%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU050+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 4.63s 1.24s
% Output : Refutation 5.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 20
% Syntax : Number of formulae : 155 ( 31 unt; 17 def)
% Number of atoms : 557 ( 145 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 694 ( 292 ~; 308 |; 64 &)
% ( 25 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 22 ( 20 usr; 18 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 151 ( 0 sgn 133 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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/sandbox2/benchmark/theBenchmark.p',d12_funct_1) ).
fof(f7,axiom,
! [X0,X1,X2] :
( X2 = unordered_pair(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( X3 = X0
| X3 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tarski) ).
fof(f27,conjecture,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X0,relation_dom(X2))
& in(X1,relation_dom(X2)) )
=> relation_image(X2,unordered_pair(X0,X1)) = unordered_pair(apply(X2,X0),apply(X2,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t118_funct_1) ).
fof(f28,negated_conjecture,
~ ! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( ( in(X0,relation_dom(X2))
& in(X1,relation_dom(X2)) )
=> relation_image(X2,unordered_pair(X0,X1)) = unordered_pair(apply(X2,X0),apply(X2,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f27]) ).
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,[],[f6]) ).
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,X2] :
( relation_image(X2,unordered_pair(X0,X1)) != unordered_pair(apply(X2,X0),apply(X2,X1))
& in(X0,relation_dom(X2))
& in(X1,relation_dom(X2))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f55,plain,
? [X0,X1,X2] :
( relation_image(X2,unordered_pair(X0,X1)) != unordered_pair(apply(X2,X0),apply(X2,X1))
& in(X0,relation_dom(X2))
& in(X1,relation_dom(X2))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f54]) ).
fof(f66,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(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) )
& ( ? [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,[],[f66]) ).
fof(f68,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))],[f67]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f7]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ( X0 != X3
& X1 != X3 ) )
& ( X3 = X0
| X3 = X1
| ~ in(X3,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(flattening,[],[f69]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ? [X3] :
( ( ( X0 != X3
& X1 != X3 )
| ~ in(X3,X2) )
& ( X3 = X0
| X3 = X1
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( X2 = unordered_pair(X0,X1)
| ( ( ( sK3(X0,X1,X2) != X0
& sK3(X0,X1,X2) != X1 )
| ~ in(sK3(X0,X1,X2),X2) )
& ( sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ( X0 != X4
& X1 != X4 ) )
& ( X0 = X4
| X1 = X4
| ~ in(X4,X2) ) )
| unordered_pair(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f71]) ).
fof(f84,plain,
( relation_image(sK17,unordered_pair(sK15,sK16)) != unordered_pair(apply(sK17,sK15),apply(sK17,sK16))
& in(sK15,relation_dom(sK17))
& in(sK16,relation_dom(sK17))
& relation(sK17)
& function(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK15,sK16,sK17]),skolemize(X0,sK15),skolemize(X1,sK16),skolemize(X2,sK17)],[f55]) ).
fof(f91,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,[],[f68]) ).
fof(f92,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,[],[f68]) ).
fof(f94,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,[],[f68]) ).
fof(f99,plain,
! [X2,X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,X2)
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f100,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X1 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f101,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| X0 != X4
| unordered_pair(X0,X1) != X2 ),
inference(cnf_transformation,[],[f72]) ).
fof(f102,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK3(X0,X1,X2) = X0
| sK3(X0,X1,X2) = X1
| in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f103,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK3(X0,X1,X2) != X1
| ~ in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f104,plain,
! [X2,X0,X1] :
( unordered_pair(X0,X1) = X2
| sK3(X0,X1,X2) != X0
| ~ in(sK3(X0,X1,X2),X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f135,plain,
function(sK17),
inference(cnf_transformation,[],[f84]) ).
fof(f136,plain,
relation(sK17),
inference(cnf_transformation,[],[f84]) ).
fof(f137,plain,
in(sK16,relation_dom(sK17)),
inference(cnf_transformation,[],[f84]) ).
fof(f138,plain,
in(sK15,relation_dom(sK17)),
inference(cnf_transformation,[],[f84]) ).
fof(f139,plain,
relation_image(sK17,unordered_pair(sK15,sK16)) != unordered_pair(apply(sK17,sK15),apply(sK17,sK16)),
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,[],[f94]) ).
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,[],[f92]) ).
