%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU254+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 : n010.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 5.87s 1.72s
% Output : Refutation 6.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 105 ( 26 unt; 1 def)
% Number of atoms : 305 ( 7 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 342 ( 142 ~; 149 |; 33 &)
% ( 6 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-2 aty)
% Number of variables : 165 ( 155 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,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(f85,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f148,axiom,
! [X0] :
( relation(X0)
=> ( transitive(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) )
=> in(ordered_pair(X1,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l2_wellord1) ).
fof(f181,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(f204,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(f210,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(f228,conjecture,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f229,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f228]) ).
fof(f237,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(ordered_pair(X0,X1),X2)
=> ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f290,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f392,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f445,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f148]) ).
fof(f446,plain,
! [X0] :
( ( transitive(X0)
<=> ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f445]) ).
fof(f493,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f204]) ).
fof(f500,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,[],[f210]) ).
fof(f501,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f500]) ).
fof(f528,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f229]) ).
fof(f529,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(flattening,[],[f528]) ).
fof(f537,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(ennf_transformation,[],[f237]) ).
fof(f538,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f537]) ).
fof(f769,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X1,X2,X3] :
( in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(ordered_pair(X2,X3),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f446]) ).
fof(f770,plain,
! [X0] :
( ( ( transitive(X0)
| ? [X1,X2,X3] :
( ~ in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0)
& in(ordered_pair(X2,X3),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X6),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f769]) ).
fof(f771,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK80(X0),sK82(X0)),X0)
& in(ordered_pair(sK80(X0),sK81(X0)),X0)
& in(ordered_pair(sK81(X0),sK82(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X6),X0) )
| ~ transitive(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80,sK81,sK82]),skolemize(X1,sK80(X0)),skolemize(X2,sK81(X0)),skolemize(X3,sK82(X0))],[f770]) ).
fof(f802,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,[],[f181]) ).
fof(f803,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,[],[f802]) ).
fof(f813,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,[],[f493]) ).
fof(f814,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,[],[f813]) ).
fof(f817,plain,
( ~ transitive(relation_restriction(sK106,sK105))
& transitive(sK106)
& relation(sK106) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105,sK106]),skolemize(X0,sK105),skolemize(X1,sK106)],[f529]) ).
fof(f1081,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f1134,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f392]) ).
fof(f1216,plain,
! [X0,X6,X4,X5] :
( in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0)
| ~ in(ordered_pair(X5,X6),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f771]) ).
fof(f1217,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK81(X0),sK82(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f771]) ).
fof(f1218,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK80(X0),sK81(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f771]) ).
fof(f1219,plain,
! [X0] :
( transitive(X0)
| ~ in(ordered_pair(sK80(X0),sK82(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f771]) ).
fof(f1295,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f803]) ).
fof(f1329,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f814]) ).
fof(f1330,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f814]) ).
fof(f1331,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f814]) ).
fof(f1337,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f501]) ).
fof(f1360,plain,
relation(sK106),
inference(cnf_transformation,[],[f817]) ).
fof(f1361,plain,
transitive(sK106),
inference(cnf_transformation,[],[f817]) ).
fof(f1362,plain,
~ transitive(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f817]) ).
fof(f1372,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f538]) ).
fof(f1373,plain,
! [X2,X0,X1] :
( in(X0,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f538]) ).
fof(f1472,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f290]) ).
fof(f1510,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1081,f1472]) ).
fof(f1616,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK80(X0),sK82(X0)),unordered_pair(sK80(X0),sK80(X0))),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1219,f1510]) ).
fof(f1617,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK80(X0),sK81(X0)),unordered_pair(sK80(X0),sK80(X0))),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1218,f1510]) ).
fof(f1618,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK81(X0),sK82(X0)),unordered_pair(sK81(X0),sK81(X0))),X0)
| transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1217,f1510]) ).
fof(f1619,plain,
! [X0,X6,X4,X5] :
( ~ in(unordered_pair(unordered_pair(X5,X6),unordered_pair(X5,X5)),X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X4,X6),unordered_pair(X4,X4)),X0)
| ~ transitive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1216,f1510,f1510,f1510]) ).
fof(f1635,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f1295,f1510]) ).
fof(f1653,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1373,f1510]) ).
