%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU205+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 : n016.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 12:47:43 PM UTC 2026
% Result : Theorem 2.54s 1.29s
% Output : Refutation 3.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 12 unt; 6 def)
% Number of atoms : 353 ( 34 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 445 ( 183 ~; 191 |; 53 &)
% ( 14 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-3 aty)
% Number of variables : 177 ( 0 sgn 160 !; 17 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f6,axiom,
! [X0,X1,X2] :
( X2 = set_intersection2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X0)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_xboole_0) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(f30,axiom,
! [X0,X1,X2] :
( relation(X2)
=> ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t143_relat_1) ).
fof(f31,conjecture,
! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t145_relat_1) ).
fof(f32,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> relation_image(X1,X0) = relation_image(X1,set_intersection2(relation_dom(X1),X0)) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f43,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( in(X0,relation_image(X2,X1))
<=> ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) ) )
| ~ relation(X2) ),
inference(ennf_transformation,[],[f30]) ).
fof(f50,plain,
? [X0,X1] :
( relation_image(X1,X0) != relation_image(X1,set_intersection2(relation_dom(X1),X0))
& relation(X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f58,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X4,X3),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f59,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X4,X3),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X5,X3),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X8,X6),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1) )
| ~ in(sK0(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
& in(sK1(X0,X1,X2),X1) )
| in(sK0(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(sK2(X0,X1,X6),X6),X0)
& in(sK2(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_image(X0,X1) != X2 ) )
| ~ relation(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))],[f59]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ~ in(X3,X0)
| ~ in(X3,X1) )
& ( ( in(X3,X0)
& in(X3,X1) )
| ~ in(X3,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ? [X3] :
( ( ~ in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) )
& ( ( in(X3,X0)
& in(X3,X1) )
| in(X3,X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( X2 = set_intersection2(X0,X1)
| ( ( ~ in(sK3(X0,X1,X2),X0)
| ~ in(sK3(X0,X1,X2),X1)
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(sK3(X0,X1,X2),X0)
& in(sK3(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X4] :
( ( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1) )
& ( ( in(X4,X0)
& in(X4,X1) )
| ~ in(X4,X2) ) )
| set_intersection2(X0,X1) != X2 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X3,sK3(X0,X1,X2))],[f63]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X3] :
( in(X3,relation_dom(X2))
& in(ordered_pair(X3,X0),X2)
& in(X3,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(nnf_transformation,[],[f49]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ? [X4] :
( in(X4,relation_dom(X2))
& in(ordered_pair(X4,X0),X2)
& in(X4,X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(rectify,[],[f70]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ( ( in(X0,relation_image(X2,X1))
| ! [X3] :
( ~ in(X3,relation_dom(X2))
| ~ in(ordered_pair(X3,X0),X2)
| ~ in(X3,X1) ) )
& ( ( in(sK9(X0,X1,X2),relation_dom(X2))
& in(ordered_pair(sK9(X0,X1,X2),X0),X2)
& in(sK9(X0,X1,X2),X1) )
| ~ in(X0,relation_image(X2,X1)) ) )
| ~ relation(X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X4,sK9(X0,X1,X2))],[f71]) ).
fof(f73,plain,
( relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10))
& relation(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X0,sK10),skolemize(X1,sK11)],[f50]) ).
fof(f82,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X7,X6),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(ordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),X0)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f85,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| ~ in(ordered_pair(X4,sK0(X0,X1,X2)),X0)
| ~ in(X4,X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f86,plain,
! [X2,X0,X1,X4] :
( in(X4,X1)
| ~ in(X4,X2)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f88,plain,
! [X2,X0,X1,X4] :
( in(X4,X2)
| ~ in(X4,X0)
| ~ in(X4,X1)
| set_intersection2(X0,X1) != X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f92,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f111,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f112,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK9(X0,X1,X2),X0),X2)
| ~ in(X0,relation_image(X2,X1))
| ~ relation(X2) ),
inference(cnf_transformation,[],[f72]) ).
fof(f113,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(sK9(X0,X1,X2),relation_dom(X2)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f115,plain,
relation(sK11),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
relation_image(sK11,sK10) != relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)),
inference(cnf_transformation,[],[f73]) ).
fof(f125,plain,
! [X2,X0,X1,X4] :
( relation_image(X0,X1) = X2
| ~ in(unordered_pair(unordered_pair(X4,sK0(X0,X1,X2)),singleton(X4)),X0)
| ~ in(X4,X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f85,f92]) ).
fof(f126,plain,
! [X2,X0,X1] :
( relation_image(X0,X1) = X2
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f84,f92]) ).
fof(f127,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| relation_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f92]) ).