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,[],[f91]) ).
fof(f153,plain,
! [X2,X1,X4] :
( in(X4,X2)
| unordered_pair(X4,X1) != X2 ),
inference(equality_resolution,[],[f101]) ).
fof(f154,plain,
! [X1,X4] : in(X4,unordered_pair(X4,X1)),
inference(equality_resolution,[],[f153]) ).
fof(f155,plain,
! [X2,X0,X4] :
( in(X4,X2)
| unordered_pair(X0,X4) != X2 ),
inference(equality_resolution,[],[f100]) ).
fof(f156,plain,
! [X0,X4] : in(X4,unordered_pair(X0,X4)),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X0,X1,X4] :
( X0 = X4
| X1 = X4
| ~ in(X4,unordered_pair(X0,X1)) ),
inference(equality_resolution,[],[f99]) ).
fof(f161,definition,
( spl19_1
<=> relation_image(sK17,unordered_pair(sK15,sK16)) = unordered_pair(apply(sK17,sK15),apply(sK17,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f163,plain,
( relation_image(sK17,unordered_pair(sK15,sK16)) != unordered_pair(apply(sK17,sK15),apply(sK17,sK16))
| spl19_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
~ spl19_1,
inference(avatar_split_clause,[],[f139,f161]) ).
fof(f165,plain,
( ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| spl19_1 ),
inference(superposition,[],[f163,f102]) ).
fof(f166,plain,
( ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK16) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| spl19_1 ),
inference(superposition,[],[f163,f103]) ).
fof(f167,plain,
( ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK15) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| spl19_1 ),
inference(superposition,[],[f163,f104]) ).
fof(f169,definition,
( spl19_2
<=> relation(sK17) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f171,plain,
( relation(sK17)
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f169]) ).
fof(f172,plain,
spl19_2,
inference(avatar_split_clause,[],[f136,f169]) ).
fof(f181,plain,
( ! [X0,X1] :
( apply(sK17,sK2(sK17,X0,X1)) = X1
| ~ in(X1,relation_image(sK17,X0))
| ~ function(sK17) )
| ~ spl19_2 ),
inference(resolution,[],[f171,f152]) ).
fof(f182,plain,
( ! [X0,X1] :
( apply(sK17,sK2(sK17,X0,X1)) = X1
| ~ in(X1,relation_image(sK17,X0)) )
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f181,f135]) ).
fof(f191,definition,
( spl19_3
<=> function(sK17) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f193,plain,
( function(sK17)
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
spl19_3,
inference(avatar_split_clause,[],[f135,f191]) ).
fof(f204,definition,
( spl19_4
<=> in(sK15,relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f206,plain,
( in(sK15,relation_dom(sK17))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f204]) ).
fof(f207,plain,
spl19_4,
inference(avatar_split_clause,[],[f138,f204]) ).
fof(f223,definition,
( spl19_5
<=> in(sK16,relation_dom(sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_5])],[avatar_definition]) ).
fof(f225,plain,
( in(sK16,relation_dom(sK17))
| ~ spl19_5 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f226,plain,
spl19_5,
inference(avatar_split_clause,[],[f137,f223]) ).
fof(f316,definition,
( spl19_10
<=> ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK16) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_10])],[avatar_definition]) ).
fof(f317,plain,
( ! [X0] :
( apply(sK17,sK16) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| ~ spl19_10 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f318,plain,
( spl19_10
| spl19_1 ),
inference(avatar_split_clause,[],[f166,f161,f316]) ).
fof(f323,definition,
( spl19_11
<=> ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK15) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_11])],[avatar_definition]) ).
fof(f324,plain,
( ! [X0] :
( apply(sK17,sK15) != sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| ~ spl19_11 ),
inference(avatar_component_clause,[],[f323]) ).
fof(f325,plain,
( spl19_11
| spl19_1 ),
inference(avatar_split_clause,[],[f167,f161,f323]) ).
fof(f371,definition,
( spl19_13
<=> ! [X0,X1] :
( apply(sK17,sK2(sK17,X0,X1)) = X1
| ~ in(X1,relation_image(sK17,X0)) ) ),
introduced(definition,[new_symbols(definition,[spl19_13])],[avatar_definition]) ).
fof(f372,plain,
( ! [X0,X1] :
( apply(sK17,sK2(sK17,X0,X1)) = X1
| ~ in(X1,relation_image(sK17,X0)) )
| ~ spl19_13 ),
inference(avatar_component_clause,[],[f371]) ).
