%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 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 12:47:08 PM UTC 2026
% Result : Theorem 4.25s 1.52s
% Output : Refutation 5.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 14
% Syntax : Number of formulae : 109 ( 22 unt; 11 def)
% Number of atoms : 399 ( 97 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 498 ( 208 ~; 218 |; 48 &)
% ( 19 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 109 ( 0 sgn 94 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( X1 = singleton(X0)
<=> ! [X2] :
( in(X2,X1)
<=> X2 = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_tarski) ).
fof(f26,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f27,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f26]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f54,plain,
? [X0,X1] :
( relation_image(X1,singleton(X0)) != singleton(apply(X1,X0))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f27]) ).
fof(f55,plain,
? [X0,X1] :
( relation_image(X1,singleton(X0)) != singleton(apply(X1,X0))
& in(X0,relation_dom(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f54]) ).
fof(f67,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 ) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& in(X4,X1)
& X3 = apply(X0,X4) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f68,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != X3 )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(X5,relation_dom(X0))
& in(X5,X1)
& apply(X0,X5) = X3 )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ? [X8] :
( in(X8,relation_dom(X0))
& in(X8,X1)
& apply(X0,X8) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f67]) ).
fof(f69,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(X4,relation_dom(X0))
| ~ in(X4,X1)
| apply(X0,X4) != sK0(X0,X1,X2) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(sK1(X0,X1,X2),relation_dom(X0))
& in(sK1(X0,X1,X2),X1)
& sK0(X0,X1,X2) = apply(X0,sK1(X0,X1,X2)) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6 ) )
& ( ( in(sK2(X0,X1,X6),relation_dom(X0))
& in(sK2(X0,X1,X6),X1)
& apply(X0,sK2(X0,X1,X6)) = X6 )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X3,sK0(X0,X1,X2)),skolemize(X5,sK1(X0,X1,X2)),skolemize(X8,sK2(X0,X1,X6))],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| X0 != X2 )
& ( X2 = X0
| ~ in(X2,X1) ) )
| singleton(X0) != X1 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f71,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ? [X2] :
( ( X0 != X2
| ~ in(X2,X1) )
& ( X2 = X0
| in(X2,X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1] :
( ( X1 = singleton(X0)
| ( ( sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) )
& ( sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ) ) )
& ( ! [X3] :
( ( in(X3,X1)
| X0 != X3 )
& ( X0 = X3
| ~ in(X3,X1) ) )
| singleton(X0) != X1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f71]) ).
fof(f84,plain,
( relation_image(sK16,singleton(sK15)) != singleton(apply(sK16,sK15))
& in(sK15,relation_dom(sK16))
& relation(sK16)
& function(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16]),skolemize(X0,sK15),skolemize(X1,sK16)],[f55]) ).
fof(f92,plain,
! [X2,X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f93,plain,
! [X2,X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,X2)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f95,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| apply(X0,X7) != X6
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f69]) ).
fof(f100,plain,
! [X3,X0,X1] :
( X0 = X3
| ~ in(X3,X1)
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X3,X0,X1] :
( in(X3,X1)
| X0 != X3
| singleton(X0) != X1 ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK3(X0,X1) = X0
| in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f103,plain,
! [X0,X1] :
( singleton(X0) = X1
| sK3(X0,X1) != X0
| ~ in(sK3(X0,X1),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f134,plain,
function(sK16),
inference(cnf_transformation,[],[f84]) ).
fof(f135,plain,
relation(sK16),
inference(cnf_transformation,[],[f84]) ).
fof(f136,plain,
in(sK15,relation_dom(sK16)),
inference(cnf_transformation,[],[f84]) ).
fof(f137,plain,
relation_image(sK16,singleton(sK15)) != singleton(apply(sK16,sK15)),
inference(cnf_transformation,[],[f84]) ).
fof(f148,plain,
! [X2,X0,X1,X7] :
( in(apply(X0,X7),X2)
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f95]) ).
fof(f149,plain,
! [X0,X1,X7] :
( in(apply(X0,X7),relation_image(X0,X1))
| ~ in(X7,relation_dom(X0))
| ~ in(X7,X1)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f151,plain,
! [X0,X1,X6] :
( in(sK2(X0,X1,X6),X1)
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f152,plain,
! [X0,X1,X6] :
( apply(X0,sK2(X0,X1,X6)) = X6
| ~ in(X6,relation_image(X0,X1))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f92]) ).
