%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU258+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 : n017.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 12:48:03 PM UTC 2026
% Result : Theorem 8.04s 2.16s
% Output : Refutation 9.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 16
% Syntax : Number of formulae : 97 ( 26 unt; 3 def)
% Number of atoms : 318 ( 27 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 361 ( 140 ~; 136 |; 62 &)
% ( 10 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 160 ( 152 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f14,axiom,
! [X0,X1] :
( X0 = X1
<=> ( subset(X0,X1)
& subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_xboole_0) ).
fof(f42,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f51,axiom,
! [X0] :
( relation(X0)
=> ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_wellord1) ).
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(f142,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_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(f217,axiom,
! [X0,X1] :
( relation(X1)
=> ( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X0)),X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t20_wellord1) ).
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/sandbox/benchmark/theBenchmark.p',t30_relat_1) ).
fof(f252,conjecture,
! [X0,X1] :
( relation(X1)
=> ( ( well_ordering(X1)
& subset(X0,relation_field(X1)) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_wellord1) ).
fof(f253,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( ( well_ordering(X1)
& subset(X0,relation_field(X1)) )
=> relation_field(relation_restriction(X1,X0)) = X0 ) ),
inference(negated_conjecture,[status(cth)],[f252]) ).
fof(f294,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t69_enumset1) ).
fof(f366,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f373,plain,
! [X0] :
( ( well_ordering(X0)
<=> ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f396,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f444,plain,
! [X0] :
( ( reflexive(X0)
<=> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f142]) ).
fof(f497,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(f513,plain,
! [X0,X1] :
( ( subset(relation_field(relation_restriction(X1,X0)),relation_field(X1))
& subset(relation_field(relation_restriction(X1,X0)),X0) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f217]) ).
fof(f543,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(f544,plain,
! [X0,X1,X2] :
( ( in(X0,relation_field(X2))
& in(X1,relation_field(X2)) )
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(flattening,[],[f543]) ).
fof(f559,plain,
? [X0,X1] :
( relation_field(relation_restriction(X1,X0)) != X0
& well_ordering(X1)
& subset(X0,relation_field(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f253]) ).
fof(f560,plain,
? [X0,X1] :
( relation_field(relation_restriction(X1,X0)) != X0
& well_ordering(X1)
& subset(X0,relation_field(X1))
& relation(X1) ),
inference(flattening,[],[f559]) ).
fof(f640,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(nnf_transformation,[],[f14]) ).
fof(f641,plain,
! [X0,X1] :
( ( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) )
& ( ( subset(X0,X1)
& subset(X1,X0) )
| X0 != X1 ) ),
inference(flattening,[],[f640]) ).
fof(f719,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f366]) ).
fof(f720,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f719]) ).
fof(f721,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK45(X0,X1),X1)
& in(sK45(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(X2,sK45(X0,X1))],[f720]) ).
fof(f741,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f373]) ).
fof(f742,plain,
! [X0] :
( ( ( well_ordering(X0)
| ~ reflexive(X0)
| ~ transitive(X0)
| ~ antisymmetric(X0)
| ~ connected(X0)
| ~ well_founded_relation(X0) )
& ( ( reflexive(X0)
& transitive(X0)
& antisymmetric(X0)
& connected(X0)
& well_founded_relation(X0) )
| ~ well_ordering(X0) ) )
| ~ relation(X0) ),
inference(flattening,[],[f741]) ).
fof(f778,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f444]) ).
fof(f779,plain,
! [X0] :
( ( ( reflexive(X0)
| ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(rectify,[],[f778]) ).
fof(f780,plain,
! [X0] :
( ( ( reflexive(X0)
| ( ~ in(ordered_pair(sK79(X0),sK79(X0)),X0)
& in(sK79(X0),relation_field(X0)) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(X1,sK79(X0))],[f779]) ).
fof(f814,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(f815,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,[],[f814]) ).
fof(f825,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,[],[f497]) ).
fof(f826,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,[],[f825]) ).
fof(f842,plain,
( sK109 != relation_field(relation_restriction(sK110,sK109))
& well_ordering(sK110)
& subset(sK109,relation_field(sK110))
& relation(sK110) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK109,sK110]),skolemize(X0,sK109),skolemize(X1,sK110)],[f560]) ).
fof(f891,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f9]) ).
fof(f903,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[],[f641]) ).
fof(f1032,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f721]) ).
fof(f1033,plain,
! [X0,X1] :
( in(sK45(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f721]) ).
fof(f1034,plain,
! [X0,X1] :
( ~ in(sK45(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f721]) ).
