%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU253+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:48:01 PM UTC 2026
% Result : Theorem 5.82s 1.79s
% Output : Refutation 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 80 ( 15 unt; 1 def)
% Number of atoms : 304 ( 28 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 382 ( 158 ~; 171 |; 39 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-2 aty)
% Number of variables : 150 ( 142 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f56,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f85,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f154,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/sandbox/benchmark/theBenchmark.p',l4_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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',t19_wellord1) ).
fof(f226,conjecture,
! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_wellord1) ).
fof(f227,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( connected(X1)
=> connected(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f226]) ).
fof(f289,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f391,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f451,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,[],[f154]) ).
fof(f492,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(f499,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(f500,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X0,X1) )
| ~ in(X0,relation_field(relation_restriction(X2,X1)))
| ~ relation(X2) ),
inference(flattening,[],[f499]) ).
fof(f523,plain,
? [X0,X1] :
( ~ connected(relation_restriction(X1,X0))
& connected(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f227]) ).
fof(f524,plain,
? [X0,X1] :
( ~ connected(relation_restriction(X1,X0))
& connected(X1)
& relation(X1) ),
inference(flattening,[],[f523]) ).
fof(f774,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,[],[f451]) ).
fof(f775,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,[],[f774]) ).
fof(f776,plain,
! [X0] :
( ( ( connected(X0)
| ( in(sK85(X0),relation_field(X0))
& in(sK86(X0),relation_field(X0))
& sK85(X0) != sK86(X0)
& ~ in(ordered_pair(sK85(X0),sK86(X0)),X0)
& ~ in(ordered_pair(sK86(X0),sK85(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,[sK85,sK86]),skolemize(X1,sK85(X0)),skolemize(X2,sK86(X0))],[f775]) ).
fof(f799,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(f800,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,[],[f799]) ).
fof(f810,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,[],[f492]) ).
fof(f811,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,[],[f810]) ).
fof(f814,plain,
( ~ connected(relation_restriction(sK106,sK105))
& connected(sK106)
& relation(sK106) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK105,sK106]),skolemize(X0,sK105),skolemize(X1,sK106)],[f524]) ).
fof(f1078,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f1131,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f391]) ).
fof(f1227,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,[],[f776]) ).
fof(f1228,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK86(X0),sK85(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f776]) ).
fof(f1229,plain,
! [X0] :
( connected(X0)
| ~ in(ordered_pair(sK85(X0),sK86(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f776]) ).
fof(f1230,plain,
! [X0] :
( sK85(X0) != sK86(X0)
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f776]) ).
fof(f1231,plain,
! [X0] :
( in(sK86(X0),relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f776]) ).
fof(f1232,plain,
! [X0] :
( in(sK85(X0),relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f776]) ).
fof(f1292,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f800]) ).
fof(f1328,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f811]) ).
fof(f1334,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,X1)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f1335,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_field(relation_restriction(X2,X1)))
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f500]) ).
fof(f1355,plain,
relation(sK106),
inference(cnf_transformation,[],[f814]) ).
fof(f1356,plain,
connected(sK106),
inference(cnf_transformation,[],[f814]) ).
fof(f1357,plain,
~ connected(relation_restriction(sK106,sK105)),
inference(cnf_transformation,[],[f814]) ).
fof(f1468,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f289]) ).
fof(f1506,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1078,f1468]) ).
fof(f1622,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK85(X0),sK86(X0)),unordered_pair(sK85(X0),sK85(X0))),X0)
| connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1229,f1506]) ).
fof(f1623,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(sK86(X0),sK85(X0)),unordered_pair(sK86(X0),sK86(X0))),X0)
| connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1228,f1506]) ).
fof(f1624,plain,
! [X3,X0,X4] :
( in(unordered_pair(unordered_pair(X4,X3),unordered_pair(X4,X4)),X0)
| in(unordered_pair(unordered_pair(X3,X4),unordered_pair(X3,X3)),X0)
| X3 = X4
| ~ in(X4,relation_field(X0))
| ~ in(X3,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1227,f1506,f1506]) ).
