%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU254+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:48:01 PM UTC 2026
% Result : Theorem 2.68s 1.28s
% Output : Refutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 113 ( 18 unt; 9 def)
% Number of atoms : 312 ( 2 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 347 ( 148 ~; 149 |; 27 &)
% ( 15 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 14 ( 12 usr; 10 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-2 aty)
% Number of variables : 144 ( 0 sgn 134 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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(f11,axiom,
! [X0,X1] :
( relation(X0)
=> relation(relation_restriction(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k2_wellord1) ).
fof(f20,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(f26,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(f27,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(f29,conjecture,
! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t24_wellord1) ).
fof(f30,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( transitive(X1)
=> transitive(relation_restriction(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f45,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,[],[f20]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( in(X0,relation_restriction(X2,X1))
<=> ( in(X0,X2)
& in(X0,cartesian_product2(X1,X1)) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f49,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(ennf_transformation,[],[f30]) ).
fof(f50,plain,
? [X0,X1] :
( ~ transitive(relation_restriction(X1,X0))
& transitive(X1)
& relation(X1) ),
inference(flattening,[],[f49]) ).
fof(f57,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,[],[f46]) ).
fof(f58,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,[],[f57]) ).
fof(f59,plain,
! [X0] :
( ( ( transitive(X0)
| ( ~ in(ordered_pair(sK1(X0),sK3(X0)),X0)
& in(ordered_pair(sK1(X0),sK2(X0)),X0)
& in(ordered_pair(sK2(X0),sK3(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,[sK1,sK2,sK3]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0)),skolemize(X3,sK3(X0))],[f58]) ).
fof(f65,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,[],[f26]) ).
fof(f66,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,[],[f65]) ).
fof(f67,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,[],[f47]) ).
fof(f68,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,[],[f67]) ).
fof(f69,plain,
( ~ transitive(relation_restriction(sK10,sK9))
& transitive(sK10)
& relation(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10]),skolemize(X0,sK9),skolemize(X1,sK10)],[f50]) ).
fof(f76,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f6]) ).
fof(f78,plain,
! [X0,X1] :
( relation(relation_restriction(X0,X1))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f83,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,[],[f59]) ).
fof(f84,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK2(X0),sK3(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f85,plain,
! [X0] :
( transitive(X0)
| in(ordered_pair(sK1(X0),sK2(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f86,plain,
! [X0] :
( transitive(X0)
| ~ in(ordered_pair(sK1(X0),sK3(X0)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f59]) ).
fof(f96,plain,
! [X2,X3,X0,X1] :
( in(X1,X3)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f97,plain,
! [X2,X3,X0,X1] :
( in(X0,X2)
| ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3)) ),
inference(cnf_transformation,[],[f66]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,cartesian_product2(X1,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_restriction(X2,X1))
| in(X0,X2) ),
inference(cnf_transformation,[],[f68]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,X2)
| ~ in(X0,cartesian_product2(X1,X1))
| in(X0,relation_restriction(X2,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f103,plain,
relation(sK10),
inference(cnf_transformation,[],[f69]) ).
fof(f104,plain,
transitive(sK10),
inference(cnf_transformation,[],[f69]) ).
fof(f105,plain,
~ transitive(relation_restriction(sK10,sK9)),
inference(cnf_transformation,[],[f69]) ).
fof(f112,plain,
! [X0] :
( transitive(X0)
| ~ in(unordered_pair(unordered_pair(sK1(X0),sK3(X0)),singleton(sK1(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f86,f76]) ).
fof(f113,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK1(X0),sK2(X0)),singleton(sK1(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f85,f76]) ).
fof(f114,plain,
! [X0] :
( transitive(X0)
| in(unordered_pair(unordered_pair(sK2(X0),sK3(X0)),singleton(sK2(X0))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f84,f76]) ).
fof(f115,plain,
! [X0,X6,X4,X5] :
( ~ transitive(X0)
| ~ in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| ~ in(unordered_pair(unordered_pair(X5,X6),singleton(X5)),X0)
| in(unordered_pair(unordered_pair(X4,X6),singleton(X4)),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f83,f76,f76,f76]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(definition_unfolding,[],[f98,f76]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(definition_unfolding,[],[f97,f76]) ).
fof(f118,plain,
! [X2,X3,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(definition_unfolding,[],[f96,f76]) ).