fof(f1074,plain,
! [X0] :
( ~ well_ordering(X0)
| reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f742]) ).
fof(f1093,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f56]) ).
fof(f1146,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f396]) ).
fof(f1220,plain,
! [X2,X0] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f780]) ).
fof(f1307,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f815]) ).
fof(f1343,plain,
! [X2,X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,X2)
| in(X0,relation_restriction(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f826]) ).
fof(f1358,plain,
! [X0,X1] :
( subset(relation_field(relation_restriction(X1,X0)),X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f513]) ).
fof(f1383,plain,
! [X2,X0,X1] :
( in(X1,relation_field(X2))
| ~ in(ordered_pair(X0,X1),X2)
| ~ relation(X2) ),
inference(cnf_transformation,[],[f544]) ).
fof(f1412,plain,
relation(sK110),
inference(cnf_transformation,[],[f842]) ).
fof(f1413,plain,
subset(sK109,relation_field(sK110)),
inference(cnf_transformation,[],[f842]) ).
fof(f1414,plain,
well_ordering(sK110),
inference(cnf_transformation,[],[f842]) ).
fof(f1415,plain,
sK109 != relation_field(relation_restriction(sK110,sK109)),
inference(cnf_transformation,[],[f842]) ).
fof(f1489,plain,
! [X0] : singleton(X0) = unordered_pair(X0,X0),
inference(cnf_transformation,[],[f294]) ).
fof(f1527,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),
inference(definition_unfolding,[],[f1093,f1489]) ).
fof(f1628,plain,
! [X2,X0] :
( in(unordered_pair(unordered_pair(X2,X2),unordered_pair(X2,X2)),X0)
| ~ in(X2,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f1220,f1527]) ).
fof(f1652,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,[],[f1307,f1527]) ).
fof(f1671,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,[],[f1383,f1527]) ).
fof(f1817,definition,
sF123 = relation_restriction(sK110,sK109),
introduced(definition,[new_symbols(definition,[sF123])],[function_definition]) ).
fof(f1818,plain,
relation_restriction(sK110,sK109) = sF123,
inference(reorient_equations,[],[f1817]) ).
fof(f1819,definition,
sF124 = relation_field(sF123),
introduced(definition,[new_symbols(definition,[sF124])],[function_definition]) ).
fof(f1820,plain,
relation_field(sF123) = sF124,
inference(reorient_equations,[],[f1819]) ).
fof(f1821,plain,
sK109 != sF124,
inference(definition_folding,[],[f1415,f1820,f1818]) ).
fof(f1822,definition,
sF125 = relation_field(sK110),
introduced(definition,[new_symbols(definition,[sF125])],[function_definition]) ).
fof(f1823,plain,
relation_field(sK110) = sF125,
inference(reorient_equations,[],[f1822]) ).
fof(f1824,plain,
subset(sK109,sF125),
inference(definition_folding,[],[f1413,f1823]) ).
fof(f1864,plain,
( relation(sF123)
| ~ relation(sK110) ),
inference(superposition,[],[f1146,f1818]) ).
fof(f1865,plain,
relation(sF123),
inference(forward_subsumption_resolution,[],[f1864,f1412]) ).
fof(f1866,plain,
( subset(relation_field(sF123),sK109)
| ~ relation(sK110) ),
inference(superposition,[],[f1358,f1818]) ).
fof(f1867,plain,
subset(relation_field(sF123),sK109),
inference(forward_subsumption_resolution,[],[f1866,f1412]) ).
fof(f1868,plain,
subset(sF124,sK109),
inference(forward_demodulation,[],[f1867,f1820]) ).
fof(f1883,plain,
( ~ subset(sK109,sF124)
| sK109 = sF124 ),
inference(resolution,[],[f903,f1868]) ).
fof(f1894,plain,
~ subset(sK109,sF124),
inference(forward_subsumption_resolution,[],[f1883,f1821]) ).
fof(f1911,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X1,X1)),X2)
| in(X0,relation_field(X2))
| ~ relation(X2) ),
inference(superposition,[],[f1671,f891]) ).
fof(f1918,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X1,X0)),X2)
| in(X1,relation_field(X2))
| ~ relation(X2) ),
inference(superposition,[],[f1911,f891]) ).
fof(f1962,plain,
( reflexive(sK110)
| ~ relation(sK110) ),
inference(resolution,[],[f1074,f1414]) ).
fof(f1967,plain,
reflexive(sK110),
inference(forward_subsumption_resolution,[],[f1962,f1412]) ).