fof(f373,plain,
( spl19_13
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f182,f169,f371]) ).
fof(f481,definition,
( spl19_20
<=> ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl19_20])],[avatar_definition]) ).
fof(f482,plain,
( ! [X0] :
( relation_image(sK17,unordered_pair(sK15,sK16)) != X0
| apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),X0)
| in(sK3(apply(sK17,sK15),apply(sK17,sK16),X0),X0) )
| ~ spl19_20 ),
inference(avatar_component_clause,[],[f481]) ).
fof(f483,plain,
( spl19_20
| spl19_1 ),
inference(avatar_split_clause,[],[f165,f161,f481]) ).
fof(f491,plain,
( apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_20 ),
inference(equality_resolution,[],[f482]) ).
fof(f501,definition,
( spl19_21
<=> in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_21])],[avatar_definition]) ).
fof(f503,plain,
( in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_21 ),
inference(avatar_component_clause,[],[f501]) ).
fof(f505,definition,
( spl19_22
<=> apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_22])],[avatar_definition]) ).
fof(f506,plain,
( apply(sK17,sK16) != sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| spl19_22 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f507,plain,
( apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_22 ),
inference(avatar_component_clause,[],[f505]) ).
fof(f509,definition,
( spl19_23
<=> apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_23])],[avatar_definition]) ).
fof(f510,plain,
( apply(sK17,sK15) != sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| spl19_23 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f511,plain,
( apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_23 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f512,plain,
( spl19_21
| spl19_22
| spl19_23
| ~ spl19_20 ),
inference(avatar_split_clause,[],[f491,f481,f509,f505,f501]) ).
fof(f522,plain,
( apply(sK17,sK16) != apply(sK17,sK16)
| relation_image(sK17,unordered_pair(sK15,sK16)) != relation_image(sK17,unordered_pair(sK15,sK16))
| ~ in(apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_10
| ~ spl19_22 ),
inference(superposition,[],[f317,f507]) ).
fof(f529,plain,
( ~ in(apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_10
| ~ spl19_22 ),
inference(trivial_inequality_removal,[],[f522]) ).
fof(f544,definition,
( spl19_24
<=> in(apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_24])],[avatar_definition]) ).
fof(f546,plain,
( ~ in(apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| spl19_24 ),
inference(avatar_component_clause,[],[f544]) ).
fof(f547,plain,
( ~ spl19_24
| ~ spl19_10
| ~ spl19_22 ),
inference(avatar_split_clause,[],[f529,f505,f316,f544]) ).
fof(f550,plain,
( ~ in(sK16,relation_dom(sK17))
| ~ in(sK16,unordered_pair(sK15,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| spl19_24 ),
inference(resolution,[],[f546,f149]) ).
fof(f563,plain,
( ~ in(sK16,unordered_pair(sK15,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_5
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f550,f225]) ).
fof(f571,plain,
( ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_5
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f563,f156]) ).
fof(f574,plain,
( ~ function(sK17)
| ~ spl19_2
| ~ spl19_5
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f571,f171]) ).
fof(f575,plain,
( $false
| ~ spl19_2
| ~ spl19_3
| ~ spl19_5
| spl19_24 ),
inference(forward_subsumption_resolution,[],[f574,f193]) ).
fof(f576,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_5
| spl19_24 ),
inference(avatar_contradiction_clause,[],[f575]) ).
fof(f588,plain,
( apply(sK17,sK15) != apply(sK17,sK15)
| relation_image(sK17,unordered_pair(sK15,sK16)) != relation_image(sK17,unordered_pair(sK15,sK16))
| ~ in(apply(sK17,sK15),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_11
| ~ spl19_23 ),
inference(superposition,[],[f324,f511]) ).
fof(f597,plain,
( ~ in(apply(sK17,sK15),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_11
| ~ spl19_23 ),
inference(trivial_inequality_removal,[],[f588]) ).
fof(f722,definition,
( spl19_28
<=> in(apply(sK17,sK15),relation_image(sK17,unordered_pair(sK15,sK16))) ),
introduced(definition,[new_symbols(definition,[spl19_28])],[avatar_definition]) ).
fof(f724,plain,
( ~ in(apply(sK17,sK15),relation_image(sK17,unordered_pair(sK15,sK16)))
| spl19_28 ),
inference(avatar_component_clause,[],[f722]) ).