fof(f1654,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(definition_unfolding,[],[f1372,f1510]) ).
fof(f1800,definition,
sF123 = relation_restriction(sK106,sK105),
introduced(definition,[new_symbols(definition,[sF123])],[function_definition]) ).
fof(f1801,plain,
relation_restriction(sK106,sK105) = sF123,
inference(reorient_equations,[],[f1800]) ).
fof(f1802,plain,
~ transitive(sF123),
inference(definition_folding,[],[f1362,f1801]) ).
fof(f1832,plain,
( relation(sF123)
| ~ relation(sK106) ),
inference(superposition,[],[f1134,f1801]) ).
fof(f1833,plain,
relation(sF123),
inference(forward_subsumption_resolution,[],[f1832,f1360]) ).
fof(f1836,plain,
! [X0] :
( ~ in(X0,sF123)
| in(X0,sK106)
| ~ relation(sK106) ),
inference(superposition,[],[f1330,f1801]) ).
fof(f1837,plain,
! [X0] :
( ~ in(X0,sF123)
| in(X0,sK106) ),
inference(forward_subsumption_resolution,[],[f1836,f1360]) ).
fof(f1840,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sK106)
| transitive(sF123)
| ~ relation(sF123) ),
inference(resolution,[],[f1837,f1617]) ).
fof(f1841,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sK106)
| transitive(sF123)
| ~ relation(sF123) ),
inference(resolution,[],[f1837,f1618]) ).
fof(f1842,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sK106)
| ~ relation(sF123) ),
inference(forward_subsumption_resolution,[],[f1841,f1802]) ).
fof(f1843,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sK106)
| ~ relation(sF123) ),
inference(forward_subsumption_resolution,[],[f1840,f1802]) ).
fof(f1844,plain,
in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sK106),
inference(forward_subsumption_resolution,[],[f1842,f1833]) ).
fof(f1845,plain,
in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sK106),
inference(forward_subsumption_resolution,[],[f1843,f1833]) ).
fof(f1870,plain,
! [X0] :
( ~ in(X0,relation_field(sF123))
| in(X0,sK105)
| ~ relation(sK106) ),
inference(superposition,[],[f1337,f1801]) ).
fof(f1871,plain,
! [X0] :
( ~ in(X0,relation_field(sF123))
| in(X0,sK105) ),
inference(forward_subsumption_resolution,[],[f1870,f1360]) ).
fof(f1908,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK80(relation_restriction(X0,X1)),sK81(relation_restriction(X0,X1))),unordered_pair(sK80(relation_restriction(X0,X1)),sK80(relation_restriction(X0,X1)))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1329,f1617]) ).
fof(f1910,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK81(relation_restriction(X0,X1)),sK82(relation_restriction(X0,X1))),unordered_pair(sK81(relation_restriction(X0,X1)),sK81(relation_restriction(X0,X1)))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1329,f1618]) ).
fof(f1915,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK81(relation_restriction(X0,X1)),sK82(relation_restriction(X0,X1))),unordered_pair(sK81(relation_restriction(X0,X1)),sK81(relation_restriction(X0,X1)))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1910,f1134]) ).
fof(f1917,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK80(relation_restriction(X0,X1)),sK81(relation_restriction(X0,X1))),unordered_pair(sK80(relation_restriction(X0,X1)),sK80(relation_restriction(X0,X1)))),cartesian_product2(X1,X1))
| ~ relation(X0)
| transitive(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1908,f1134]) ).
fof(f1961,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK81(sF123)),unordered_pair(X0,X0)),sK106)
| in(unordered_pair(unordered_pair(X0,sK82(sF123)),unordered_pair(X0,X0)),sK106)
| ~ transitive(sK106)
| ~ relation(sK106) ),
inference(resolution,[],[f1619,f1844]) ).
fof(f1971,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK81(sF123)),unordered_pair(X0,X0)),sK106)
| in(unordered_pair(unordered_pair(X0,sK82(sF123)),unordered_pair(X0,X0)),sK106)
| ~ relation(sK106) ),
inference(forward_subsumption_resolution,[],[f1961,f1361]) ).
fof(f1973,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK81(sF123)),unordered_pair(X0,X0)),sK106)
| in(unordered_pair(unordered_pair(X0,sK82(sF123)),unordered_pair(X0,X0)),sK106) ),
inference(forward_subsumption_resolution,[],[f1971,f1360]) ).