fof(f1968,plain,
! [X0] :
( ~ in(X0,sK109)
| in(X0,sF125) ),
inference(resolution,[],[f1032,f1824]) ).
fof(f2768,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,[],[f1652,f1343]) ).
fof(f2787,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF123)
| ~ in(X1,sK109)
| ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK110)
| ~ in(X0,sK109)
| ~ relation(sK110) ),
inference(superposition,[],[f2768,f1818]) ).
fof(f2796,plain,
! [X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sK110)
| ~ in(X1,sK109)
| in(unordered_pair(unordered_pair(X0,X1),unordered_pair(X0,X0)),sF123)
| ~ in(X0,sK109) ),
inference(forward_subsumption_resolution,[],[f2787,f1412]) ).
fof(f2823,plain,
! [X0] :
( ~ in(X0,sK109)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123)
| ~ in(X0,sK109)
| ~ in(X0,relation_field(sK110))
| ~ reflexive(sK110)
| ~ relation(sK110) ),
inference(resolution,[],[f2796,f1628]) ).
fof(f2830,plain,
! [X0] :
( ~ in(X0,sK109)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123)
| ~ in(X0,relation_field(sK110))
| ~ reflexive(sK110)
| ~ relation(sK110) ),
inference(duplicate_literal_removal,[],[f2823]) ).
fof(f2837,plain,
! [X0] :
( ~ in(X0,sK109)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123)
| ~ in(X0,relation_field(sK110))
| ~ relation(sK110) ),
inference(forward_subsumption_resolution,[],[f2830,f1967]) ).
fof(f2847,plain,
! [X0] :
( ~ in(X0,sK109)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123)
| ~ in(X0,relation_field(sK110)) ),
inference(forward_subsumption_resolution,[],[f2837,f1412]) ).
fof(f2856,plain,
! [X0] :
( ~ in(X0,sF125)
| ~ in(X0,sK109)
| in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123) ),
inference(forward_demodulation,[],[f2847,f1823]) ).
fof(f2861,plain,
! [X0] :
( in(unordered_pair(unordered_pair(X0,X0),unordered_pair(X0,X0)),sF123)
| ~ in(X0,sK109) ),
inference(forward_subsumption_resolution,[],[f2856,f1968]) ).
fof(f2881,plain,
! [X0] :
( ~ in(X0,sK109)
| in(X0,relation_field(sF123))
| ~ relation(sF123) ),
inference(resolution,[],[f2861,f1918]) ).
fof(f2883,plain,
! [X0] :
( ~ in(X0,sK109)
| in(X0,relation_field(sF123)) ),
inference(forward_subsumption_resolution,[],[f2881,f1865]) ).
fof(f2891,plain,
! [X0] :
( ~ in(X0,sK109)
| in(X0,sF124) ),
inference(forward_demodulation,[],[f2883,f1820]) ).
fof(f2900,plain,
! [X0] :
( in(sK45(sK109,X0),sF124)
| subset(sK109,X0) ),
inference(resolution,[],[f2891,f1033]) ).
fof(f3150,plain,
( subset(sK109,sF124)
| subset(sK109,sF124) ),
inference(resolution,[],[f2900,f1034]) ).
fof(f3153,plain,
subset(sK109,sF124),
inference(duplicate_literal_removal,[],[f3150]) ).
fof(f3154,plain,
$false,
inference(forward_subsumption_resolution,[],[f3153,f1894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU258+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n017.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:16:51 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 8.04/2.16 % (3196082)Detected formulas, will run a generic FOF schedule.
% 8.04/2.16 % (3196090)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2804021351:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 8.04/2.16 % (3196090)Instruction limit reached!
% 8.04/2.16 % (3196090)------------------------------
% 8.04/2.16 % (3196090)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196090)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196090)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196090)Termination reason: Instruction limit
% 8.04/2.16 % (3196090)Termination phase: Saturation
% 8.04/2.16 % (3196090)Time elapsed: 0.039 s
% 8.04/2.16 % (3196090)Peak memory usage: 90 MB
% 8.04/2.16 % (3196090)Instructions burned: 110 (million)
% 8.04/2.16 % (3196093)dis-21_1_sil=8000:lcm=predicate:random_seed=2143005095: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)
% 8.04/2.16 % (3196091)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=184176726:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 8.04/2.16 % (3196092)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2481204552:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 8.04/2.16 % (3196089)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=3854738630:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 8.04/2.16 % (3196088)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=2598276391:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 8.04/2.16 % (3196087)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=3506565484:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 8.04/2.16 % (3196093)Instruction limit reached!