fof(f139,plain,
! [X0,X1] :
( ~ in(X0,relation_restriction(sK10,X1))
| in(X0,sK10) ),
inference(resolution,[],[f100,f103]) ).
fof(f147,plain,
! [X0,X1] :
( in(X0,cartesian_product2(X1,X1))
| ~ in(X0,relation_restriction(sK10,X1)) ),
inference(resolution,[],[f99,f103]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_restriction(sK10,X1))
| in(X0,X1) ),
inference(resolution,[],[f117,f147]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X2,X0),singleton(X2)),relation_restriction(sK10,X1))
| in(X0,X1) ),
inference(resolution,[],[f118,f147]) ).
fof(f158,plain,
! [X0,X1] :
( ~ in(X0,cartesian_product2(X1,X1))
| ~ in(X0,sK10)
| in(X0,relation_restriction(sK10,X1)) ),
inference(resolution,[],[f101,f103]) ).
fof(f159,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| ~ relation(relation_restriction(sK10,sK9)) ),
inference(resolution,[],[f112,f105]) ).
fof(f161,definition,
( spl12_1
<=> relation(relation_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f162,plain,
( ~ relation(relation_restriction(sK10,sK9))
| spl12_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl12_2
<=> in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f165,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| spl12_2 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f166,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(avatar_split_clause,[],[f159,f164,f161]) ).
fof(f167,plain,
( ~ relation(sK10)
| spl12_1 ),
inference(resolution,[],[f162,f78]) ).
fof(f168,plain,
( $false
| spl12_1 ),
inference(resolution,[],[f167,f103]) ).
fof(f169,plain,
spl12_1,
inference(avatar_contradiction_clause,[],[f168]) ).
fof(f171,plain,
( in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK2(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| ~ relation(relation_restriction(sK10,sK9)) ),
inference(resolution,[],[f113,f105]) ).
fof(f173,definition,
( spl12_3
<=> in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK2(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f174,plain,
( in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK2(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f175,plain,
( ~ spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f171,f173,f161]) ).
fof(f176,plain,
( in(sK1(relation_restriction(sK10,sK9)),sK9)
| ~ spl12_3 ),
inference(resolution,[],[f174,f151]) ).
fof(f178,plain,
( in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK2(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),sK10)
| ~ spl12_3 ),
inference(resolution,[],[f174,f139]) ).
fof(f185,plain,
( in(unordered_pair(unordered_pair(sK2(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK2(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| ~ relation(relation_restriction(sK10,sK9)) ),
inference(resolution,[],[f114,f105]) ).
fof(f187,definition,
( spl12_4
<=> in(unordered_pair(unordered_pair(sK2(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK2(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9)) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f188,plain,
( in(unordered_pair(unordered_pair(sK2(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK2(relation_restriction(sK10,sK9)))),relation_restriction(sK10,sK9))
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f189,plain,
( ~ spl12_1
| spl12_4 ),
inference(avatar_split_clause,[],[f185,f187,f161]) ).
fof(f192,plain,
( in(unordered_pair(unordered_pair(sK2(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK2(relation_restriction(sK10,sK9)))),sK10)
| ~ spl12_4 ),
inference(resolution,[],[f188,f139]) ).
fof(f200,plain,
( in(sK3(relation_restriction(sK10,sK9)),sK9)
| ~ spl12_4 ),
inference(resolution,[],[f152,f188]) ).
fof(f205,plain,
! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),relation_restriction(sK10,X1))
| ~ in(X2,X1)
| ~ in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK10)
| ~ in(X0,X1) ),
inference(resolution,[],[f116,f158]) ).
fof(f209,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK10)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK10)
| ~ relation(sK10) ),
inference(resolution,[],[f115,f104]) ).
fof(f217,definition,
( spl12_5
<=> relation(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f218,plain,
( ~ relation(sK10)
| spl12_5 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f220,definition,
( spl12_6
<=> ! [X2,X0,X1] :
( ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10)
| in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK10)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK10) ) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f221,plain,
( ! [X2,X0,X1] :
( in(unordered_pair(unordered_pair(X0,X2),singleton(X0)),sK10)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK10)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),sK10) )
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f222,plain,
( ~ spl12_5
| spl12_6 ),
inference(avatar_split_clause,[],[f209,f220,f217]) ).
