%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU227+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:52:29 PM UTC 2026
% Result : Theorem 0.18s 0.54s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 91 ( 18 unt; 6 def)
% Number of atoms : 352 ( 32 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 432 ( 171 ~; 178 |; 55 &)
% ( 20 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 2 con; 0-3 aty)
% Number of variables : 194 ( 0 sgn 164 !; 30 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,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/sandbox/benchmark/theBenchmark.p',d13_relat_1) ).
fof(f7,axiom,
! [X0] :
( relation(X0)
=> ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_1) ).
fof(f8,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_tarski) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f10,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f41,conjecture,
! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t146_funct_1) ).
fof(f42,negated_conjecture,
~ ! [X0,X1] :
( relation(X1)
=> ( subset(X0,relation_dom(X1))
=> subset(X0,relation_inverse_image(X1,relation_image(X1,X0))) ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f61,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,[],[f6]) ).
fof(f62,plain,
! [X0] :
( ! [X1,X2] :
( X2 = relation_inverse_image(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) ) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f63,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f69,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f70,plain,
? [X0,X1] :
( ~ subset(X0,relation_inverse_image(X1,relation_image(X1,X0)))
& subset(X0,relation_dom(X1))
& relation(X1) ),
inference(flattening,[],[f69]) ).
fof(f80,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,[],[f61]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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))],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| in(X3,X2) ) ) )
& ( ! [X3] :
( ( in(X3,X2)
| ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) ) )
& ( ? [X4] :
( in(ordered_pair(X3,X4),X0)
& in(X4,X1) )
| ~ in(X3,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f62]) ).
fof(f84,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ? [X3] :
( ( ! [X4] :
( ~ in(ordered_pair(X3,X4),X0)
| ~ in(X4,X1) )
| ~ in(X3,X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(X5,X1) )
| in(X3,X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ? [X8] :
( in(ordered_pair(X6,X8),X0)
& in(X8,X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(rectify,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ! [X1,X2] :
( ( X2 = relation_inverse_image(X0,X1)
| ( ( ! [X4] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X4),X0)
| ~ in(X4,X1) )
| ~ in(sK3(X0,X1,X2),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X0)
& in(sK4(X0,X1,X2),X1) )
| in(sK3(X0,X1,X2),X2) ) ) )
& ( ! [X6] :
( ( in(X6,X2)
| ! [X7] :
( ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1) ) )
& ( ( in(ordered_pair(X6,sK5(X0,X1,X6)),X0)
& in(sK5(X0,X1,X6),X1) )
| ~ in(X6,X2) ) )
| relation_inverse_image(X0,X1) != X2 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X5,sK4(X0,X1,X2)),skolemize(X8,sK5(X0,X1,X6))],[f84]) ).
fof(f86,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X2] :
( in(X2,X1)
| ~ in(X2,X0) )
| ~ subset(X0,X1) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f87,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ? [X2] :
( ~ in(X2,X1)
& in(X2,X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(rectify,[],[f86]) ).
fof(f88,plain,
! [X0,X1] :
( ( subset(X0,X1)
| ( ~ in(sK6(X0,X1),X1)
& in(sK6(X0,X1),X0) ) )
& ( ! [X3] :
( in(X3,X1)
| ~ in(X3,X0) )
| ~ subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(X2,sK6(X0,X1))],[f87]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f64]) ).
fof(f90,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f89]) ).
fof(f91,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK7(X0,X1),X3),X0)
| ~ in(sK7(X0,X1),X1) )
& ( in(ordered_pair(sK7(X0,X1),sK8(X0,X1)),X0)
| in(sK7(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9]),skolemize(X2,sK7(X0,X1)),skolemize(X4,sK8(X0,X1)),skolemize(X7,sK9(X0,X5))],[f90]) ).
fof(f103,plain,
( ~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
& subset(sK21,relation_dom(sK22))
& relation(sK22) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21,sK22]),skolemize(X0,sK21),skolemize(X1,sK22)],[f70]) ).
fof(f113,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,[],[f82]) ).
fof(f119,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(ordered_pair(X6,X7),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(cnf_transformation,[],[f85]) ).