% 8.04/2.16 % (3196093)------------------------------
% 8.04/2.16 % (3196093)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196093)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196093)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196093)Termination reason: Instruction limit
% 8.04/2.16 % (3196093)Termination phase: Saturation
% 8.04/2.16 % (3196093)Time elapsed: 0.078 s
% 8.04/2.16 % (3196093)Peak memory usage: 90 MB
% 8.04/2.16 % (3196093)Instructions burned: 129 (million)
% 8.04/2.16 % (3196091)Instruction limit reached!
% 8.04/2.16 % (3196091)------------------------------
% 8.04/2.16 % (3196091)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196091)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196091)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196091)Termination reason: Instruction limit
% 8.04/2.16 % (3196091)Termination phase: Saturation
% 8.04/2.16 % (3196091)Time elapsed: 0.082 s
% 8.04/2.16 % (3196091)Peak memory usage: 89 MB
% 8.04/2.16 % (3196091)Instructions burned: 120 (million)
% 8.04/2.16 % (3196092)Instruction limit reached!
% 8.04/2.16 % (3196092)------------------------------
% 8.04/2.16 % (3196092)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196092)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196092)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196092)Termination reason: Instruction limit
% 8.04/2.16 % (3196092)Termination phase: Saturation
% 8.04/2.16 % (3196092)Time elapsed: 0.103 s
% 8.04/2.16 % (3196092)Peak memory usage: 91 MB
% 8.04/2.16 % (3196092)Instructions burned: 139 (million)
% 8.04/2.16 % (3196101)lrs+10_1_sil=8000:sp=occurrence:random_seed=3537696893:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 8.04/2.16 % (3196101)Instruction limit reached!
% 8.04/2.16 % (3196101)------------------------------
% 8.04/2.16 % (3196101)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196101)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196101)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196101)Termination reason: Instruction limit
% 8.04/2.16 % (3196101)Termination phase: Saturation
% 8.04/2.16 % (3196101)Time elapsed: 0.104 s
% 8.04/2.16 % (3196101)Peak memory usage: 93 MB
% 8.04/2.16 % (3196101)Instructions burned: 286 (million)
% 8.04/2.16 % (3196103)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2356093524:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 8.04/2.16 % (3196102)lrs+10_1_sil=32000:urr=on:br=off:random_seed=665667794:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 8.04/2.16 % (3196104)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=94937611:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 8.04/2.16 % (3196102)Instruction limit reached!
% 8.04/2.16 % (3196102)------------------------------
% 8.04/2.16 % (3196102)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196102)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196102)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196102)Termination reason: Instruction limit
% 8.04/2.16 % (3196102)Termination phase: Saturation
% 8.04/2.16 % (3196102)Time elapsed: 0.084 s
% 8.04/2.16 % (3196102)Peak memory usage: 89 MB
% 8.04/2.16 % (3196102)Instructions burned: 158 (million)
% 8.04/2.16 % (3196106)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2056386669:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 8.04/2.16 % (3196104)Instruction limit reached!
% 8.04/2.16 % (3196104)------------------------------
% 8.04/2.16 % (3196104)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196104)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196104)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196104)Termination reason: Instruction limit
% 8.04/2.16 % (3196104)Termination phase: Saturation
% 8.04/2.16 % (3196104)Time elapsed: 0.156 s
% 8.04/2.16 % (3196104)Peak memory usage: 93 MB
% 8.04/2.16 % (3196104)Instructions burned: 248 (million)
% 8.04/2.16 % (3196106)Instruction limit reached!
% 8.04/2.16 % (3196106)------------------------------
% 8.04/2.16 % (3196106)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196106)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196106)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196106)Termination reason: Instruction limit
% 8.04/2.16 % (3196106)Termination phase: Saturation
% 8.04/2.16 % (3196106)Time elapsed: 0.102 s
% 8.04/2.16 % (3196106)Peak memory usage: 91 MB
% 8.04/2.16 % (3196106)Instructions burned: 297 (million)
% 8.04/2.16 % (3196103)Instruction limit reached!
% 8.04/2.16 % (3196103)------------------------------
% 8.04/2.16 % (3196103)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196103)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196103)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196103)Termination reason: Instruction limit
% 8.04/2.16 % (3196103)Termination phase: Saturation
% 8.04/2.16 % (3196103)Time elapsed: 0.231 s
% 8.04/2.16 % (3196103)Peak memory usage: 93 MB
% 8.04/2.16 % (3196103)Instructions burned: 325 (million)
% 8.04/2.16 % (3196110)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=4256558727:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 8.04/2.16 % (3196113)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=3168307049:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 8.04/2.16 % (3196112)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=974089186:cts=off:i=113:fsr=off:ss=included:sgt=4_2993 on theBenchmark for (2993ds/113Mi)
% 8.04/2.16 % (3196113)Instruction limit reached!