fof(f1631,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,[],[f1292,f1506]) ).
fof(f1796,definition,
sF123 = relation_restriction(sK106,sK105),
introduced(definition,[new_symbols(definition,[sF123])],[function_definition]) ).
fof(f1797,plain,
relation_restriction(sK106,sK105) = sF123,
inference(reorient_equations,[],[f1796]) ).
fof(f1798,plain,
~ connected(sF123),
inference(definition_folding,[],[f1357,f1797]) ).
fof(f1828,plain,
( relation(sF123)
| ~ relation(sK106) ),
inference(superposition,[],[f1131,f1797]) ).
fof(f1829,plain,
relation(sF123),
inference(forward_subsumption_resolution,[],[f1828,f1355]) ).
fof(f1836,plain,
! [X0,X1] :
( in(sK85(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1334,f1232]) ).
fof(f1837,plain,
! [X0,X1] :
( in(sK86(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1334,f1231]) ).
fof(f1840,plain,
! [X0,X1] :
( in(sK86(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1837,f1131]) ).
fof(f1841,plain,
! [X0,X1] :
( in(sK85(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1836,f1131]) ).
fof(f1910,plain,
! [X0,X1] :
( in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1335,f1232]) ).
fof(f1911,plain,
! [X0,X1] :
( in(sK86(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f1335,f1231]) ).
fof(f1916,plain,
! [X0,X1] :
( in(sK86(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1911,f1131]) ).
fof(f1917,plain,
! [X0,X1] :
( in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f1910,f1131]) ).
fof(f2028,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,[],[f1631,f1328]) ).
fof(f2033,plain,
! [X0,X1] :
( ~ in(sK85(relation_restriction(X0,X1)),X1)
| ~ in(unordered_pair(unordered_pair(sK86(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1))),unordered_pair(sK86(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1)))),X0)
| ~ in(sK86(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f2028,f1623]) ).
fof(f2034,plain,
! [X0,X1] :
( ~ in(sK86(relation_restriction(X0,X1)),X1)
| ~ in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| ~ in(sK85(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(resolution,[],[f2028,f1622]) ).
fof(f2045,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| ~ in(sK85(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2034,f1840]) ).
fof(f2046,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK86(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1))),unordered_pair(sK86(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1)))),X0)
| ~ in(sK86(relation_restriction(X0,X1)),X1)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2033,f1841]) ).
fof(f2047,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2045,f1841]) ).
fof(f2048,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK86(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1))),unordered_pair(sK86(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1)))),X0)
| ~ relation(X0)
| connected(relation_restriction(X0,X1))
| ~ relation(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2046,f1840]) ).
fof(f2049,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2047,f1131]) ).
fof(f2050,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(sK86(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1))),unordered_pair(sK86(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1)))),X0)
| ~ relation(X0)
| connected(relation_restriction(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f2048,f1131]) ).
fof(f2077,plain,
! [X0,X1] :
( ~ relation(X0)
| connected(relation_restriction(X0,X1))
| in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| sK85(relation_restriction(X0,X1)) = sK86(relation_restriction(X0,X1))
| ~ in(sK86(relation_restriction(X0,X1)),relation_field(X0))
| ~ in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(resolution,[],[f2050,f1624]) ).
fof(f2085,plain,
! [X0,X1] :
( ~ relation(X0)
| connected(relation_restriction(X0,X1))
| in(unordered_pair(unordered_pair(sK85(relation_restriction(X0,X1)),sK86(relation_restriction(X0,X1))),unordered_pair(sK85(relation_restriction(X0,X1)),sK85(relation_restriction(X0,X1)))),X0)
| sK85(relation_restriction(X0,X1)) = sK86(relation_restriction(X0,X1))
| ~ in(sK86(relation_restriction(X0,X1)),relation_field(X0))
| ~ in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ connected(X0) ),
inference(duplicate_literal_removal,[],[f2077]) ).
