%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU297+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 : n008.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 12:48:13 PM UTC 2026
% Result : Theorem 3.93s 1.53s
% Output : Refutation 5.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 9
% Syntax : Number of formulae : 92 ( 13 unt; 7 def)
% Number of atoms : 406 ( 48 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 493 ( 179 ~; 209 |; 82 &)
% ( 13 <=>; 8 =>; 0 <=; 2 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 163 ( 0 sgn 116 !; 47 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_xboole_0__e6_27__finset_1) ).
fof(f2,negated_conjecture,
~ ! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f38,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
=> X4 = X5 )
=> ? [X3] :
! [X4] :
( in(X4,X3)
<=> ? [X5] :
( in(X5,powerset(relation_dom(X2)))
& X5 = X4
& in(relation_image(X2,X4),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s1_tarski__e6_27__finset_1__1) ).
fof(f39,plain,
! [X0,X1,X2] :
( ( element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) )
=> ( ! [X3,X4,X5] :
( ( X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
=> X4 = X5 )
=> ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) ) ) ),
inference(rectify,[],[f38]) ).
fof(f47,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f48,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( in(X4,X3)
<~> ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f39]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f49]) ).
fof(f72,definition,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ sP0(X1,X2) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( in(X7,X6)
<=> ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(definition_folding,[],[f50,f72]) ).
fof(f74,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,X3) )
& ( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(nnf_transformation,[],[f48]) ).
fof(f75,plain,
? [X0,X1,X2] :
( ! [X3] :
? [X4] :
( ( ~ in(X4,powerset(relation_dom(X2)))
| ~ in(relation_image(X2,X4),X1)
| ~ in(X4,X3) )
& ( ( in(X4,powerset(relation_dom(X2)))
& in(relation_image(X2,X4),X1) )
| in(X4,X3) ) )
& element(X1,powerset(powerset(X0)))
& relation(X2)
& function(X2) ),
inference(flattening,[],[f74]) ).
fof(f76,plain,
( ! [X3] :
( ( ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),X3) )
& ( ( in(sK4(X3),powerset(relation_dom(sK3)))
& in(relation_image(sK3,sK4(X3)),sK2) )
| in(sK4(X3),X3) ) )
& element(sK2,powerset(powerset(sK1)))
& relation(sK3)
& function(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X4,sK4(X3))],[f75]) ).
fof(f77,plain,
! [X1,X2] :
( ? [X3,X4,X5] :
( X4 != X5
& X3 = X4
& in(relation_image(X2,X4),X1)
& X3 = X5
& in(relation_image(X2,X5),X1) )
| ~ sP0(X1,X2) ),
inference(nnf_transformation,[],[f72]) ).
fof(f78,plain,
! [X0,X1] :
( ? [X2,X3,X4] :
( X3 != X4
& X2 = X3
& in(relation_image(X1,X3),X0)
& X2 = X4
& in(relation_image(X1,X4),X0) )
| ~ sP0(X0,X1) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1] :
( ( sK6(X0,X1) != sK7(X0,X1)
& sK5(X0,X1) = sK6(X0,X1)
& in(relation_image(X1,sK6(X0,X1)),X0)
& sK5(X0,X1) = sK7(X0,X1)
& in(relation_image(X1,sK7(X0,X1)),X0) )
| ~ sP0(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6,sK7]),skolemize(X2,sK5(X0,X1)),skolemize(X3,sK6(X0,X1)),skolemize(X4,sK7(X0,X1))],[f78]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ? [X6] :
! [X7] :
( ( in(X7,X6)
| ! [X8] :
( ~ in(X8,powerset(relation_dom(X2)))
| X7 != X8
| ~ in(relation_image(X2,X7),X1) ) )
& ( ? [X8] :
( in(X8,powerset(relation_dom(X2)))
& X7 = X8
& in(relation_image(X2,X7),X1) )
| ~ in(X7,X6) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f73]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ? [X3] :
! [X4] :
( ( in(X4,X3)
| ! [X5] :
( ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1) ) )
& ( ? [X6] :
( in(X6,powerset(relation_dom(X2)))
& X4 = X6
& in(relation_image(X2,X4),X1) )
| ~ in(X4,X3) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(rectify,[],[f80]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ! [X4] :
( ( in(X4,sK8(X1,X2))
| ! [X5] :
( ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1) ) )
& ( ( in(sK9(X1,X2,X4),powerset(relation_dom(X2)))
& sK9(X1,X2,X4) = X4
& in(relation_image(X2,X4),X1) )
| ~ in(X4,sK8(X1,X2)) ) )
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X3,sK8(X1,X2)),skolemize(X6,sK9(X1,X2,X4))],[f81]) ).