% 8.04/2.16 % (3196113)------------------------------
% 8.04/2.16 % (3196113)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196113)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196113)Termination reason: Instruction limit
% 8.04/2.16 % (3196113)Termination phase: Saturation
% 8.04/2.16 % (3196113)Time elapsed: 0.036 s
% 8.04/2.16 % (3196113)Peak memory usage: 90 MB
% 8.04/2.16 % (3196113)Instructions burned: 130 (million)
% 8.04/2.16 % (3196115)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=3649140767:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2993 on theBenchmark for (2993ds/114Mi)
% 8.04/2.16 % (3196112)Instruction limit reached!
% 8.04/2.16 % (3196112)------------------------------
% 8.04/2.16 % (3196112)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196112)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196112)Termination reason: Instruction limit
% 8.04/2.16 % (3196112)Termination phase: Saturation
% 8.04/2.16 % (3196112)Time elapsed: 0.072 s
% 8.04/2.16 % (3196112)Peak memory usage: 90 MB
% 8.04/2.16 % (3196112)Instructions burned: 114 (million)
% 8.04/2.16 % (3196115)Instruction limit reached!
% 8.04/2.16 % (3196115)------------------------------
% 8.04/2.16 % (3196115)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196115)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196115)Termination reason: Instruction limit
% 8.04/2.16 % (3196115)Termination phase: Saturation
% 8.04/2.16 % (3196115)Time elapsed: 0.073 s
% 8.04/2.16 % (3196115)Peak memory usage: 89 MB
% 8.04/2.16 % (3196115)Instructions burned: 115 (million)
% 8.04/2.16 % (3196118)lrs+10_1_sil=8000:sp=occurrence:random_seed=1876209606:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2992 on theBenchmark for (2992ds/907Mi)
% 8.04/2.16 % (3196120)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=3911144323:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 8.04/2.16 % (3196087)First to succeed.
% 8.04/2.16 % (3196087)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3196082"
% 8.04/2.16 % (3196121)lrs-1002_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:npcc=on:random_seed=549646598:i=5202:ss=axioms:sgt=16_2991 on theBenchmark for (2991ds/5202Mi)
% 8.04/2.16 % (3196118)Instruction limit reached!
% 8.04/2.16 % (3196118)------------------------------
% 8.04/2.16 % (3196118)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196118)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196118)Termination reason: Instruction limit
% 8.04/2.16 % (3196118)Termination phase: Saturation
% 8.04/2.16 % (3196118)Time elapsed: 0.309 s
% 8.04/2.16 % (3196118)Peak memory usage: 102 MB
% 8.04/2.16 % (3196118)Instructions burned: 907 (million)
% 8.04/2.16 % (3196120)Instruction limit reached!
% 8.04/2.16 % (3196120)------------------------------
% 8.04/2.16 % (3196120)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.04/2.16 % (3196120)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.04/2.16 % (3196120)CaDiCaL version: 2.1.3
% 8.04/2.16 % (3196120)Termination reason: Instruction limit
% 8.04/2.16 % (3196120)Termination phase: Saturation
% 8.04/2.16 % (3196120)Time elapsed: 0.268 s
% 8.04/2.16 % (3196120)Peak memory usage: 93 MB
% 8.04/2.16 % (3196120)Instructions burned: 438 (million)
% 8.04/2.16 % (3196087)Refutation found. Thanks to Tanya!
% 8.04/2.16 % SZS status Theorem for theBenchmark
% 8.04/2.16 % SZS output start Proof for theBenchmark
% See solution above
% 9.68/2.36 % (3196087)------------------------------
% 9.68/2.36 % (3196087)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.68/2.36 % (3196087)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.68/2.36 % (3196087)CaDiCaL version: 2.1.3
% 9.68/2.36 % (3196087)Termination reason: Refutation
% 9.68/2.36 % (3196087)Time elapsed: 0.850 s
% 9.68/2.36 % (3196087)Peak memory usage: 137 MB
% 9.68/2.36 % (3196087)Instructions burned: 1298 (million)
% 9.68/2.36 % (3196087)------------------------------
% 9.68/2.36 % (3196087)------------------------------
% 9.68/2.36 % (3196082)Success in time 1.291 s
% 9.68/2.36 % Vampire exiting
%------------------------------------------------------------------------------