fof(f725,plain,
( ~ spl19_28
| ~ spl19_11
| ~ spl19_23 ),
inference(avatar_split_clause,[],[f597,f509,f323,f722]) ).
fof(f728,plain,
( ~ in(sK15,relation_dom(sK17))
| ~ in(sK15,unordered_pair(sK15,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| spl19_28 ),
inference(resolution,[],[f724,f149]) ).
fof(f742,plain,
( ~ in(sK15,unordered_pair(sK15,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_4
| spl19_28 ),
inference(forward_subsumption_resolution,[],[f728,f206]) ).
fof(f750,plain,
( ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_4
| spl19_28 ),
inference(forward_subsumption_resolution,[],[f742,f154]) ).
fof(f753,plain,
( ~ function(sK17)
| ~ spl19_2
| ~ spl19_4
| spl19_28 ),
inference(forward_subsumption_resolution,[],[f750,f171]) ).
fof(f754,plain,
( $false
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| spl19_28 ),
inference(forward_subsumption_resolution,[],[f753,f193]) ).
fof(f755,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| spl19_28 ),
inference(avatar_contradiction_clause,[],[f754]) ).
fof(f814,plain,
( in(sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))),unordered_pair(sK15,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_21 ),
inference(resolution,[],[f503,f151]) ).
fof(f838,plain,
( in(sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))),unordered_pair(sK15,sK16))
| ~ function(sK17)
| ~ spl19_2
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f814,f171]) ).
fof(f845,plain,
( in(sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))),unordered_pair(sK15,sK16))
| ~ spl19_2
| ~ spl19_3
| ~ spl19_21 ),
inference(forward_subsumption_resolution,[],[f838,f193]) ).
fof(f848,definition,
( spl19_30
<=> in(sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))),unordered_pair(sK15,sK16)) ),
introduced(definition,[new_symbols(definition,[spl19_30])],[avatar_definition]) ).
fof(f850,plain,
( in(sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))),unordered_pair(sK15,sK16))
| ~ spl19_30 ),
inference(avatar_component_clause,[],[f848]) ).
fof(f851,plain,
( spl19_30
| ~ spl19_2
| ~ spl19_3
| ~ spl19_21 ),
inference(avatar_split_clause,[],[f845,f501,f191,f169,f848]) ).
fof(f852,plain,
( sK15 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))))
| sK16 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))))
| ~ spl19_30 ),
inference(resolution,[],[f850,f157]) ).
fof(f916,definition,
( spl19_33
<=> sK16 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))) ),
introduced(definition,[new_symbols(definition,[spl19_33])],[avatar_definition]) ).
fof(f918,plain,
( sK16 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))))
| ~ spl19_33 ),
inference(avatar_component_clause,[],[f916]) ).
fof(f920,definition,
( spl19_34
<=> sK15 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))) ),
introduced(definition,[new_symbols(definition,[spl19_34])],[avatar_definition]) ).
fof(f922,plain,
( sK15 = sK2(sK17,unordered_pair(sK15,sK16),sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))))
| ~ spl19_34 ),
inference(avatar_component_clause,[],[f920]) ).
fof(f923,plain,
( spl19_33
| spl19_34
| ~ spl19_30 ),
inference(avatar_split_clause,[],[f852,f848,f920,f916]) ).
fof(f979,plain,
( apply(sK17,sK15) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_13
| ~ spl19_34 ),
inference(superposition,[],[f372,f922]) ).
fof(f984,plain,
( ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_13
| spl19_23
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f979,f510]) ).
fof(f992,plain,
( $false
| ~ spl19_13
| ~ spl19_21
| spl19_23
| ~ spl19_34 ),
inference(forward_subsumption_resolution,[],[f984,f503]) ).
fof(f993,plain,
( ~ spl19_13
| ~ spl19_21
| spl19_23
| ~ spl19_34 ),
inference(avatar_contradiction_clause,[],[f992]) ).
fof(f1025,plain,
( apply(sK17,sK16) = sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_13
| ~ spl19_33 ),
inference(superposition,[],[f372,f918]) ).
fof(f1030,plain,
( ~ in(sK3(apply(sK17,sK15),apply(sK17,sK16),relation_image(sK17,unordered_pair(sK15,sK16))),relation_image(sK17,unordered_pair(sK15,sK16)))
| ~ spl19_13
| spl19_22
| ~ spl19_33 ),
inference(forward_subsumption_resolution,[],[f1025,f506]) ).