fof(f99,plain,
function(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f100,plain,
relation(sK3),
inference(cnf_transformation,[],[f76]) ).
fof(f101,plain,
element(sK2,powerset(powerset(sK1))),
inference(cnf_transformation,[],[f76]) ).
fof(f102,plain,
! [X3] :
( in(relation_image(sK3,sK4(X3)),sK2)
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f103,plain,
! [X3] :
( in(sK4(X3),powerset(relation_dom(sK3)))
| in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X3] :
( ~ in(sK4(X3),powerset(relation_dom(sK3)))
| ~ in(relation_image(sK3,sK4(X3)),sK2)
| ~ in(sK4(X3),X3) ),
inference(cnf_transformation,[],[f76]) ).
fof(f106,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK5(X0,X1) = sK7(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f108,plain,
! [X0,X1] :
( ~ sP0(X0,X1)
| sK5(X0,X1) = sK6(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f109,plain,
! [X0,X1] :
( sK6(X0,X1) != sK7(X0,X1)
| ~ sP0(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f110,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK8(X1,X2))
| in(relation_image(X2,X4),X1)
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f111,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK8(X1,X2))
| sK9(X1,X2,X4) = X4
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f112,plain,
! [X2,X0,X1,X4] :
( ~ in(X4,sK8(X1,X2))
| in(sK9(X1,X2,X4),powerset(relation_dom(X2)))
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f113,plain,
! [X2,X0,X1,X4,X5] :
( in(X4,sK8(X1,X2))
| ~ in(X5,powerset(relation_dom(X2)))
| X4 != X5
| ~ in(relation_image(X2,X4),X1)
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f185,plain,
! [X2,X0,X1,X5] :
( ~ in(relation_image(X2,X5),X1)
| ~ in(X5,powerset(relation_dom(X2)))
| in(X5,sK8(X1,X2))
| sP0(X1,X2)
| ~ element(X1,powerset(powerset(X0)))
| ~ relation(X2)
| ~ function(X2) ),
inference(equality_resolution,[],[f113]) ).
fof(f349,plain,
! [X0,X1] :
( ~ in(sK4(X0),powerset(relation_dom(sK3)))
| in(sK4(X0),sK8(sK2,sK3))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X1)))
| ~ relation(sK3)
| ~ function(sK3)
| in(sK4(X0),X0) ),
inference(resolution,[],[f185,f102]) ).
fof(f354,plain,
! [X0,X1] :
( ~ in(sK4(X0),powerset(relation_dom(sK3)))
| in(sK4(X0),sK8(sK2,sK3))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X1)))
| ~ function(sK3)
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f349,f100]) ).
fof(f355,plain,
! [X0,X1] :
( ~ in(sK4(X0),powerset(relation_dom(sK3)))
| in(sK4(X0),sK8(sK2,sK3))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f354,f99]) ).
fof(f356,plain,
! [X0,X1] :
( in(sK4(X0),sK8(sK2,sK3))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X1)))
| in(sK4(X0),X0) ),
inference(forward_subsumption_resolution,[],[f355,f103]) ).
fof(f358,definition,
( spl26_5
<=> ! [X1] : ~ element(sK2,powerset(powerset(X1))) ),
introduced(definition,[new_symbols(definition,[spl26_5])],[avatar_definition]) ).
fof(f359,plain,
( ! [X1] : ~ element(sK2,powerset(powerset(X1)))
| ~ spl26_5 ),
inference(avatar_component_clause,[],[f358]) ).
fof(f361,definition,
( spl26_6
<=> sP0(sK2,sK3) ),
introduced(definition,[new_symbols(definition,[spl26_6])],[avatar_definition]) ).
fof(f362,plain,
( ~ sP0(sK2,sK3)
| spl26_6 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f363,plain,
( sP0(sK2,sK3)
| ~ spl26_6 ),
inference(avatar_component_clause,[],[f361]) ).