fof(f131,plain,
! [X2,X0,X1] :
( ~ relation(X2)
| ~ in(X0,relation_image(X2,X1))
| in(unordered_pair(unordered_pair(sK9(X0,X1,X2),X0),singleton(sK9(X0,X1,X2))),X2) ),
inference(definition_unfolding,[],[f112,f92]) ).
fof(f132,plain,
! [X0,X1,X6,X7] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| in(X6,relation_image(X0,X1)) ),
inference(equality_resolution,[],[f127]) ).
fof(f135,plain,
! [X0,X1,X4] :
( in(X4,set_intersection2(X0,X1))
| ~ in(X4,X0)
| ~ in(X4,X1) ),
inference(equality_resolution,[],[f88]) ).
fof(f137,plain,
! [X0,X1,X4] :
( ~ in(X4,set_intersection2(X0,X1))
| in(X4,X1) ),
inference(equality_resolution,[],[f86]) ).
fof(f138,definition,
! [X0,X1] :
( sQ13_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ13_eqProxy])],[equality_proxy_definition]) ).
fof(f141,plain,
! [X2,X0,X1,X4] :
( sQ13_eqProxy(relation_image(X0,X1),X2)
| ~ in(unordered_pair(unordered_pair(X4,sK0(X0,X1,X2)),singleton(X4)),X0)
| ~ in(X4,X1)
| ~ in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f125,f138]) ).
fof(f142,plain,
! [X2,X0,X1] :
( sQ13_eqProxy(relation_image(X0,X1),X2)
| in(unordered_pair(unordered_pair(sK1(X0,X1,X2),sK0(X0,X1,X2)),singleton(sK1(X0,X1,X2))),X0)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f126,f138]) ).
fof(f143,plain,
! [X2,X0,X1] :
( sQ13_eqProxy(relation_image(X0,X1),X2)
| in(sK1(X0,X1,X2),X1)
| in(sK0(X0,X1,X2),X2)
| ~ relation(X0) ),
inference(equality_proxy_replacement,[],[f83,f138]) ).
fof(f148,plain,
~ sQ13_eqProxy(relation_image(sK11,sK10),relation_image(sK11,set_intersection2(relation_dom(sK11),sK10))),
inference(equality_proxy_replacement,[],[f116,f138]) ).
fof(f155,plain,
! [X0,X1] :
( sQ13_eqProxy(X1,X0)
| ~ sQ13_eqProxy(X0,X1) ),
inference(equality_proxy_axiom,[],[f138]) ).
fof(f161,plain,
~ sQ13_eqProxy(relation_image(sK11,set_intersection2(relation_dom(sK11),sK10)),relation_image(sK11,sK10)),
inference(resolution,[],[f155,f148]) ).
fof(f236,plain,
! [X0,X1] :
( in(sK9(X0,X1,sK11),X1)
| ~ in(X0,relation_image(sK11,X1)) ),
inference(resolution,[],[f111,f115]) ).
fof(f294,plain,
! [X0,X1] :
( in(sK9(X0,X1,sK11),relation_dom(sK11))
| ~ in(X0,relation_image(sK11,X1)) ),
inference(resolution,[],[f113,f115]) ).
fof(f304,plain,
! [X2,X0,X1] :
( in(X1,relation_image(sK11,X2))
| ~ in(X0,X2)
| ~ in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK11) ),
inference(resolution,[],[f132,f115]) ).
fof(f307,plain,
( in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),set_intersection2(relation_dom(sK11),sK10))
| in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ relation(sK11) ),
inference(resolution,[],[f143,f161]) ).
fof(f309,definition,
( spl14_11
<=> relation(sK11) ),
introduced(definition,[new_symbols(definition,[spl14_11])],[avatar_definition]) ).
fof(f310,plain,
( ~ relation(sK11)
| spl14_11 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f312,definition,
( spl14_12
<=> in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_12])],[avatar_definition]) ).
fof(f315,definition,
( spl14_13
<=> in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),set_intersection2(relation_dom(sK11),sK10)) ),
introduced(definition,[new_symbols(definition,[spl14_13])],[avatar_definition]) ).
fof(f316,plain,
( in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),set_intersection2(relation_dom(sK11),sK10))
| ~ spl14_13 ),
inference(avatar_component_clause,[],[f315]) ).
fof(f317,plain,
( ~ spl14_11
| spl14_12
| spl14_13 ),
inference(avatar_split_clause,[],[f307,f315,f312,f309]) ).
fof(f325,plain,
( $false
| spl14_11 ),
inference(resolution,[],[f310,f115]) ).
fof(f327,plain,
spl14_11,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f339,plain,
! [X0,X1] :
( in(unordered_pair(unordered_pair(sK9(X0,X1,sK11),X0),singleton(sK9(X0,X1,sK11))),sK11)
| ~ in(X0,relation_image(sK11,X1)) ),
inference(resolution,[],[f131,f115]) ).