fof(f2090,plain,
! [X0,X1] :
( ~ relation(X0)
| connected(relation_restriction(X0,X1))
| sK85(relation_restriction(X0,X1)) = sK86(relation_restriction(X0,X1))
| ~ in(sK86(relation_restriction(X0,X1)),relation_field(X0))
| ~ in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ connected(X0) ),
inference(forward_subsumption_resolution,[],[f2085,f2049]) ).
fof(f2094,plain,
! [X0,X1] :
( ~ relation(X0)
| connected(relation_restriction(X0,X1))
| sK85(relation_restriction(X0,X1)) = sK86(relation_restriction(X0,X1))
| ~ in(sK85(relation_restriction(X0,X1)),relation_field(X0))
| ~ connected(X0) ),
inference(forward_subsumption_resolution,[],[f2090,f1916]) ).
fof(f2097,plain,
! [X0,X1] :
( connected(relation_restriction(X0,X1))
| ~ relation(X0)
| sK85(relation_restriction(X0,X1)) = sK86(relation_restriction(X0,X1))
| ~ connected(X0) ),
inference(forward_subsumption_resolution,[],[f2094,f1917]) ).
fof(f2099,plain,
( connected(sF123)
| ~ relation(sK106)
| sK85(sF123) = sK86(sF123)
| ~ connected(sK106) ),
inference(superposition,[],[f2097,f1797]) ).
fof(f2100,plain,
( ~ relation(sK106)
| sK85(sF123) = sK86(sF123)
| ~ connected(sK106) ),
inference(forward_subsumption_resolution,[],[f2099,f1798]) ).
fof(f2101,plain,
( sK85(sF123) = sK86(sF123)
| ~ connected(sK106) ),
inference(forward_subsumption_resolution,[],[f2100,f1355]) ).
fof(f2102,plain,
sK85(sF123) = sK86(sF123),
inference(forward_subsumption_resolution,[],[f2101,f1356]) ).
fof(f2110,plain,
( sK85(sF123) != sK85(sF123)
| connected(sF123)
| ~ relation(sF123) ),
inference(superposition,[],[f1230,f2102]) ).
fof(f2113,plain,
( connected(sF123)
| ~ relation(sF123) ),
inference(trivial_inequality_removal,[],[f2110]) ).
fof(f2116,plain,
~ relation(sF123),
inference(forward_subsumption_resolution,[],[f2113,f1798]) ).
fof(f2121,plain,
$false,
inference(forward_subsumption_resolution,[],[f2116,f1829]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU253+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:21:57 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.82/1.79 % (1184181)Detected formulas, will run a generic FOF schedule.
% 5.82/1.79 % (1184186)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=1721687652:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.82/1.79 % (1184191)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2011920417:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.82/1.79 % (1184188)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=3239165447:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.82/1.79 % (1184187)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=963825479:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.82/1.79 % (1184189)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1204059445:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.82/1.79 % (1184190)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1117718452:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.82/1.79 % (1184192)dis-21_1_sil=8000:lcm=predicate:random_seed=2859390202: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)
% 5.82/1.79 % (1184189)Instruction limit reached!
% 5.82/1.79 % (1184189)------------------------------
% 5.82/1.79 % (1184189)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184189)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184189)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184189)Termination reason: Instruction limit
% 5.82/1.79 % (1184189)Termination phase: Saturation
% 5.82/1.79 % (1184189)Time elapsed: 0.068 s
% 5.82/1.79 % (1184189)Peak memory usage: 90 MB
% 5.82/1.79 % (1184189)Instructions burned: 110 (million)
% 5.82/1.79 % (1184190)Instruction limit reached!