fof(f153,plain,
! [X3,X1] :
( in(X3,X1)
| singleton(X3) != X1 ),
inference(equality_resolution,[],[f101]) ).
fof(f154,plain,
! [X3] : in(X3,singleton(X3)),
inference(equality_resolution,[],[f153]) ).
fof(f155,plain,
! [X3,X0] :
( X0 = X3
| ~ in(X3,singleton(X0)) ),
inference(equality_resolution,[],[f100]) ).
fof(f159,definition,
( spl19_1
<=> relation(sK16) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f161,plain,
( relation(sK16)
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f162,plain,
spl19_1,
inference(avatar_split_clause,[],[f135,f159]) ).
fof(f181,definition,
( spl19_2
<=> function(sK16) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f183,plain,
( function(sK16)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f184,plain,
spl19_2,
inference(avatar_split_clause,[],[f134,f181]) ).
fof(f194,definition,
( spl19_3
<=> in(sK15,relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f196,plain,
( in(sK15,relation_dom(sK16))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f197,plain,
spl19_3,
inference(avatar_split_clause,[],[f136,f194]) ).
fof(f213,definition,
( spl19_4
<=> relation_image(sK16,singleton(sK15)) = singleton(apply(sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f215,plain,
( relation_image(sK16,singleton(sK15)) != singleton(apply(sK16,sK15))
| spl19_4 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f216,plain,
~ spl19_4,
inference(avatar_split_clause,[],[f137,f213]) ).
fof(f218,plain,
( ! [X0] :
( relation_image(sK16,singleton(sK15)) != X0
| apply(sK16,sK15) != sK3(apply(sK16,sK15),X0)
| ~ in(sK3(apply(sK16,sK15),X0),X0) )
| spl19_4 ),
inference(superposition,[],[f215,f103]) ).
fof(f338,definition,
( spl19_11
<=> ! [X0] :
( relation_image(sK16,singleton(sK15)) != X0
| apply(sK16,sK15) != sK3(apply(sK16,sK15),X0)
| ~ in(sK3(apply(sK16,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f339,plain,
( ! [X0] :
( apply(sK16,sK15) != sK3(apply(sK16,sK15),X0)
| relation_image(sK16,singleton(sK15)) != X0
| ~ in(sK3(apply(sK16,sK15),X0),X0) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f340,plain,
( spl19_11
| spl19_4 ),
inference(avatar_split_clause,[],[f218,f213,f338]) ).
fof(f341,plain,
( ! [X0] :
( apply(sK16,sK15) != apply(sK16,sK15)
| relation_image(sK16,singleton(sK15)) != X0
| ~ in(apply(sK16,sK15),X0)
| singleton(apply(sK16,sK15)) = X0
| in(sK3(apply(sK16,sK15),X0),X0) )
| ~ spl19_11 ),
inference(superposition,[],[f339,f102]) ).
fof(f342,plain,
( ! [X0] :
( relation_image(sK16,singleton(sK15)) != X0
| ~ in(apply(sK16,sK15),X0)
| singleton(apply(sK16,sK15)) = X0
| in(sK3(apply(sK16,sK15),X0),X0) )
| ~ spl19_11 ),
inference(trivial_inequality_removal,[],[f341]) ).
fof(f384,definition,
( spl19_15
<=> ! [X0] :
( relation_image(sK16,singleton(sK15)) != X0
| ~ in(apply(sK16,sK15),X0)
| singleton(apply(sK16,sK15)) = X0
| in(sK3(apply(sK16,sK15),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_15])],[avatar_definition]) ).
fof(f385,plain,
( ! [X0] :
( relation_image(sK16,singleton(sK15)) != X0
| ~ in(apply(sK16,sK15),X0)
| singleton(apply(sK16,sK15)) = X0
| in(sK3(apply(sK16,sK15),X0),X0) )
| ~ spl19_15 ),
inference(avatar_component_clause,[],[f384]) ).
fof(f386,plain,
( spl19_15
| ~ spl19_11 ),
inference(avatar_split_clause,[],[f342,f338,f384]) ).
fof(f393,plain,
( ~ in(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| relation_image(sK16,singleton(sK15)) = singleton(apply(sK16,sK15))
| in(sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))),relation_image(sK16,singleton(sK15)))
| ~ spl19_15 ),
inference(equality_resolution,[],[f385]) ).