fof(f123,plain,
! [X3,X0,X1] :
( in(X3,X1)
| ~ in(X3,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f124,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sK6(X0,X1),X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f125,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f126,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK9(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f130,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f10]) ).
fof(f163,plain,
relation(sK22),
inference(cnf_transformation,[],[f103]) ).
fof(f164,plain,
subset(sK21,relation_dom(sK22)),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
~ subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),
inference(cnf_transformation,[],[f103]) ).
fof(f177,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,[],[f113,f130]) ).
fof(f181,plain,
! [X2,X0,X1,X6,X7] :
( in(X6,X2)
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| relation_inverse_image(X0,X1) != X2
| ~ relation(X0) ),
inference(definition_unfolding,[],[f119,f130]) ).
fof(f186,plain,
! [X0,X1,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(definition_unfolding,[],[f126,f130]) ).
fof(f188,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_image(X0,X1))
| ~ in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f177]) ).
fof(f191,plain,
! [X0,X1,X6,X7] :
( in(X6,relation_inverse_image(X0,X1))
| ~ in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X7,X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f181]) ).
fof(f195,plain,
! [X0,X5] :
( in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f186]) ).
fof(f204,plain,
! [X0,X1,X6,X7] :
( in(unordered_pair(unordered_pair(X7,X6),singleton(X7)),X0)
| ~ in(X6,relation_image(X0,X1))
| in(X7,X1)
| ~ relation(X0) ),
inference(consistent_polarity_flipping,[],[f188]) ).
fof(f210,plain,
! [X0,X1,X6,X7] :
( in(unordered_pair(unordered_pair(X6,X7),singleton(X6)),X0)
| ~ in(X6,relation_inverse_image(X0,X1))
| in(X7,X1)
| ~ relation(X0) ),
inference(consistent_polarity_flipping,[],[f191]) ).
fof(f213,plain,
! [X0,X1] :
( in(sK6(X0,X1),X1)
| subset(X0,X1) ),
inference(consistent_polarity_flipping,[],[f125]) ).
fof(f214,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sK6(X0,X1),X0) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f215,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| in(X3,X0)
| ~ in(X3,X1) ),
inference(consistent_polarity_flipping,[],[f123]) ).
fof(f219,plain,
! [X0,X5] :
( in(X5,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X5,sK9(X0,X5)),singleton(X5)),X0)
| ~ relation(X0) ),
inference(consistent_polarity_flipping,[],[f195]) ).
fof(f420,plain,
~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21),
inference(resolution,[],[f214,f165]) ).
fof(f779,plain,
! [X0] :
( in(X0,sK21)
| ~ in(X0,relation_dom(sK22)) ),
inference(resolution,[],[f215,f164]) ).
fof(f780,plain,
~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_dom(sK22)),
inference(resolution,[],[f779,f420]) ).
fof(f2348,plain,
( ~ in(unordered_pair(unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),sK22)
| ~ relation(sK22) ),
inference(resolution,[],[f219,f780]) ).
fof(f2407,definition,
( spl23_11
<=> relation(sK22) ),
introduced(definition,[new_symbols(definition,[spl23_11])],[avatar_definition]) ).
fof(f2409,plain,
( ~ relation(sK22)
| spl23_11 ),
inference(avatar_component_clause,[],[f2407]) ).
fof(f2416,definition,
( spl23_13
<=> in(unordered_pair(unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),sK22) ),
introduced(definition,[new_symbols(definition,[spl23_13])],[avatar_definition]) ).
fof(f2418,plain,
( ~ in(unordered_pair(unordered_pair(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),singleton(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))))),sK22)
| spl23_13 ),
inference(avatar_component_clause,[],[f2416]) ).
fof(f2419,plain,
( ~ spl23_11
| ~ spl23_13 ),
inference(avatar_split_clause,[],[f2348,f2416,f2407]) ).
fof(f2420,plain,
( $false
| spl23_11 ),
inference(resolution,[],[f2409,f163]) ).
fof(f2422,plain,
spl23_11,
inference(avatar_contradiction_clause,[],[f2420]) ).