fof(f1038,plain,
( $false
| ~ spl19_13
| ~ spl19_21
| spl19_22
| ~ spl19_33 ),
inference(forward_subsumption_resolution,[],[f1030,f503]) ).
fof(f1039,plain,
( ~ spl19_13
| ~ spl19_21
| spl19_22
| ~ spl19_33 ),
inference(avatar_contradiction_clause,[],[f1038]) ).
cnf(s1,plain,
~ spl19_1,
inference(sat_conversion,[],[f164]) ).
cnf(s2,plain,
spl19_2,
inference(sat_conversion,[],[f172]) ).
cnf(s3,plain,
spl19_3,
inference(sat_conversion,[],[f194]) ).
cnf(s4,plain,
spl19_4,
inference(sat_conversion,[],[f207]) ).
cnf(s5,plain,
spl19_5,
inference(sat_conversion,[],[f226]) ).
cnf(s10,plain,
( spl19_1
| spl19_10 ),
inference(sat_conversion,[],[f318]) ).
cnf(s11,plain,
( spl19_1
| spl19_11 ),
inference(sat_conversion,[],[f325]) ).
cnf(s13,plain,
( ~ spl19_2
| spl19_13 ),
inference(sat_conversion,[],[f373]) ).
cnf(s20,plain,
( spl19_1
| spl19_20 ),
inference(sat_conversion,[],[f483]) ).
cnf(s21,plain,
( ~ spl19_20
| spl19_21
| spl19_22
| spl19_23 ),
inference(sat_conversion,[],[f512]) ).
cnf(s22,plain,
( ~ spl19_10
| ~ spl19_22
| ~ spl19_24 ),
inference(sat_conversion,[],[f547]) ).
cnf(s25,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_5
| spl19_24 ),
inference(sat_conversion,[],[f576]) ).
cnf(s29,plain,
( ~ spl19_11
| ~ spl19_23
| ~ spl19_28 ),
inference(sat_conversion,[],[f725]) ).
cnf(s32,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_4
| spl19_28 ),
inference(sat_conversion,[],[f755]) ).
cnf(s34,plain,
( ~ spl19_2
| ~ spl19_3
| ~ spl19_21
| spl19_30 ),
inference(sat_conversion,[],[f851]) ).
cnf(s37,plain,
( ~ spl19_30
| spl19_33
| spl19_34 ),
inference(sat_conversion,[],[f923]) ).
cnf(s39,plain,
( ~ spl19_13
| ~ spl19_21
| spl19_23
| ~ spl19_34 ),
inference(sat_conversion,[],[f993]) ).
cnf(s42,plain,
( ~ spl19_13
| ~ spl19_21
| spl19_22
| ~ spl19_33 ),
inference(sat_conversion,[],[f1039]) ).
cnf(s44,plain,
spl19_28,
inference(rat,[],[s32,s3,s4,s2]) ).
cnf(s45,plain,
spl19_24,
inference(rat,[],[s25,s3,s5,s2]) ).
cnf(s50,plain,
spl19_13,
inference(rat,[],[s13,s2]) ).
cnf(s60,plain,
spl19_20,
inference(rat,[],[s20,s1]) ).
cnf(s61,plain,
spl19_11,
inference(rat,[],[s11,s1]) ).
cnf(s62,plain,
spl19_10,
inference(rat,[],[s10,s1]) ).
cnf(s63,plain,
~ spl19_23,
inference(rat,[],[s29,s44,s61]) ).
cnf(s65,plain,
~ spl19_22,
inference(rat,[],[s22,s45,s62]) ).
cnf(s67,plain,
spl19_21,
inference(rat,[],[s21,s63,s60,s65]) ).
cnf(s68,plain,
~ spl19_33,
inference(rat,[],[s42,s65,s50,s67]) ).
cnf(s69,plain,
~ spl19_34,
inference(rat,[],[s39,s63,s50,s67]) ).
cnf(s72,plain,
spl19_30,
inference(rat,[],[s34,s2,s3,s67]) ).
cnf(s73,plain,
$false,
inference(rat,[],[s37,s69,s68,s72]) ).
fof(f1047,plain,
$false,
inference(avatar_sat_refutation,[],[s73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU050+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Mon Sep 28 03:27:19 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.33 Running first-order theorem proving
% 0.08/0.33 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
% 4.63/1.24 % (2989831)Detected formulas, will run a generic FOF schedule.