fof(f394,plain,
( ~ in(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| in(sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))),relation_image(sK16,singleton(sK15)))
| spl19_4
| ~ spl19_15 ),
inference(forward_subsumption_resolution,[],[f393,f215]) ).
fof(f404,definition,
( spl19_16
<=> in(sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))),relation_image(sK16,singleton(sK15))) ),
introduced(definition,[new_symbols(definition,[spl19_16])],[avatar_definition]) ).
fof(f406,plain,
( in(sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))),relation_image(sK16,singleton(sK15)))
| ~ spl19_16 ),
inference(avatar_component_clause,[],[f404]) ).
fof(f408,definition,
( spl19_17
<=> in(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) ),
introduced(definition,[new_symbols(definition,[spl19_17])],[avatar_definition]) ).
fof(f410,plain,
( ~ in(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| spl19_17 ),
inference(avatar_component_clause,[],[f408]) ).
fof(f411,plain,
( spl19_16
| ~ spl19_17
| spl19_4
| ~ spl19_15 ),
inference(avatar_split_clause,[],[f394,f384,f213,f408,f404]) ).
fof(f414,plain,
( ~ in(sK15,relation_dom(sK16))
| ~ in(sK15,singleton(sK15))
| ~ relation(sK16)
| ~ function(sK16)
| spl19_17 ),
inference(resolution,[],[f410,f149]) ).
fof(f426,plain,
( ~ in(sK15,singleton(sK15))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl19_3
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f414,f196]) ).
fof(f434,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ spl19_3
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f426,f154]) ).
fof(f437,plain,
( ~ function(sK16)
| ~ spl19_1
| ~ spl19_3
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f434,f161]) ).
fof(f438,plain,
( $false
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| spl19_17 ),
inference(forward_subsumption_resolution,[],[f437,f183]) ).
fof(f439,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| spl19_17 ),
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f440,plain,
( relation_image(sK16,singleton(sK15)) = singleton(apply(sK16,sK15))
| apply(sK16,sK15) != sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| ~ spl19_16 ),
inference(resolution,[],[f406,f103]) ).
fof(f441,plain,
( sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) = apply(sK16,sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl19_16 ),
inference(resolution,[],[f406,f152]) ).
fof(f442,plain,
( in(sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))),singleton(sK15))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl19_16 ),
inference(resolution,[],[f406,f151]) ).
fof(f464,plain,
( in(sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))),singleton(sK15))
| ~ function(sK16)
| ~ spl19_1
| ~ spl19_16 ),
inference(forward_subsumption_resolution,[],[f442,f161]) ).
fof(f465,plain,
( sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) = apply(sK16,sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))))
| ~ function(sK16)
| ~ spl19_1
| ~ spl19_16 ),
inference(forward_subsumption_resolution,[],[f441,f161]) ).
fof(f466,plain,
( apply(sK16,sK15) != sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| spl19_4
| ~ spl19_16 ),
inference(forward_subsumption_resolution,[],[f440,f215]) ).
fof(f472,plain,
( in(sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))),singleton(sK15))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_16 ),
inference(forward_subsumption_resolution,[],[f464,f183]) ).
fof(f473,plain,
( sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) = apply(sK16,sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_16 ),
inference(forward_subsumption_resolution,[],[f465,f183]) ).
fof(f475,definition,
( spl19_18
<=> in(sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))),singleton(sK15)) ),
introduced(definition,[new_symbols(definition,[spl19_18])],[avatar_definition]) ).
fof(f477,plain,
( in(sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))),singleton(sK15))
| ~ spl19_18 ),
inference(avatar_component_clause,[],[f475]) ).
fof(f478,plain,
( spl19_18
| ~ spl19_1
| ~ spl19_2
| ~ spl19_16 ),
inference(avatar_split_clause,[],[f472,f404,f181,f159,f475]) ).
fof(f479,plain,
( sK15 = sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))))
| ~ spl19_18 ),
inference(resolution,[],[f477,f155]) ).
fof(f504,definition,
( spl19_19
<=> apply(sK16,sK15) = sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) ),
introduced(definition,[new_symbols(definition,[spl19_19])],[avatar_definition]) ).
fof(f506,plain,
( apply(sK16,sK15) != sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| spl19_19 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f507,plain,
( ~ spl19_19
| spl19_4
| ~ spl19_16 ),
inference(avatar_split_clause,[],[f466,f404,f213,f504]) ).