fof(f352,plain,
! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(X0)),sK11)
| ~ in(X0,set_intersection2(relation_dom(sK11),sK10))
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ relation(sK11) ),
inference(resolution,[],[f141,f161]) ).
fof(f353,plain,
( ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| spl14_12 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f355,definition,
( spl14_16
<=> ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(X0)),sK11)
| ~ in(X0,set_intersection2(relation_dom(sK11),sK10)) ) ),
introduced(definition,[new_symbols(definition,[spl14_16])],[avatar_definition]) ).
fof(f356,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(X0)),sK11)
| ~ in(X0,set_intersection2(relation_dom(sK11),sK10)) )
| ~ spl14_16 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f357,plain,
( ~ spl14_11
| ~ spl14_12
| spl14_16 ),
inference(avatar_split_clause,[],[f352,f355,f312,f309]) ).
fof(f365,plain,
( in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10)
| ~ spl14_13 ),
inference(resolution,[],[f316,f137]) ).
fof(f375,plain,
( in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),sK11)
| in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ relation(sK11) ),
inference(resolution,[],[f142,f161]) ).
fof(f377,definition,
( spl14_18
<=> in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),sK11) ),
introduced(definition,[new_symbols(definition,[spl14_18])],[avatar_definition]) ).
fof(f378,plain,
( in(unordered_pair(unordered_pair(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)))),sK11)
| ~ spl14_18 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f379,plain,
( ~ spl14_11
| spl14_12
| spl14_18 ),
inference(avatar_split_clause,[],[f375,f377,f312,f309]) ).
fof(f444,plain,
( ! [X0] :
( ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0,sK11),set_intersection2(relation_dom(sK11),sK10))
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,X0)) )
| ~ spl14_16 ),
inference(resolution,[],[f339,f356]) ).
fof(f455,plain,
( ! [X0] :
( ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0,sK11),relation_dom(sK11))
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,X0))
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0,sK11),sK10) )
| ~ spl14_16 ),
inference(resolution,[],[f444,f135]) ).
fof(f461,plain,
( ! [X0] :
( ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,X0))
| ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0,sK11),sK10)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,X0)) )
| ~ spl14_16 ),
inference(resolution,[],[f455,f294]) ).
fof(f464,plain,
( ! [X0] :
( ~ in(sK9(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),X0,sK11),sK10)
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,X0)) )
| ~ spl14_16 ),
inference(duplicate_literal_removal,[],[f461]) ).
fof(f486,plain,
( ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ spl14_16 ),
inference(resolution,[],[f464,f236]) ).
fof(f487,plain,
( ~ in(sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),relation_image(sK11,sK10))
| ~ spl14_16 ),
inference(duplicate_literal_removal,[],[f486]) ).
fof(f488,plain,
( ~ spl14_12
| ~ spl14_16 ),
inference(avatar_split_clause,[],[f487,f355,f312]) ).
fof(f489,plain,
( ! [X0] :
( ~ in(unordered_pair(unordered_pair(X0,sK0(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10))),singleton(X0)),sK11)
| ~ in(X0,sK10) )
| spl14_12 ),
inference(resolution,[],[f353,f304]) ).
fof(f491,plain,
( ~ in(sK1(sK11,set_intersection2(relation_dom(sK11),sK10),relation_image(sK11,sK10)),sK10)
| spl14_12
| ~ spl14_18 ),
inference(resolution,[],[f378,f489]) ).
fof(f495,plain,
( $false
| spl14_12
| ~ spl14_13
| ~ spl14_18 ),
inference(resolution,[],[f491,f365]) ).
fof(f496,plain,
( spl14_12
| ~ spl14_13
| ~ spl14_18 ),
inference(avatar_contradiction_clause,[],[f495]) ).
cnf(s9,plain,
( ~ spl14_11
| spl14_12
| spl14_13 ),
inference(sat_conversion,[],[f317]) ).
cnf(s11,plain,
spl14_11,
inference(sat_conversion,[],[f327]) ).
cnf(s12,plain,
( ~ spl14_11
| ~ spl14_12
| spl14_16 ),
inference(sat_conversion,[],[f357]) ).
cnf(s14,plain,
( ~ spl14_11
| spl14_12
| spl14_18 ),
inference(sat_conversion,[],[f379]) ).
cnf(s18,plain,
( ~ spl14_12
| ~ spl14_16 ),
inference(sat_conversion,[],[f488]) ).
cnf(s19,plain,
( spl14_12
| ~ spl14_13
| ~ spl14_18 ),
inference(sat_conversion,[],[f496]) ).
cnf(s21,plain,
( spl14_12
| spl14_13 ),
inference(rat,[],[s9,s11]) ).
cnf(s22,plain,
spl14_12,
inference(rat,[],[s19,s21,s14,s11]) ).
cnf(s23,plain,
~ spl14_16,
inference(rat,[],[s18,s22]) ).
cnf(s24,plain,
$false,
inference(rat,[],[s12,s11,s23,s22]) ).
fof(f497,plain,
$false,
inference(avatar_sat_refutation,[],[s24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU205+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n016.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 04:07:33 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.54/1.29 % (3246172)Detected formulas, will run a generic FOF schedule.
