(flattening,[],[f417]) ).
fof(f419,plain,
( ( ~ in(sK51,sK53)
| ~ in(ordered_pair(sK51,sK52),sK54)
| ~ in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) )
& ( ( in(sK51,sK53)
& in(ordered_pair(sK51,sK52),sK54) )
| in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) )
& relation(sK54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51,sK52,sK53,sK54]),skolemize(X0,sK51),skolemize(X1,sK52),skolemize(X2,sK53),skolemize(X3,sK54)],[f418]) ).
fof(f428,plain,
! [X0,X1,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f324]) ).
fof(f429,plain,
! [X0,X1,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),X1)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f324]) ).
fof(f430,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f324]) ).
fof(f521,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK35(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f522,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK35(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f523,plain,
! [X2,X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),X2)
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f380]) ).
fof(f536,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f210]) ).
fof(f538,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f695,plain,
relation(sK54),
inference(cnf_transformation,[],[f419]) ).
fof(f696,plain,
( in(ordered_pair(sK51,sK52),sK54)
| in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) ),
inference(cnf_transformation,[],[f419]) ).
fof(f697,plain,
( in(sK51,sK53)
| in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) ),
inference(cnf_transformation,[],[f419]) ).
fof(f698,plain,
( ~ in(sK51,sK53)
| ~ in(ordered_pair(sK51,sK52),sK54)
| ~ in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) ),
inference(cnf_transformation,[],[f419]) ).
fof(f713,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,X5),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f430]) ).
fof(f714,plain,
! [X0,X5] :
( in(ordered_pair(X5,X5),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f713]) ).
fof(f715,plain,
! [X0,X4,X5] :
( in(X4,X0)
| ~ in(ordered_pair(X4,X5),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f429]) ).
fof(f716,plain,
! [X0,X4,X5] :
( X4 = X5
| ~ in(ordered_pair(X4,X5),identity_relation(X0))
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f428]) ).
fof(f760,plain,
! [X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f523]) ).
fof(f761,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK35(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f522]) ).
fof(f762,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK35(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f521]) ).
fof(f770,definition,
( spl57_1
<=> in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54)) ),
introduced(definition,[new_symbols(definition,[spl57_1])],[avatar_definition]) ).
fof(f771,plain,
( ~ in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54))
| spl57_1 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f772,plain,
( in(ordered_pair(sK51,sK52),relation_composition(identity_relation(sK53),sK54))
| ~ spl57_1 ),
inference(avatar_component_clause,[],[f770]) ).
fof(f774,definition,
( spl57_2
<=> in(ordered_pair(sK51,sK52),sK54) ),
introduced(definition,[new_symbols(definition,[spl57_2])],[avatar_definition]) ).
fof(f775,plain,
( ~ in(ordered_pair(sK51,sK52),sK54)
| spl57_2 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f776,plain,
( in(ordered_pair(sK51,sK52),sK54)
| ~ spl57_2 ),
inference(avatar_component_clause,[],[f774]) ).
fof(f777,plain,
( spl57_1
| spl57_2 ),
inference(avatar_split_clause,[],[f696,f774,f770]) ).
fof(f779,definition,
( spl57_3
<=> in(sK51,sK53) ),
introduced(definition,[new_symbols(definition,[spl57_3])],[avatar_definition]) ).
fof(f781,plain,
( in(sK51,sK53)
| ~ spl57_3 ),
inference(avatar_component_clause,[],[f779]) ).
fof(f782,plain,
( spl57_1
| spl57_3 ),
inference(avatar_split_clause,[],[f697,f779,f770]) ).
fof(f783,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(avatar_split_clause,[],[f698,f779,f774,f770]) ).
fof(f1600,plain,
! [X0,X5] :
( in(ordered_pair(X5,X5),identity_relation(X0))
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f714,f538]) ).
fof(f1614,plain,
! [X0,X4,X5] :
( ~ in(ordered_pair(X4,X5),identity_relation(X0))
| in(X4,X0) ),
inference(forward_subsumption_resolution,[],[f715,f538]) ).
fof(f1631,plain,
! [X0,X4,X5] :
( ~ in(ordered_pair(X4,X5),identity_relation(X0))
| X4 = X5 ),
inference(forward_subsumption_resolution,[],[f716,f538]) ).
fof(f2332,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK35(X0,X1,X7,X8)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f761,f536]) ).
fof(f2337,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK35(X0,X1,X7,X8),X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f762,f536]) ).
fof(f2383,plain,
! [X0,X1,X8,X9,X7] :
( in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f760,f536]) ).