fof(f531,definition,
( spl19_21
<=> sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) = apply(sK16,sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))))) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
fof(f533,plain,
( sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15))) = apply(sK16,sK2(sK16,singleton(sK15),sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))))
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f531]) ).
fof(f534,plain,
( spl19_21
| ~ spl19_1
| ~ spl19_2
| ~ spl19_16 ),
inference(avatar_split_clause,[],[f473,f404,f181,f159,f531]) ).
fof(f535,plain,
( apply(sK16,sK15) = sK3(apply(sK16,sK15),relation_image(sK16,singleton(sK15)))
| ~ spl19_18
| ~ spl19_21 ),
inference(forward_demodulation,[],[f533,f479]) ).
fof(f536,plain,
( $false
| ~ spl19_18
| spl19_19
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f535,f506]) ).
fof(f537,plain,
( ~ spl19_18
| spl19_19
| ~ spl19_21 ),
inference(avatar_contradiction_clause,[],[f536]) ).
cnf(s1,plain,
spl19_1,
inference(sat_conversion,[],[f162]) ).
cnf(s2,plain,
spl19_2,
inference(sat_conversion,[],[f184]) ).
cnf(s3,plain,
spl19_3,
inference(sat_conversion,[],[f197]) ).
cnf(s4,plain,
~ spl19_4,
inference(sat_conversion,[],[f216]) ).
cnf(s11,plain,
( spl19_4
| spl19_11 ),
inference(sat_conversion,[],[f340]) ).
cnf(s15,plain,
( ~ spl19_11
| spl19_15 ),
inference(sat_conversion,[],[f386]) ).
cnf(s16,plain,
( spl19_4
| ~ spl19_15
| spl19_16
| ~ spl19_17 ),
inference(sat_conversion,[],[f411]) ).
cnf(s19,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| spl19_17 ),
inference(sat_conversion,[],[f439]) ).
cnf(s20,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_16
| spl19_18 ),
inference(sat_conversion,[],[f478]) ).
cnf(s21,plain,
( spl19_4
| ~ spl19_16
| ~ spl19_19 ),
inference(sat_conversion,[],[f507]) ).
cnf(s23,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_16
| spl19_21 ),
inference(sat_conversion,[],[f534]) ).
cnf(s24,plain,
( ~ spl19_18
| spl19_19
| ~ spl19_21 ),
inference(sat_conversion,[],[f537]) ).
cnf(s25,plain,
spl19_11,
inference(rat,[],[s11,s4]) ).
cnf(s26,plain,
spl19_15,
inference(rat,[],[s15,s25]) ).
cnf(s27,plain,
spl19_17,
inference(rat,[],[s19,s2,s3,s1]) ).
cnf(s36,plain,
spl19_16,
inference(rat,[],[s16,s26,s4,s27]) ).
cnf(s38,plain,
~ spl19_19,
inference(rat,[],[s21,s4,s36]) ).
cnf(s39,plain,
spl19_21,
inference(rat,[],[s23,s1,s2,s36]) ).
cnf(s41,plain,
spl19_18,
inference(rat,[],[s20,s1,s2,s36]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s24,s39,s38,s41]) ).
fof(f538,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU049+1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n003.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 03:29:27 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 4.25/1.52 % (1154886)Detected formulas, will run a generic FOF schedule.
% 4.25/1.52 % (1154893)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=4108574794:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.25/1.52 % (1154895)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3191975804:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.25/1.52 % (1154891)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=2980358047:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.25/1.52 % (1154897)dis-21_1_sil=8000:lcm=predicate:random_seed=416898292: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)
% 4.25/1.52 % (1154896)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=479062866:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.25/1.52 % (1154894)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3699350040:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.25/1.52 % (1154892)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=4028180001:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.25/1.52 % (1154894)Refutation not found, incomplete strategy
% 4.25/1.52 % (1154894)------------------------------
% 4.25/1.52 % (1154894)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154894)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154894)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154894)Termination reason: Refutation not found, incomplete strategy
% 4.25/1.52 % (1154894)Time elapsed: 0.002 s
% 4.25/1.52 % (1154894)Peak memory usage: 88 MB
% 4.25/1.52 % (1154894)Instructions burned: 2 (million)
% 4.25/1.52 % (1154895)Instruction limit reached!