% 2.54/1.29 % (3246181)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1457023761:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.54/1.29 % (3246179)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=874495320:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.54/1.29 % (3246180)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3551981508:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.54/1.29 % (3246178)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=1310179286:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.54/1.29 % (3246177)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=1708100583:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.54/1.29 % (3246181)Instruction limit reached!
% 2.54/1.29 % (3246181)------------------------------
% 2.54/1.29 % (3246181)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (3246181)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (3246181)CaDiCaL version: 2.1.3
% 2.54/1.29 % (3246181)Termination reason: Instruction limit
% 2.54/1.29 % (3246181)Termination phase: Saturation
% 2.54/1.29 % (3246180)Refutation not found, incomplete strategy
% 2.54/1.29 % (3246180)------------------------------
% 2.54/1.29 % (3246180)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (3246181)Time elapsed: 0.038 s
% 2.54/1.29 % (3246181)Peak memory usage: 88 MB
% 2.54/1.29 % (3246181)Instructions burned: 123 (million)
% 2.54/1.29 % (3246180)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (3246180)CaDiCaL version: 2.1.3
% 2.54/1.29 % (3246180)Termination reason: Refutation not found, incomplete strategy
% 2.54/1.29 % (3246180)Time elapsed: 0.002 s
% 2.54/1.29 % (3246180)Peak memory usage: 88 MB
% 2.54/1.29 % (3246180)Instructions burned: 2 (million)
% 2.54/1.29 % (3246182)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2415502236:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.54/1.29 % (3246183)dis-21_1_sil=8000:lcm=predicate:random_seed=2772175257:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.54/1.29 % (3246183)First to succeed.
% 2.54/1.29 % (3246183)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3246172"
% 2.54/1.29 % (3246182)Instruction limit reached!
% 2.54/1.29 % (3246182)------------------------------
% 2.54/1.29 % (3246182)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (3246182)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (3246182)CaDiCaL version: 2.1.3
% 2.54/1.29 % (3246182)Termination reason: Instruction limit
% 2.54/1.29 % (3246182)Termination phase: Saturation
% 2.54/1.29 % (3246182)Time elapsed: 0.051 s
% 2.54/1.29 % (3246182)Peak memory usage: 89 MB
% 2.54/1.29 % (3246182)Instructions burned: 141 (million)
% 2.54/1.29 % (3246189)lrs+10_1_sil=8000:sp=occurrence:random_seed=4163699514:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.54/1.29 % (3246192)lrs+10_1_sil=32000:urr=on:br=off:random_seed=688842544:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.54/1.29 % (3246192)Instruction limit reached!
% 2.54/1.29 % (3246192)------------------------------
% 2.54/1.29 % (3246192)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.54/1.29 % (3246192)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.54/1.29 % (3246192)CaDiCaL version: 2.1.3
% 2.54/1.29 % (3246192)Termination reason: Instruction limit
% 2.54/1.29 % (3246192)Termination phase: Saturation
% 2.54/1.29 % (3246192)Time elapsed: 0.041 s
% 2.54/1.29 % (3246192)Peak memory usage: 90 MB
% 2.54/1.29 % (3246192)Instructions burned: 158 (million)
% 2.54/1.29 % (3246180)------------------------------
% 2.54/1.29 % (3246180)------------------------------
% 2.54/1.29 % (3246183)Refutation found. Thanks to Tanya!
% 2.54/1.29 % SZS status Theorem for theBenchmark
% 2.54/1.29 % SZS output start Proof for theBenchmark
% See solution above
% 3.77/1.51 % (3246183)------------------------------
% 3.77/1.51 % (3246183)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.77/1.51 % (3246183)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.77/1.51 % (3246183)CaDiCaL version: 2.1.3
% 3.77/1.51 % (3246183)Termination reason: Refutation
% 3.77/1.51 % (3246183)Time elapsed: 0.010 s
% 3.77/1.51 % (3246183)Peak memory usage: 89 MB
% 3.77/1.51 % (3246183)Instructions burned: 13 (million)
% 3.77/1.51 % (3246183)------------------------------
% 3.77/1.51 % (3246183)------------------------------
% 3.77/1.51 % (3246172)Success in time 0.44 s
% 3.77/1.51 % Vampire exiting
%------------------------------------------------------------------------------