% 5.82/1.79 % (1184190)------------------------------
% 5.82/1.79 % (1184190)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184190)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184190)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184190)Termination reason: Instruction limit
% 5.82/1.79 % (1184190)Termination phase: Saturation
% 5.82/1.79 % (1184190)Time elapsed: 0.084 s
% 5.82/1.79 % (1184190)Peak memory usage: 90 MB
% 5.82/1.79 % (1184190)Instructions burned: 119 (million)
% 5.82/1.79 % (1184192)Instruction limit reached!
% 5.82/1.79 % (1184192)------------------------------
% 5.82/1.79 % (1184192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184192)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184192)Termination reason: Instruction limit
% 5.82/1.79 % (1184192)Termination phase: Saturation
% 5.82/1.79 % (1184192)Time elapsed: 0.075 s
% 5.82/1.79 % (1184192)Peak memory usage: 90 MB
% 5.82/1.79 % (1184192)Instructions burned: 131 (million)
% 5.82/1.79 % (1184191)Instruction limit reached!
% 5.82/1.79 % (1184191)------------------------------
% 5.82/1.79 % (1184191)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184191)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184191)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184191)Termination reason: Instruction limit
% 5.82/1.79 % (1184191)Termination phase: Saturation
% 5.82/1.79 % (1184191)Time elapsed: 0.103 s
% 5.82/1.79 % (1184191)Peak memory usage: 90 MB
% 5.82/1.79 % (1184191)Instructions burned: 139 (million)
% 5.82/1.79 % (1184200)lrs+10_1_sil=8000:sp=occurrence:random_seed=1016680461:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 5.82/1.79 % (1184202)lrs+1011_1_sil=32000:sp=occurrence:random_seed=67926206:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 5.82/1.79 % (1184203)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=1679251057:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 5.82/1.79 % (1184201)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3590696652:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 5.82/1.79 % (1184201)Instruction limit reached!
% 5.82/1.79 % (1184201)------------------------------
% 5.82/1.79 % (1184201)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184201)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184201)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184201)Termination reason: Instruction limit
% 5.82/1.79 % (1184201)Termination phase: Saturation
% 5.82/1.79 % (1184201)Time elapsed: 0.084 s
% 5.82/1.79 % (1184201)Peak memory usage: 90 MB
% 5.82/1.79 % (1184201)Instructions burned: 158 (million)
% 5.82/1.79 % (1184203)Instruction limit reached!
% 5.82/1.79 % (1184203)------------------------------
% 5.82/1.79 % (1184203)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184203)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184203)Termination reason: Instruction limit
% 5.82/1.79 % (1184203)Termination phase: Saturation
% 5.82/1.79 % (1184203)Time elapsed: 0.152 s
% 5.82/1.79 % (1184203)Peak memory usage: 92 MB
% 5.82/1.79 % (1184203)Instructions burned: 249 (million)
% 5.82/1.79 % (1184200)Instruction limit reached!
% 5.82/1.79 % (1184200)------------------------------
% 5.82/1.79 % (1184200)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184200)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184200)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184200)Termination reason: Instruction limit
% 5.82/1.79 % (1184200)Termination phase: Saturation
% 5.82/1.79 % (1184200)Time elapsed: 0.187 s
% 5.82/1.79 % (1184200)Peak memory usage: 93 MB
% 5.82/1.79 % (1184200)Instructions burned: 285 (million)
% 5.82/1.79 % (1184208)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=3152770787:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 5.82/1.79 % (1184202)Instruction limit reached!
% 5.82/1.79 % (1184202)------------------------------
% 5.82/1.79 % (1184202)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184202)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184202)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184202)Termination reason: Instruction limit
% 5.82/1.79 % (1184202)Termination phase: Saturation
% 5.82/1.79 % (1184202)Time elapsed: 0.224 s
% 5.82/1.79 % (1184202)Peak memory usage: 93 MB
% 5.82/1.79 % (1184202)Instructions burned: 326 (million)
% 5.82/1.79 % (1184210)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=2807584925:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 5.82/1.79 % (1184209)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1163755696:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 5.82/1.79 % (1184208)Instruction limit reached!