% 4.25/1.52 % (1154895)------------------------------
% 4.25/1.52 % (1154895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154895)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154895)Termination reason: Instruction limit
% 4.25/1.52 % (1154895)Termination phase: Saturation
% 4.25/1.52 % (1154895)Time elapsed: 0.068 s
% 4.25/1.52 % (1154895)Peak memory usage: 87 MB
% 4.25/1.52 % (1154895)Instructions burned: 120 (million)
% 4.25/1.52 % (1154897)Instruction limit reached!
% 4.25/1.52 % (1154897)------------------------------
% 4.25/1.52 % (1154897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154897)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154897)Termination reason: Instruction limit
% 4.25/1.52 % (1154897)Termination phase: Saturation
% 4.25/1.52 % (1154897)Time elapsed: 0.075 s
% 4.25/1.52 % (1154897)Peak memory usage: 90 MB
% 4.25/1.52 % (1154897)Instructions burned: 130 (million)
% 4.25/1.52 % (1154896)Instruction limit reached!
% 4.25/1.52 % (1154896)------------------------------
% 4.25/1.52 % (1154896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154896)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154896)Termination reason: Instruction limit
% 4.25/1.52 % (1154896)Termination phase: Saturation
% 4.25/1.52 % (1154896)Time elapsed: 0.091 s
% 4.25/1.52 % (1154896)Peak memory usage: 89 MB
% 4.25/1.52 % (1154896)Instructions burned: 139 (million)
% 4.25/1.52 % (1154905)lrs+10_1_sil=8000:sp=occurrence:random_seed=4272252902:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 4.25/1.52 % (1154894)------------------------------
% 4.25/1.52 % (1154894)------------------------------
% 4.25/1.52 % (1154906)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3283716368:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.25/1.52 % (1154907)lrs+1011_1_sil=32000:sp=occurrence:random_seed=539273984:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.25/1.52 % (1154906)Refutation not found, incomplete strategy
% 4.25/1.52 % (1154906)------------------------------
% 4.25/1.52 % (1154906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154906)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154906)Termination reason: Refutation not found, incomplete strategy
% 4.25/1.52 % (1154906)Time elapsed: 0.016 s
% 4.25/1.52 % (1154906)Peak memory usage: 88 MB
% 4.25/1.52 % (1154906)Instructions burned: 26 (million)
% 4.25/1.52 % (1154893)First to succeed.
% 4.25/1.52 % (1154893)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1154886"
% 4.25/1.52 % (1154905)Instruction limit reached!
% 4.25/1.52 % (1154905)------------------------------
% 4.25/1.52 % (1154905)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154905)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154905)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154905)Termination reason: Instruction limit
% 4.25/1.52 % (1154905)Termination phase: Saturation
% 4.25/1.52 % (1154905)Time elapsed: 0.159 s
% 4.25/1.52 % (1154905)Peak memory usage: 91 MB
% 4.25/1.52 % (1154905)Instructions burned: 287 (million)
% 4.25/1.52 % (1154910)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=100636873:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 4.25/1.52 % (1154907)Instruction limit reached!
% 4.25/1.52 % (1154907)------------------------------
% 4.25/1.52 % (1154907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.25/1.52 % (1154907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.25/1.52 % (1154907)CaDiCaL version: 2.1.3
% 4.25/1.52 % (1154907)Termination reason: Instruction limit
% 4.25/1.52 % (1154907)Termination phase: Saturation
% 4.25/1.52 % (1154907)Time elapsed: 0.211 s
% 4.25/1.52 % (1154907)Peak memory usage: 91 MB
% 4.25/1.52 % (1154907)Instructions burned: 326 (million)
% 4.25/1.52 % (1154893)Refutation found. Thanks to Tanya!
% 4.25/1.52 % SZS status Theorem for theBenchmark
% 4.25/1.52 % SZS output start Proof for theBenchmark
% See solution above
% 5.33/1.72 % (1154893)------------------------------
% 5.33/1.72 % (1154893)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.33/1.72 % (1154893)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.33/1.72 % (1154893)CaDiCaL version: 2.1.3
% 5.33/1.72 % (1154893)Termination reason: Refutation
% 5.33/1.72 % (1154893)Time elapsed: 0.387 s
% 5.33/1.72 % (1154893)Peak memory usage: 130 MB
% 5.33/1.72 % (1154893)Instructions burned: 987 (million)
% 5.33/1.72 % (1154893)------------------------------
% 5.33/1.72 % (1154893)------------------------------
% 5.33/1.72 % (1154886)Success in time 0.673 s
% 5.33/1.72 % Vampire exiting
%------------------------------------------------------------------------------