fof(f1975,plain,
in(unordered_pair(unordered_pair(sK80(sF123),sK82(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sK106),
inference(resolution,[],[f1973,f1845]) ).
fof(f2139,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),cartesian_product2(sK105,sK105))
| ~ relation(sK106)
| transitive(sF123) ),
inference(superposition,[],[f1915,f1801]) ).
fof(f2142,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),cartesian_product2(sK105,sK105))
| transitive(sF123) ),
inference(forward_subsumption_resolution,[],[f2139,f1360]) ).
fof(f2143,plain,
in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),cartesian_product2(sK105,sK105)),
inference(forward_subsumption_resolution,[],[f2142,f1802]) ).
fof(f2161,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),cartesian_product2(sK105,sK105))
| ~ relation(sK106)
| transitive(sF123) ),
inference(superposition,[],[f1917,f1801]) ).
fof(f2165,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),cartesian_product2(sK105,sK105))
| transitive(sF123) ),
inference(forward_subsumption_resolution,[],[f2161,f1360]) ).
fof(f2166,plain,
in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),cartesian_product2(sK105,sK105)),
inference(forward_subsumption_resolution,[],[f2165,f1802]) ).
fof(f2170,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),relation_restriction(X0,sK105))
| ~ in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f2166,f1331]) ).
fof(f2191,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123)
| ~ in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sK106)
| ~ relation(sK106) ),
inference(superposition,[],[f2170,f1801]) ).
fof(f2194,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123)
| ~ relation(sK106) ),
inference(forward_subsumption_resolution,[],[f2191,f1845]) ).
fof(f2198,plain,
in(unordered_pair(unordered_pair(sK80(sF123),sK81(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123),
inference(forward_subsumption_resolution,[],[f2194,f1360]) ).
fof(f2242,plain,
! [X0] :
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),relation_restriction(X0,sK105))
| ~ in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),X0)
| ~ relation(X0) ),
inference(resolution,[],[f2143,f1331]) ).
fof(f2305,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sF123)
| ~ in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sK106)
| ~ relation(sK106) ),
inference(superposition,[],[f2242,f1801]) ).
fof(f2308,plain,
( in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sF123)
| ~ relation(sK106) ),
inference(forward_subsumption_resolution,[],[f2305,f1844]) ).
fof(f2312,plain,
in(unordered_pair(unordered_pair(sK81(sF123),sK82(sF123)),unordered_pair(sK81(sF123),sK81(sF123))),sF123),
inference(forward_subsumption_resolution,[],[f2308,f1360]) ).
fof(f2337,plain,
( in(sK82(sF123),relation_field(sF123))
| ~ relation(sF123) ),
inference(resolution,[],[f1654,f2312]) ).
fof(f2349,plain,
in(sK82(sF123),relation_field(sF123)),
inference(forward_subsumption_resolution,[],[f2337,f1833]) ).
fof(f2357,plain,
in(sK82(sF123),sK105),
inference(resolution,[],[f2349,f1871]) ).
fof(f2414,plain,
( in(sK80(sF123),relation_field(sF123))
| ~ relation(sF123) ),
inference(resolution,[],[f1653,f2198]) ).
fof(f2427,plain,
in(sK80(sF123),relation_field(sF123)),
inference(forward_subsumption_resolution,[],[f2414,f1833]) ).
fof(f2433,plain,
in(sK80(sF123),sK105),
inference(resolution,[],[f2427,f1871]) ).
fof(f2464,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),relation_restriction(X3,X1))
| ~ in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X0,X2),unordered_pair(X0,X0)),X3)
| ~ in(X0,X1)
| ~ relation(X3) ),
inference(resolution,[],[f1635,f1331]) ).
fof(f2491,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF123)
| ~ in(X1,sK105)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK106)
| ~ in(X0,sK105)
| ~ relation(sK106) ),
inference(superposition,[],[f2464,f1801]) ).
fof(f2502,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK106)
| ~ in(X1,sK105)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF123)
| ~ in(X0,sK105) ),
inference(forward_subsumption_resolution,[],[f2491,f1360]) ).