fof(f223,plain,
( $false
| spl12_5 ),
inference(resolution,[],[f218,f103]) ).
fof(f224,plain,
spl12_5,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f235,plain,
( ~ in(sK3(relation_restriction(sK10,sK9)),sK9)
| ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),sK10)
| ~ in(sK1(relation_restriction(sK10,sK9)),sK9)
| spl12_2 ),
inference(resolution,[],[f205,f165]) ).
fof(f243,definition,
( spl12_7
<=> in(sK1(relation_restriction(sK10,sK9)),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_7])],[avatar_definition]) ).
fof(f244,plain,
( ~ in(sK1(relation_restriction(sK10,sK9)),sK9)
| spl12_7 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f246,definition,
( spl12_8
<=> in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),sK10) ),
introduced(definition,[new_symbols(definition,[spl12_8])],[avatar_definition]) ).
fof(f247,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK3(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),sK10)
| spl12_8 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f249,definition,
( spl12_9
<=> in(sK3(relation_restriction(sK10,sK9)),sK9) ),
introduced(definition,[new_symbols(definition,[spl12_9])],[avatar_definition]) ).
fof(f250,plain,
( ~ in(sK3(relation_restriction(sK10,sK9)),sK9)
| spl12_9 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f251,plain,
( ~ spl12_7
| ~ spl12_8
| ~ spl12_9
| spl12_2 ),
inference(avatar_split_clause,[],[f235,f164,f249,f246,f243]) ).
fof(f252,plain,
( $false
| ~ spl12_3
| spl12_7 ),
inference(resolution,[],[f244,f176]) ).
fof(f253,plain,
( ~ spl12_3
| spl12_7 ),
inference(avatar_contradiction_clause,[],[f252]) ).
fof(f254,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),X0),singleton(sK1(relation_restriction(sK10,sK9)))),sK10)
| ~ in(unordered_pair(unordered_pair(X0,sK3(relation_restriction(sK10,sK9))),singleton(X0)),sK10) )
| ~ spl12_6
| spl12_8 ),
inference(resolution,[],[f247,f221]) ).
fof(f260,plain,
( ~ in(unordered_pair(unordered_pair(sK1(relation_restriction(sK10,sK9)),sK2(relation_restriction(sK10,sK9))),singleton(sK1(relation_restriction(sK10,sK9)))),sK10)
| ~ spl12_4
| ~ spl12_6
| spl12_8 ),
inference(resolution,[],[f254,f192]) ).
fof(f263,plain,
( $false
| ~ spl12_3
| ~ spl12_4
| ~ spl12_6
| spl12_8 ),
inference(resolution,[],[f260,f178]) ).
fof(f265,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_6
| spl12_8 ),
inference(avatar_contradiction_clause,[],[f263]) ).
fof(f266,plain,
( $false
| ~ spl12_4
| spl12_9 ),
inference(resolution,[],[f250,f200]) ).
fof(f267,plain,
( ~ spl12_4
| spl12_9 ),
inference(avatar_contradiction_clause,[],[f266]) ).
cnf(s1,plain,
( ~ spl12_1
| ~ spl12_2 ),
inference(sat_conversion,[],[f166]) ).
cnf(s2,plain,
spl12_1,
inference(sat_conversion,[],[f169]) ).
cnf(s3,plain,
( ~ spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f175]) ).
cnf(s4,plain,
( ~ spl12_1
| spl12_4 ),
inference(sat_conversion,[],[f189]) ).
cnf(s5,plain,
( ~ spl12_5
| spl12_6 ),
inference(sat_conversion,[],[f222]) ).
cnf(s6,plain,
spl12_5,
inference(sat_conversion,[],[f224]) ).
cnf(s7,plain,
( spl12_2
| ~ spl12_7
| ~ spl12_8
| ~ spl12_9 ),
inference(sat_conversion,[],[f251]) ).
cnf(s8,plain,
( ~ spl12_3
| spl12_7 ),
inference(sat_conversion,[],[f253]) ).
cnf(s9,plain,
( ~ spl12_3
| ~ spl12_4
| ~ spl12_6
| spl12_8 ),
inference(sat_conversion,[],[f265]) ).
cnf(s10,plain,
( ~ spl12_4
| spl12_9 ),
inference(sat_conversion,[],[f267]) ).