fof(f365,definition,
( spl26_7
<=> ! [X0] :
( in(sK4(X0),sK8(sK2,sK3))
| in(sK4(X0),X0) ) ),
introduced(definition,[new_symbols(definition,[spl26_7])],[avatar_definition]) ).
fof(f366,plain,
( ! [X0] :
( in(sK4(X0),sK8(sK2,sK3))
| in(sK4(X0),X0) )
| ~ spl26_7 ),
inference(avatar_component_clause,[],[f365]) ).
fof(f367,plain,
( spl26_5
| spl26_6
| spl26_7 ),
inference(avatar_split_clause,[],[f356,f365,f361,f358]) ).
fof(f368,plain,
( $false
| ~ spl26_5 ),
inference(resolution,[],[f359,f101]) ).
fof(f369,plain,
~ spl26_5,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f371,plain,
( sK5(sK2,sK3) = sK7(sK2,sK3)
| ~ spl26_6 ),
inference(resolution,[],[f363,f106]) ).
fof(f381,plain,
( sK5(sK2,sK3) != sK6(sK2,sK3)
| ~ sP0(sK2,sK3)
| ~ spl26_6 ),
inference(superposition,[],[f109,f371]) ).
fof(f383,plain,
( ~ sP0(sK2,sK3)
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f381,f108]) ).
fof(f384,plain,
( $false
| ~ spl26_6 ),
inference(forward_subsumption_resolution,[],[f383,f363]) ).
fof(f385,plain,
~ spl26_6,
inference(avatar_contradiction_clause,[],[f384]) ).
fof(f394,plain,
( in(sK4(sK8(sK2,sK3)),sK8(sK2,sK3))
| ~ spl26_7 ),
inference(factoring,[],[f366]) ).
fof(f416,plain,
( ! [X0] :
( in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3)))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| ~ spl26_7 ),
inference(resolution,[],[f394,f112]) ).
fof(f417,plain,
( ! [X0] :
( sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3)))
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| ~ spl26_7 ),
inference(resolution,[],[f394,f111]) ).
fof(f418,plain,
( ! [X0] :
( in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| sP0(sK2,sK3)
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| ~ spl26_7 ),
inference(resolution,[],[f394,f110]) ).
fof(f420,plain,
( ! [X0] :
( in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f418,f362]) ).
fof(f421,plain,
( ! [X0] :
( sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3)))
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f417,f362]) ).
fof(f422,plain,
( ! [X0] :
( in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X0)))
| ~ relation(sK3)
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f416,f362]) ).
fof(f423,plain,
( ! [X0] :
( in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| ~ element(sK2,powerset(powerset(X0)))
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f420,f100]) ).
fof(f424,plain,
( ! [X0] :
( sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3)))
| ~ element(sK2,powerset(powerset(X0)))
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f421,f100]) ).
fof(f425,plain,
( ! [X0] :
( in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X0)))
| ~ function(sK3) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f422,f100]) ).
fof(f426,plain,
( ! [X0] :
( in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f423,f99]) ).
fof(f427,plain,
( ! [X0] :
( sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3)))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f424,f99]) ).
fof(f428,plain,
( ! [X0] :
( in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ element(sK2,powerset(powerset(X0))) )
| spl26_6
| ~ spl26_7 ),
inference(forward_subsumption_resolution,[],[f425,f99]) ).
fof(f430,definition,
( spl26_10
<=> in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2) ),
introduced(definition,[new_symbols(definition,[spl26_10])],[avatar_definition]) ).
fof(f432,plain,
( in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| ~ spl26_10 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f433,plain,
( spl26_5
| spl26_10
| spl26_6
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f426,f365,f361,f430,f358]) ).
fof(f435,definition,
( spl26_11
<=> sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3))) ),
introduced(definition,[new_symbols(definition,[spl26_11])],[avatar_definition]) ).
fof(f437,plain,
( sK4(sK8(sK2,sK3)) = sK9(sK2,sK3,sK4(sK8(sK2,sK3)))
| ~ spl26_11 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f438,plain,
( spl26_5
| spl26_11
| spl26_6
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f427,f365,f361,f435,f358]) ).
fof(f440,definition,
( spl26_12
<=> in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3))) ),
introduced(definition,[new_symbols(definition,[spl26_12])],[avatar_definition]) ).
fof(f442,plain,
( in(sK9(sK2,sK3,sK4(sK8(sK2,sK3))),powerset(relation_dom(sK3)))
| ~ spl26_12 ),
inference(avatar_component_clause,[],[f440]) ).