fof(f2387,plain,
( ! [X0] :
( ~ in(ordered_pair(sK51,X0),identity_relation(sK53))
| ~ in(ordered_pair(X0,sK52),sK54)
| ~ relation(sK54)
| ~ relation(identity_relation(sK53)) )
| spl57_1 ),
inference(resolution,[],[f2383,f771]) ).
fof(f2405,plain,
( ! [X0] :
( ~ in(ordered_pair(sK51,X0),identity_relation(sK53))
| ~ in(ordered_pair(X0,sK52),sK54)
| ~ relation(identity_relation(sK53)) )
| spl57_1 ),
inference(forward_subsumption_resolution,[],[f2387,f695]) ).
fof(f2406,plain,
( ! [X0] :
( ~ in(ordered_pair(sK51,X0),identity_relation(sK53))
| ~ in(ordered_pair(X0,sK52),sK54) )
| spl57_1 ),
inference(forward_subsumption_resolution,[],[f2405,f538]) ).
fof(f2582,plain,
( ~ in(ordered_pair(sK51,sK52),sK54)
| ~ in(sK51,sK53)
| spl57_1 ),
inference(resolution,[],[f2406,f1600]) ).
fof(f2583,plain,
( ~ in(sK51,sK53)
| spl57_1
| ~ spl57_2 ),
inference(forward_subsumption_resolution,[],[f2582,f776]) ).
fof(f2584,plain,
( $false
| spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(forward_subsumption_resolution,[],[f2583,f781]) ).
fof(f2585,plain,
( spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(avatar_contradiction_clause,[],[f2584]) ).
fof(f2586,plain,
( in(ordered_pair(sK35(identity_relation(sK53),sK54,sK51,sK52),sK52),sK54)
| ~ relation(sK54)
| ~ relation(identity_relation(sK53))
| ~ spl57_1 ),
inference(resolution,[],[f772,f2337]) ).
fof(f2587,plain,
( in(ordered_pair(sK51,sK35(identity_relation(sK53),sK54,sK51,sK52)),identity_relation(sK53))
| ~ relation(sK54)
| ~ relation(identity_relation(sK53))
| ~ spl57_1 ),
inference(resolution,[],[f772,f2332]) ).
fof(f2619,plain,
( in(ordered_pair(sK51,sK35(identity_relation(sK53),sK54,sK51,sK52)),identity_relation(sK53))
| ~ relation(identity_relation(sK53))
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f2587,f695]) ).
fof(f2620,plain,
( in(ordered_pair(sK35(identity_relation(sK53),sK54,sK51,sK52),sK52),sK54)
| ~ relation(identity_relation(sK53))
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f2586,f695]) ).
fof(f2621,plain,
( in(ordered_pair(sK51,sK35(identity_relation(sK53),sK54,sK51,sK52)),identity_relation(sK53))
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f2619,f538]) ).
fof(f2622,plain,
( in(ordered_pair(sK35(identity_relation(sK53),sK54,sK51,sK52),sK52),sK54)
| ~ spl57_1 ),
inference(forward_subsumption_resolution,[],[f2620,f538]) ).
fof(f2680,plain,
( sK51 = sK35(identity_relation(sK53),sK54,sK51,sK52)
| ~ spl57_1 ),
inference(resolution,[],[f2621,f1631]) ).
fof(f2681,plain,
( in(sK51,sK53)
| ~ spl57_1 ),
inference(resolution,[],[f2621,f1614]) ).
fof(f2699,plain,
( spl57_3
| ~ spl57_1 ),
inference(avatar_split_clause,[],[f2681,f770,f779]) ).
fof(f3169,plain,
( in(ordered_pair(sK51,sK52),sK54)
| ~ spl57_1 ),
inference(superposition,[],[f2622,f2680]) ).
fof(f3170,plain,
( $false
| ~ spl57_1
| spl57_2 ),
inference(forward_subsumption_resolution,[],[f3169,f775]) ).
fof(f3171,plain,
( ~ spl57_1
| spl57_2 ),
inference(avatar_contradiction_clause,[],[f3170]) ).
cnf(s1,plain,
( spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f777]) ).
cnf(s2,plain,
( spl57_1
| spl57_3 ),
inference(sat_conversion,[],[f782]) ).
cnf(s3,plain,
( ~ spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(sat_conversion,[],[f783]) ).
cnf(s33,plain,
( spl57_1
| ~ spl57_2
| ~ spl57_3 ),
inference(sat_conversion,[],[f2585]) ).
cnf(s42,plain,
( ~ spl57_1
| spl57_3 ),
inference(sat_conversion,[],[f2699]) ).
cnf(s46,plain,
( ~ spl57_1
| spl57_2 ),
inference(sat_conversion,[],[f3171]) ).
cnf(s52,plain,
spl57_1,
inference(rat,[],[s33,s1,s2]) ).
cnf(s53,plain,
spl57_2,
inference(rat,[],[s46,s52]) ).
cnf(s54,plain,
spl57_3,
inference(rat,[],[s42,s52]) ).
cnf(s59,plain,
$false,
inference(rat,[],[s3,s53,s54,s52]) ).
fof(f3172,plain,
$false,
inference(avatar_sat_refutation,[],[s59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU191+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 28 04:00:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 3.06/1.35 % (1172612)Detected formulas, will run a generic FOF schedule.