% 4.63/1.24 % (2989841)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3161685504:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.63/1.24 % (2989842)dis-21_1_sil=8000:lcm=predicate:random_seed=3869152095: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)
% 4.63/1.24 % (2989840)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=691310460:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.63/1.24 % (2989838)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=2476916275:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.63/1.24 % (2989837)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=2335230301:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.63/1.24 % (2989839)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1115076499:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.63/1.24 % (2989836)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=331240385:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.63/1.24 % (2989839)Refutation not found, incomplete strategy
% 4.63/1.24 % (2989839)------------------------------
% 4.63/1.24 % (2989839)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989839)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989839)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989839)Termination reason: Refutation not found, incomplete strategy
% 4.63/1.24 % (2989839)Time elapsed: 0.001 s
% 4.63/1.24 % (2989839)Peak memory usage: 88 MB
% 4.63/1.24 % (2989839)Instructions burned: 2 (million)
% 4.63/1.24 % (2989840)Instruction limit reached!
% 4.63/1.24 % (2989840)------------------------------
% 4.63/1.24 % (2989840)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989840)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989840)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989840)Termination reason: Instruction limit
% 4.63/1.24 % (2989840)Termination phase: Saturation
% 4.63/1.24 % (2989840)Time elapsed: 0.036 s
% 4.63/1.24 % (2989840)Peak memory usage: 88 MB
% 4.63/1.24 % (2989840)Instructions burned: 121 (million)
% 4.63/1.24 % (2989842)Instruction limit reached!
% 4.63/1.24 % (2989842)------------------------------
% 4.63/1.24 % (2989842)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989842)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989842)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989842)Termination reason: Instruction limit
% 4.63/1.24 % (2989842)Termination phase: Saturation
% 4.63/1.24 % (2989842)Time elapsed: 0.042 s
% 4.63/1.24 % (2989842)Peak memory usage: 90 MB
% 4.63/1.24 % (2989842)Instructions burned: 132 (million)
% 4.63/1.24 % (2989841)Instruction limit reached!
% 4.63/1.24 % (2989841)------------------------------
% 4.63/1.24 % (2989841)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989841)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989841)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989841)Termination reason: Instruction limit
% 4.63/1.24 % (2989841)Termination phase: Saturation
% 4.63/1.24 % (2989841)Time elapsed: 0.047 s
% 4.63/1.24 % (2989841)Peak memory usage: 89 MB
% 4.63/1.24 % (2989841)Instructions burned: 140 (million)
% 4.63/1.24 % (2989850)lrs+10_1_sil=8000:sp=occurrence:random_seed=1437926976:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.63/1.24 % (2989839)------------------------------
% 4.63/1.24 % (2989839)------------------------------
% 4.63/1.24 % (2989851)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2105215198:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/157Mi)
% 4.63/1.24 % (2989852)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1381037376:i=325:sd=1:ss=axioms:sgt=32_2998 on theBenchmark for (2998ds/325Mi)
% 4.63/1.24 % (2989851)Instruction limit reached!
% 4.63/1.24 % (2989851)------------------------------
% 4.63/1.24 % (2989851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989851)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989851)Termination reason: Instruction limit
% 4.63/1.24 % (2989851)Termination phase: Saturation
% 4.63/1.24 % (2989851)Time elapsed: 0.038 s
% 4.63/1.24 % (2989851)Peak memory usage: 89 MB
% 4.63/1.24 % (2989851)Instructions burned: 159 (million)
% 4.63/1.24 % (2989850)Instruction limit reached!
% 4.63/1.24 % (2989850)------------------------------
% 4.63/1.24 % (2989850)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989850)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989850)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989850)Termination reason: Instruction limit
% 4.63/1.24 % (2989850)Termination phase: Saturation
% 4.63/1.24 % (2989850)Time elapsed: 0.083 s
% 4.63/1.24 % (2989850)Peak memory usage: 91 MB
% 4.63/1.24 % (2989850)Instructions burned: 288 (million)
% 4.63/1.24 % (2989852)Instruction limit reached!