cnf(s11,plain,
spl12_6,
inference(rat,[],[s5,s6]) ).
cnf(s12,plain,
spl12_4,
inference(rat,[],[s4,s2]) ).
cnf(s13,plain,
spl12_3,
inference(rat,[],[s3,s2]) ).
cnf(s14,plain,
spl12_9,
inference(rat,[],[s10,s12]) ).
cnf(s15,plain,
spl12_8,
inference(rat,[],[s9,s12,s11,s13]) ).
cnf(s16,plain,
spl12_7,
inference(rat,[],[s8,s13]) ).
cnf(s17,plain,
spl12_2,
inference(rat,[],[s7,s14,s15,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s17,s2]) ).
fof(f268,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU254+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n004.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 04:20:37 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 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
% 2.68/1.28 % (4143921)Detected formulas, will run a generic FOF schedule.
% 2.68/1.28 % (4143926)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=1518314298:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.68/1.28 % (4143931)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3056993254:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.68/1.28 % (4143927)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=2797142137:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.68/1.28 % (4143930)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4036169808:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.68/1.28 % (4143929)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=531796155:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.68/1.28 % (4143928)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=3588397794:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.68/1.28 % (4143932)dis-21_1_sil=8000:lcm=predicate:random_seed=72078225:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.68/1.28 % (4143929)Refutation not found, incomplete strategy
% 2.68/1.28 % (4143929)------------------------------
% 2.68/1.28 % (4143929)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (4143929)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (4143929)CaDiCaL version: 2.1.3
% 2.68/1.28 % (4143929)Termination reason: Refutation not found, incomplete strategy
% 2.68/1.28 % (4143929)Time elapsed: 0.001 s
% 2.68/1.28 % (4143929)Peak memory usage: 87 MB
% 2.68/1.28 % (4143932)First to succeed.
% 2.68/1.28 % (4143932)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4143921"
% 2.68/1.28 % (4143930)Instruction limit reached!
% 2.68/1.28 % (4143930)------------------------------
% 2.68/1.28 % (4143930)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (4143930)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (4143930)CaDiCaL version: 2.1.3
% 2.68/1.28 % (4143930)Termination reason: Instruction limit
% 2.68/1.28 % (4143930)Termination phase: Saturation
% 2.68/1.28 % (4143930)Time elapsed: 0.049 s
% 2.68/1.28 % (4143930)Peak memory usage: 87 MB
% 2.68/1.28 % (4143930)Instructions burned: 121 (million)
% 2.68/1.28 % (4143931)Instruction limit reached!
% 2.68/1.28 % (4143931)------------------------------
% 2.68/1.28 % (4143931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.28 % (4143931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.28 % (4143931)CaDiCaL version: 2.1.3
% 2.68/1.28 % (4143931)Termination reason: Instruction limit
% 2.68/1.28 % (4143931)Termination phase: Saturation
% 2.68/1.28 % (4143931)Time elapsed: 0.085 s
% 2.68/1.28 % (4143931)Peak memory usage: 89 MB
% 2.68/1.28 % (4143931)Instructions burned: 140 (million)
% 2.68/1.28 % (4143940)lrs+10_1_sil=8000:sp=occurrence:random_seed=654814389:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.68/1.28 % (4143940)Also succeeded, but the first one will report.
% 2.68/1.28 % (4143929)------------------------------
% 2.68/1.28 % (4143929)------------------------------
% 2.68/1.28 % (4143932)Refutation found. Thanks to Tanya!
% 2.68/1.28 % SZS status Theorem for theBenchmark
% 2.68/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.61/1.48 % (4143932)------------------------------
% 3.61/1.48 % (4143932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.61/1.48 % (4143932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.61/1.48 % (4143932)CaDiCaL version: 2.1.3
% 3.61/1.48 % (4143932)Termination reason: Refutation
% 3.61/1.48 % (4143932)Time elapsed: 0.007 s
% 3.61/1.48 % (4143932)Peak memory usage: 89 MB
% 3.61/1.48 % (4143932)Instructions burned: 8 (million)
% 3.61/1.48 % (4143932)------------------------------
% 3.61/1.48 % (4143932)------------------------------
% 3.61/1.48 % (4143921)Success in time 0.433 s
% 3.61/1.48 % Vampire exiting
%------------------------------------------------------------------------------