% 3.06/1.35 % (1172619)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=1738974053:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.06/1.35 % (1172623)dis-21_1_sil=8000:lcm=predicate:random_seed=3721704472: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)
% 3.06/1.35 % (1172622)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3967522249:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.06/1.35 % (1172620)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2272640932:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.06/1.35 % (1172618)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=2234030959:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.06/1.35 % (1172617)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=1936674627:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.06/1.35 % (1172621)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=636524125:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.06/1.35 % (1172620)Instruction limit reached!
% 3.06/1.35 % (1172620)------------------------------
% 3.06/1.35 % (1172620)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (1172620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (1172620)CaDiCaL version: 2.1.3
% 3.06/1.35 % (1172620)Termination reason: Instruction limit
% 3.06/1.35 % (1172620)Termination phase: Saturation
% 3.06/1.35 % (1172620)Time elapsed: 0.072 s
% 3.06/1.35 % (1172620)Peak memory usage: 90 MB
% 3.06/1.35 % (1172620)Instructions burned: 110 (million)
% 3.06/1.35 % (1172623)Instruction limit reached!
% 3.06/1.35 % (1172623)------------------------------
% 3.06/1.35 % (1172623)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (1172623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (1172623)CaDiCaL version: 2.1.3
% 3.06/1.35 % (1172623)Termination reason: Instruction limit
% 3.06/1.35 % (1172623)Termination phase: Saturation
% 3.06/1.35 % (1172623)Time elapsed: 0.075 s
% 3.06/1.35 % (1172623)Peak memory usage: 90 MB
% 3.06/1.35 % (1172623)Instructions burned: 129 (million)
% 3.06/1.35 % (1172621)Instruction limit reached!
% 3.06/1.35 % (1172621)------------------------------
% 3.06/1.35 % (1172621)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (1172621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (1172621)CaDiCaL version: 2.1.3
% 3.06/1.35 % (1172621)Termination reason: Instruction limit
% 3.06/1.35 % (1172621)Termination phase: Saturation
% 3.06/1.35 % (1172621)Time elapsed: 0.076 s
% 3.06/1.35 % (1172621)Peak memory usage: 89 MB
% 3.06/1.35 % (1172621)Instructions burned: 120 (million)
% 3.06/1.35 % (1172622)First to succeed.
% 3.06/1.35 % (1172622)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1172612"
% 3.06/1.35 % (1172632)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1215752373:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.06/1.35 % (1172631)lrs+10_1_sil=8000:sp=occurrence:random_seed=4162720054:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.06/1.35 % (1172633)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2539403889:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.06/1.35 % (1172632)Instruction limit reached!
% 3.06/1.35 % (1172632)------------------------------
% 3.06/1.35 % (1172632)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.06/1.35 % (1172632)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.06/1.35 % (1172632)CaDiCaL version: 2.1.3
% 3.06/1.35 % (1172632)Termination reason: Instruction limit
% 3.06/1.35 % (1172632)Termination phase: Saturation
% 3.06/1.35 % (1172632)Time elapsed: 0.082 s
% 3.06/1.35 % (1172632)Peak memory usage: 91 MB
% 3.06/1.35 % (1172632)Instructions burned: 158 (million)
% 3.06/1.35 % (1172622)Refutation found. Thanks to Tanya!
% 3.06/1.35 % SZS status Theorem for theBenchmark
% 3.06/1.35 % SZS output start Proof for theBenchmark
% See solution above
% 4.24/1.53 % (1172622)------------------------------
% 4.24/1.53 % (1172622)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.24/1.53 % (1172622)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.24/1.53 % (1172622)CaDiCaL version: 2.1.3
% 4.24/1.53 % (1172622)Termination reason: Refutation
% 4.24/1.53 % (1172622)Time elapsed: 0.087 s
% 4.24/1.53 % (1172622)Peak memory usage: 91 MB
% 4.24/1.53 % (1172622)Instructions burned: 125 (million)
% 4.24/1.53 % (1172622)------------------------------
% 4.24/1.53 % (1172622)------------------------------
% 4.24/1.53 % (1172612)Success in time 0.517 s
% 4.24/1.53 % Vampire exiting
%------------------------------------------------------------------------------