fof(f443,plain,
( spl26_5
| spl26_12
| spl26_6
| ~ spl26_7 ),
inference(avatar_split_clause,[],[f428,f365,f361,f440,f358]) ).
fof(f444,plain,
( in(sK4(sK8(sK2,sK3)),powerset(relation_dom(sK3)))
| ~ spl26_11
| ~ spl26_12 ),
inference(forward_demodulation,[],[f442,f437]) ).
fof(f468,plain,
( ~ in(relation_image(sK3,sK4(sK8(sK2,sK3))),sK2)
| ~ in(sK4(sK8(sK2,sK3)),sK8(sK2,sK3))
| ~ spl26_11
| ~ spl26_12 ),
inference(resolution,[],[f444,f104]) ).
fof(f470,plain,
( ~ in(sK4(sK8(sK2,sK3)),sK8(sK2,sK3))
| ~ spl26_10
| ~ spl26_11
| ~ spl26_12 ),
inference(forward_subsumption_resolution,[],[f468,f432]) ).
fof(f471,plain,
( $false
| ~ spl26_7
| ~ spl26_10
| ~ spl26_11
| ~ spl26_12 ),
inference(forward_subsumption_resolution,[],[f470,f394]) ).
fof(f472,plain,
( ~ spl26_7
| ~ spl26_10
| ~ spl26_11
| ~ spl26_12 ),
inference(avatar_contradiction_clause,[],[f471]) ).
cnf(s3,plain,
( spl26_5
| spl26_6
| spl26_7 ),
inference(sat_conversion,[],[f367]) ).
cnf(s4,plain,
~ spl26_5,
inference(sat_conversion,[],[f369]) ).
cnf(s5,plain,
~ spl26_6,
inference(sat_conversion,[],[f385]) ).
cnf(s8,plain,
( spl26_5
| spl26_6
| ~ spl26_7
| spl26_10 ),
inference(sat_conversion,[],[f433]) ).
cnf(s9,plain,
( spl26_5
| spl26_6
| ~ spl26_7
| spl26_11 ),
inference(sat_conversion,[],[f438]) ).
cnf(s10,plain,
( spl26_5
| spl26_6
| ~ spl26_7
| spl26_12 ),
inference(sat_conversion,[],[f443]) ).
cnf(s11,plain,
( ~ spl26_7
| ~ spl26_10
| ~ spl26_11
| ~ spl26_12 ),
inference(sat_conversion,[],[f472]) ).
cnf(s12,plain,
spl26_7,
inference(rat,[],[s3,s5,s4]) ).
cnf(s13,plain,
spl26_12,
inference(rat,[],[s10,s4,s5,s12]) ).
cnf(s14,plain,
spl26_11,
inference(rat,[],[s9,s4,s5,s12]) ).
cnf(s15,plain,
spl26_10,
inference(rat,[],[s8,s4,s5,s12]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s11,s13,s12,s14,s15]) ).
fof(f473,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU297+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n008.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:35:24 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 3.93/1.53 % (1876700)Detected formulas, will run a generic FOF schedule.
% 3.93/1.53 % (1876708)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2365171470:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.93/1.53 % (1876708)Refutation not found, incomplete strategy
% 3.93/1.53 % (1876708)------------------------------
% 3.93/1.53 % (1876708)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876708)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876708)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.53 % (1876708)Time elapsed: 0.001 s
% 3.93/1.53 % (1876708)Peak memory usage: 88 MB
% 3.93/1.53 % (1876708)Instructions burned: 1 (million)
% 3.93/1.53 % (1876707)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=2226325386:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.93/1.53 % (1876711)dis-21_1_sil=8000:lcm=predicate:random_seed=4053739524: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)
% 3.93/1.53 % (1876709)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2569722047:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.93/1.53 % (1876706)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=2877435522:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.93/1.53 % (1876705)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=658138895:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.93/1.53 % (1876710)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1368685637:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.93/1.53 % (1876709)Refutation not found, incomplete strategy
% 3.93/1.53 % (1876709)------------------------------
% 3.93/1.53 % (1876709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876709)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876709)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.53 % (1876709)Time elapsed: 0.003 s
% 3.93/1.53 % (1876709)Peak memory usage: 88 MB
% 3.93/1.53 % (1876709)Instructions burned: 2 (million)
% 3.93/1.53 % (1876710)Refutation not found, incomplete strategy
% 3.93/1.53 % (1876710)------------------------------
% 3.93/1.53 % (1876710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876710)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876710)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.53 % (1876710)Time elapsed: 0.006 s
% 3.93/1.53 % (1876710)Peak memory usage: 89 MB
% 3.93/1.53 % (1876710)Instructions burned: 7 (million)
% 3.93/1.53 % (1876711)Instruction limit reached!