fof(f2520,plain,
( ~ in(sK82(sF123),sK105)
| in(unordered_pair(unordered_pair(sK80(sF123),sK82(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123)
| ~ in(sK80(sF123),sK105) ),
inference(resolution,[],[f2502,f1975]) ).
fof(f2532,plain,
( in(unordered_pair(unordered_pair(sK80(sF123),sK82(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123)
| ~ in(sK80(sF123),sK105) ),
inference(forward_subsumption_resolution,[],[f2520,f2357]) ).
fof(f2533,plain,
in(unordered_pair(unordered_pair(sK80(sF123),sK82(sF123)),unordered_pair(sK80(sF123),sK80(sF123))),sF123),
inference(forward_subsumption_resolution,[],[f2532,f2433]) ).
fof(f2591,plain,
( transitive(sF123)
| ~ relation(sF123) ),
inference(resolution,[],[f2533,f1616]) ).
fof(f2600,plain,
~ relation(sF123),
inference(forward_subsumption_resolution,[],[f2591,f1802]) ).
fof(f2601,plain,
$false,
inference(forward_subsumption_resolution,[],[f2600,f1833]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU254+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 28 04:21:02 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 5.87/1.72 % (1552533)Detected formulas, will run a generic FOF schedule.
% 5.87/1.72 % (1552538)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=3594549321:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.87/1.72 % (1552539)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=4132614064:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.87/1.72 % (1552540)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=3035985316:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.87/1.72 % (1552544)dis-21_1_sil=8000:lcm=predicate:random_seed=557318293: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)
% 5.87/1.72 % (1552542)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3768272446:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.87/1.72 % (1552541)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4091738242:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.87/1.72 % (1552543)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2284628694:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.87/1.72 % (1552541)Instruction limit reached!
% 5.87/1.72 % (1552541)------------------------------
% 5.87/1.72 % (1552541)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552541)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552541)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552541)Termination reason: Instruction limit
% 5.87/1.72 % (1552541)Termination phase: Saturation
% 5.87/1.72 % (1552541)Time elapsed: 0.069 s
% 5.87/1.72 % (1552541)Peak memory usage: 90 MB
% 5.87/1.72 % (1552541)Instructions burned: 110 (million)
% 5.87/1.72 % (1552544)Instruction limit reached!
% 5.87/1.72 % (1552544)------------------------------
% 5.87/1.72 % (1552544)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552544)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552544)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552544)Termination reason: Instruction limit
% 5.87/1.72 % (1552544)Termination phase: Saturation
% 5.87/1.72 % (1552544)Time elapsed: 0.077 s
% 5.87/1.72 % (1552544)Peak memory usage: 90 MB
% 5.87/1.72 % (1552544)Instructions burned: 132 (million)
% 5.87/1.72 % (1552542)Instruction limit reached!
% 5.87/1.72 % (1552542)------------------------------
% 5.87/1.72 % (1552542)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552542)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552542)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552542)Termination reason: Instruction limit
% 5.87/1.72 % (1552542)Termination phase: Saturation
% 5.87/1.72 % (1552542)Time elapsed: 0.080 s
% 5.87/1.72 % (1552542)Peak memory usage: 89 MB
% 5.87/1.72 % (1552542)Instructions burned: 120 (million)
% 5.87/1.72 % (1552543)Instruction limit reached!
% 5.87/1.72 % (1552543)------------------------------
% 5.87/1.72 % (1552543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552543)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552543)Termination reason: Instruction limit
% 5.87/1.72 % (1552543)Termination phase: Saturation
% 5.87/1.72 % (1552543)Time elapsed: 0.099 s
% 5.87/1.72 % (1552543)Peak memory usage: 91 MB
% 5.87/1.72 % (1552543)Instructions burned: 140 (million)
% 5.87/1.72 % (1552553)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1415391596:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.87/1.72 % (1552552)lrs+10_1_sil=8000:sp=occurrence:random_seed=3540728565:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.87/1.72 % (1552554)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2066004040:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.87/1.72 % (1552555)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=311871415:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.87/1.72 % (1552553)Instruction limit reached!