% 5.82/1.79 % (1184208)------------------------------
% 5.82/1.79 % (1184208)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184208)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184208)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184208)Termination reason: Instruction limit
% 5.82/1.79 % (1184208)Termination phase: Saturation
% 5.82/1.79 % (1184208)Time elapsed: 0.103 s
% 5.82/1.79 % (1184208)Peak memory usage: 91 MB
% 5.82/1.79 % (1184208)Instructions burned: 297 (million)
% 5.82/1.79 % (1184186)First to succeed.
% 5.82/1.79 % (1184186)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1184181"
% 5.82/1.79 % (1184212)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1370363424:i=127:av=off:fsr=off:sup=off_2994 on theBenchmark for (2994ds/127Mi)
% 5.82/1.79 % (1184210)Instruction limit reached!
% 5.82/1.79 % (1184210)------------------------------
% 5.82/1.79 % (1184210)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184210)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184210)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184210)Termination reason: Instruction limit
% 5.82/1.79 % (1184210)Termination phase: Saturation
% 5.82/1.79 % (1184210)Time elapsed: 0.071 s
% 5.82/1.79 % (1184210)Peak memory usage: 90 MB
% 5.82/1.79 % (1184210)Instructions burned: 114 (million)
% 5.82/1.79 % (1184215)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4103047849:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 5.82/1.79 % (1184212)Instruction limit reached!
% 5.82/1.79 % (1184212)------------------------------
% 5.82/1.79 % (1184212)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184212)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184212)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184212)Termination reason: Instruction limit
% 5.82/1.79 % (1184212)Termination phase: Saturation
% 5.82/1.79 % (1184212)Time elapsed: 0.066 s
% 5.82/1.79 % (1184212)Peak memory usage: 90 MB
% 5.82/1.79 % (1184212)Instructions burned: 127 (million)
% 5.82/1.79 % (1184215)Instruction limit reached!
% 5.82/1.79 % (1184215)------------------------------
% 5.82/1.79 % (1184215)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.82/1.79 % (1184215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.82/1.79 % (1184215)CaDiCaL version: 2.1.3
% 5.82/1.79 % (1184215)Termination reason: Instruction limit
% 5.82/1.79 % (1184215)Termination phase: Saturation
% 5.82/1.79 % (1184215)Time elapsed: 0.036 s
% 5.82/1.79 % (1184215)Peak memory usage: 89 MB
% 5.82/1.79 % (1184215)Instructions burned: 117 (million)
% 5.82/1.79 % (1184217)lrs+10_1_sil=8000:sp=occurrence:random_seed=3622401180:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 5.82/1.79 % (1184220)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=2649206739:i=5202:ss=axioms:sgt=16_2992 on theBenchmark for (2992ds/5202Mi)
% 5.82/1.79 % (1184219)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=1946055291:i=437:sd=1:aac=none:ss=included_2992 on theBenchmark for (2992ds/437Mi)
% 5.82/1.79 % (1184186)Refutation found. Thanks to Tanya!
% 5.82/1.79 % SZS status Theorem for theBenchmark
% 5.82/1.79 % SZS output start Proof for theBenchmark
% See solution above
% 7.15/1.98 % (1184186)------------------------------
% 7.15/1.98 % (1184186)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 7.15/1.98 % (1184186)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 7.15/1.98 % (1184186)CaDiCaL version: 2.1.3
% 7.15/1.98 % (1184186)Termination reason: Refutation
% 7.15/1.98 % (1184186)Time elapsed: 0.551 s
% 7.15/1.98 % (1184186)Peak memory usage: 134 MB
% 7.15/1.98 % (1184186)Instructions burned: 1211 (million)
% 7.15/1.98 % (1184186)------------------------------
% 7.15/1.98 % (1184186)------------------------------
% 7.15/1.98 % (1184181)Success in time 0.94 s
% 7.15/1.98 % Vampire exiting
%------------------------------------------------------------------------------