% 3.93/1.53 % (1876711)------------------------------
% 3.93/1.53 % (1876711)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876711)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876711)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876711)Termination reason: Instruction limit
% 3.93/1.53 % (1876711)Termination phase: Saturation
% 3.93/1.53 % (1876711)Time elapsed: 0.073 s
% 3.93/1.53 % (1876711)Peak memory usage: 89 MB
% 3.93/1.53 % (1876711)Instructions burned: 129 (million)
% 3.93/1.53 % (1876708)------------------------------
% 3.93/1.53 % (1876708)------------------------------
% 3.93/1.53 % (1876719)lrs+10_1_sil=8000:sp=occurrence:random_seed=2416772480:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.93/1.53 % (1876719)First to succeed.
% 3.93/1.53 % (1876720)lrs+10_1_sil=32000:urr=on:br=off:random_seed=310690867:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.93/1.53 % (1876719)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1876700"
% 3.93/1.53 % (1876710)------------------------------
% 3.93/1.53 % (1876710)------------------------------
% 3.93/1.53 % (1876709)------------------------------
% 3.93/1.53 % (1876709)------------------------------
% 3.93/1.53 % (1876720)Instruction limit reached!
% 3.93/1.53 % (1876720)------------------------------
% 3.93/1.53 % (1876720)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876720)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876720)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876720)Termination reason: Instruction limit
% 3.93/1.53 % (1876720)Termination phase: Saturation
% 3.93/1.53 % (1876720)Time elapsed: 0.048 s
% 3.93/1.53 % (1876720)Peak memory usage: 91 MB
% 3.93/1.53 % (1876720)Instructions burned: 160 (million)
% 3.93/1.53 % (1876725)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1401047491:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 3.93/1.53 % (1876723)lrs+1011_1_sil=32000:sp=occurrence:random_seed=692591853:i=325:sd=1:ss=axioms:sgt=32_2995 on theBenchmark for (2995ds/325Mi)
% 3.93/1.53 % (1876725)Refutation not found, incomplete strategy
% 3.93/1.53 % (1876725)------------------------------
% 3.93/1.53 % (1876725)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.93/1.53 % (1876725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.93/1.53 % (1876725)CaDiCaL version: 2.1.3
% 3.93/1.53 % (1876725)Termination reason: Refutation not found, incomplete strategy
% 3.93/1.53 % (1876725)Time elapsed: 0.002 s
% 3.93/1.53 % (1876725)Peak memory usage: 88 MB
% 3.93/1.53 % (1876725)Instructions burned: 4 (million)
% 3.93/1.53 % (1876724)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=2742484595:s2a=on:i=248:s2at=1.23:gtg=position_2995 on theBenchmark for (2995ds/248Mi)
% 3.93/1.53 % (1876723)Also succeeded, but the first one will report.
% 3.93/1.53 % (1876719)Refutation found. Thanks to Tanya!
% 3.93/1.53 % SZS status Theorem for theBenchmark
% 3.93/1.53 % SZS output start Proof for theBenchmark
% See solution above
% 5.29/1.75 % (1876719)------------------------------
% 5.29/1.75 % (1876719)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.29/1.75 % (1876719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.29/1.75 % (1876719)CaDiCaL version: 2.1.3
% 5.29/1.75 % (1876719)Termination reason: Refutation
% 5.29/1.75 % (1876719)Time elapsed: 0.012 s
% 5.29/1.75 % (1876719)Peak memory usage: 89 MB
% 5.29/1.75 % (1876719)Instructions burned: 15 (million)
% 5.29/1.75 % (1876719)------------------------------
% 5.29/1.75 % (1876719)------------------------------
% 5.29/1.75 % (1876700)Success in time 0.661 s
% 5.29/1.75 % Vampire exiting
%------------------------------------------------------------------------------