% 5.87/1.72 % (1552553)------------------------------
% 5.87/1.72 % (1552553)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552553)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552553)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552553)Termination reason: Instruction limit
% 5.87/1.72 % (1552553)Termination phase: Saturation
% 5.87/1.72 % (1552553)Time elapsed: 0.081 s
% 5.87/1.72 % (1552553)Peak memory usage: 90 MB
% 5.87/1.72 % (1552553)Instructions burned: 157 (million)
% 5.87/1.72 % (1552555)Instruction limit reached!
% 5.87/1.72 % (1552555)------------------------------
% 5.87/1.72 % (1552555)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552555)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552555)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552555)Termination reason: Instruction limit
% 5.87/1.72 % (1552555)Termination phase: Saturation
% 5.87/1.72 % (1552555)Time elapsed: 0.150 s
% 5.87/1.72 % (1552555)Peak memory usage: 93 MB
% 5.87/1.72 % (1552555)Instructions burned: 248 (million)
% 5.87/1.72 % (1552552)Instruction limit reached!
% 5.87/1.72 % (1552552)------------------------------
% 5.87/1.72 % (1552552)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552552)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552552)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552552)Termination reason: Instruction limit
% 5.87/1.72 % (1552552)Termination phase: Saturation
% 5.87/1.72 % (1552552)Time elapsed: 0.185 s
% 5.87/1.72 % (1552552)Peak memory usage: 93 MB
% 5.87/1.72 % (1552552)Instructions burned: 286 (million)
% 5.87/1.72 % (1552554)Instruction limit reached!
% 5.87/1.72 % (1552554)------------------------------
% 5.87/1.72 % (1552554)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552554)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552554)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552554)Termination reason: Instruction limit
% 5.87/1.72 % (1552554)Termination phase: Saturation
% 5.87/1.72 % (1552554)Time elapsed: 0.223 s
% 5.87/1.72 % (1552554)Peak memory usage: 93 MB
% 5.87/1.72 % (1552554)Instructions burned: 325 (million)
% 5.87/1.72 % (1552560)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2309405848:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.87/1.72 % (1552538)First to succeed.
% 5.87/1.72 % (1552538)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1552533"
% 5.87/1.72 % (1552561)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=2380189827:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.87/1.72 % (1552562)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=721425449:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.87/1.72 % (1552563)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=4263465232:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 5.87/1.72 % (1552562)Instruction limit reached!
% 5.87/1.72 % (1552562)------------------------------
% 5.87/1.72 % (1552562)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552562)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552562)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552562)Termination reason: Instruction limit
% 5.87/1.72 % (1552562)Termination phase: Saturation
% 5.87/1.72 % (1552562)Time elapsed: 0.070 s
% 5.87/1.72 % (1552562)Peak memory usage: 90 MB
% 5.87/1.72 % (1552562)Instructions burned: 114 (million)
% 5.87/1.72 % (1552560)Instruction limit reached!
% 5.87/1.72 % (1552560)------------------------------
% 5.87/1.72 % (1552560)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.87/1.72 % (1552560)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.87/1.72 % (1552560)CaDiCaL version: 2.1.3
% 5.87/1.72 % (1552560)Termination reason: Instruction limit
% 5.87/1.72 % (1552560)Termination phase: Saturation
% 5.87/1.72 % (1552560)Time elapsed: 0.188 s
% 5.87/1.72 % (1552560)Peak memory usage: 91 MB
% 5.87/1.72 % (1552560)Instructions burned: 294 (million)
% 5.87/1.72 % (1552538)Refutation found. Thanks to Tanya!
% 5.87/1.72 % SZS status Theorem for theBenchmark
% 5.87/1.72 % SZS output start Proof for theBenchmark
% See solution above
% 6.63/1.82 % (1552538)------------------------------
% 6.63/1.82 % (1552538)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.82 % (1552538)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.82 % (1552538)CaDiCaL version: 2.1.3
% 6.63/1.82 % (1552538)Termination reason: Refutation
% 6.63/1.82 % (1552538)Time elapsed: 0.576 s
% 6.63/1.82 % (1552538)Peak memory usage: 135 MB
% 6.63/1.82 % (1552538)Instructions burned: 1326 (million)
% 6.63/1.82 % (1552538)------------------------------
% 6.63/1.82 % (1552538)------------------------------
% 6.63/1.82 % (1552533)Success in time 0.873 s
% 6.63/1.82 % Vampire exiting
%------------------------------------------------------------------------------