% 4.63/1.24 % (2989852)------------------------------
% 4.63/1.24 % (2989852)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989852)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989852)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989852)Termination reason: Instruction limit
% 4.63/1.24 % (2989852)Termination phase: Saturation
% 4.63/1.24 % (2989852)Time elapsed: 0.111 s
% 4.63/1.24 % (2989852)Peak memory usage: 91 MB
% 4.63/1.24 % (2989852)Instructions burned: 326 (million)
% 4.63/1.24 % (2989854)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=2936503209:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.63/1.24 % (2989857)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2975100591:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2996 on theBenchmark for (2996ds/294Mi)
% 4.63/1.24 % (2989857)Refutation not found, incomplete strategy
% 4.63/1.24 % (2989857)------------------------------
% 4.63/1.24 % (2989857)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989857)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989857)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989857)Termination reason: Refutation not found, incomplete strategy
% 4.63/1.24 % (2989857)Time elapsed: 0.001 s
% 4.63/1.24 % (2989857)Peak memory usage: 88 MB
% 4.63/1.24 % (2989857)Instructions burned: 2 (million)
% 4.63/1.24 % (2989854)Instruction limit reached!
% 4.63/1.24 % (2989854)------------------------------
% 4.63/1.24 % (2989854)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989854)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989854)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989854)Termination reason: Instruction limit
% 4.63/1.24 % (2989854)Termination phase: Saturation
% 4.63/1.24 % (2989854)Time elapsed: 0.073 s
% 4.63/1.24 % (2989854)Peak memory usage: 91 MB
% 4.63/1.24 % (2989854)Instructions burned: 251 (million)
% 4.63/1.24 % (2989858)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=573094175:i=2350_2996 on theBenchmark for (2996ds/2350Mi)
% 4.63/1.24 % (2989838)First to succeed.
% 4.63/1.24 % (2989860)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=345958516:cts=off:i=113:fsr=off:ss=included:sgt=4_2995 on theBenchmark for (2995ds/113Mi)
% 4.63/1.24 % (2989838)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2989831"
% 4.63/1.24 % (2989860)Instruction limit reached!
% 4.63/1.24 % (2989860)------------------------------
% 4.63/1.24 % (2989860)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989860)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989860)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989860)Termination reason: Instruction limit
% 4.63/1.24 % (2989860)Termination phase: Saturation
% 4.63/1.24 % (2989860)Time elapsed: 0.045 s
% 4.63/1.24 % (2989860)Peak memory usage: 89 MB
% 4.63/1.24 % (2989860)Instructions burned: 116 (million)
% 4.63/1.24 % (2989862)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=751550047:i=127:av=off:fsr=off:sup=off_2995 on theBenchmark for (2995ds/127Mi)
% 4.63/1.24 % (2989857)------------------------------
% 4.63/1.24 % (2989857)------------------------------
% 4.63/1.24 % (2989836)Also succeeded, but the first one will report.
% 4.63/1.24 % (2989862)Instruction limit reached!
% 4.63/1.24 % (2989862)------------------------------
% 4.63/1.24 % (2989862)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.63/1.24 % (2989862)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.63/1.24 % (2989862)CaDiCaL version: 2.1.3
% 4.63/1.24 % (2989862)Termination reason: Instruction limit
% 4.63/1.24 % (2989862)Termination phase: Saturation
% 4.63/1.24 % (2989862)Time elapsed: 0.036 s
% 4.63/1.24 % (2989862)Peak memory usage: 88 MB
% 4.63/1.24 % (2989862)Instructions burned: 127 (million)
% 4.63/1.24 % (2989838)Refutation found. Thanks to Tanya!
% 4.63/1.24 % SZS status Theorem for theBenchmark
% 4.63/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 5.15/1.34 % (2989838)------------------------------
% 5.15/1.34 % (2989838)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.15/1.34 % (2989838)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.15/1.34 % (2989838)CaDiCaL version: 2.1.3
% 5.15/1.34 % (2989838)Termination reason: Refutation
% 5.15/1.34 % (2989838)Time elapsed: 0.403 s
% 5.15/1.34 % (2989838)Peak memory usage: 128 MB
% 5.15/1.34 % (2989838)Instructions burned: 1065 (million)
% 5.15/1.34 % (2989838)------------------------------
% 5.15/1.34 % (2989838)------------------------------
% 5.15/1.34 % (2989831)Success in time 0.703 s
% 5.15/1.34 % Vampire exiting
%------------------------------------------------------------------------------