fof(f2619,plain,
( ! [X0] :
( ~ in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,X0))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0)
| ~ relation(sK22) )
| spl23_13 ),
inference(resolution,[],[f204,f2418]) ).
fof(f2625,definition,
( spl23_14
<=> ! [X0] :
( ~ in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,X0))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl23_14])],[avatar_definition]) ).
fof(f2626,plain,
( ! [X0] :
( ~ in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),relation_image(sK22,X0))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0) )
| ~ spl23_14 ),
inference(avatar_component_clause,[],[f2625]) ).
fof(f2627,plain,
( ~ spl23_11
| spl23_14
| spl23_13 ),
inference(avatar_split_clause,[],[f2619,f2416,f2625,f2407]) ).
fof(f2679,plain,
( ! [X0] :
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,X0))
| in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),X0)
| ~ relation(sK22) )
| spl23_13 ),
inference(resolution,[],[f210,f2418]) ).
fof(f2685,definition,
( spl23_22
<=> ! [X0] :
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,X0))
| in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),X0) ) ),
introduced(definition,[new_symbols(definition,[spl23_22])],[avatar_definition]) ).
fof(f2686,plain,
( ! [X0] :
( in(sK9(sK22,sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))),X0)
| ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,X0)) )
| ~ spl23_22 ),
inference(avatar_component_clause,[],[f2685]) ).
fof(f2687,plain,
( ~ spl23_11
| spl23_22
| spl23_13 ),
inference(avatar_split_clause,[],[f2679,f2416,f2685,f2407]) ).
fof(f2737,plain,
( ! [X0] :
( ~ in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),relation_inverse_image(sK22,relation_image(sK22,X0)))
| in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),X0) )
| ~ spl23_14
| ~ spl23_22 ),
inference(resolution,[],[f2686,f2626]) ).
fof(f2738,plain,
( in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
| ~ spl23_14
| ~ spl23_22 ),
inference(resolution,[],[f2737,f213]) ).
fof(f2747,definition,
( spl23_31
<=> subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))) ),
introduced(definition,[new_symbols(definition,[spl23_31])],[avatar_definition]) ).
fof(f2749,plain,
( subset(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21)))
| ~ spl23_31 ),
inference(avatar_component_clause,[],[f2747]) ).
fof(f2751,definition,
( spl23_32
<=> in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21) ),
introduced(definition,[new_symbols(definition,[spl23_32])],[avatar_definition]) ).
fof(f2753,plain,
( in(sK6(sK21,relation_inverse_image(sK22,relation_image(sK22,sK21))),sK21)
| ~ spl23_32 ),
inference(avatar_component_clause,[],[f2751]) ).
fof(f2754,plain,
( spl23_31
| spl23_32
| ~ spl23_14
| ~ spl23_22 ),
inference(avatar_split_clause,[],[f2738,f2685,f2625,f2751,f2747]) ).
fof(f2766,plain,
( $false
| ~ spl23_31 ),
inference(resolution,[],[f2749,f165]) ).
fof(f2768,plain,
~ spl23_31,
inference(avatar_contradiction_clause,[],[f2766]) ).
fof(f2769,plain,
( $false
| ~ spl23_32 ),
inference(resolution,[],[f2753,f420]) ).
fof(f2770,plain,
~ spl23_32,
inference(avatar_contradiction_clause,[],[f2769]) ).
cnf(s17,plain,
( ~ spl23_11
| ~ spl23_13 ),
inference(sat_conversion,[],[f2419]) ).
cnf(s18,plain,
spl23_11,
inference(sat_conversion,[],[f2422]) ).
cnf(s19,plain,
( ~ spl23_11
| spl23_13
| spl23_14 ),
inference(sat_conversion,[],[f2627]) ).
cnf(s27,plain,
( ~ spl23_11
| spl23_13
| spl23_22 ),
inference(sat_conversion,[],[f2687]) ).
cnf(s36,plain,
( ~ spl23_14
| ~ spl23_22
| spl23_31
| spl23_32 ),
inference(sat_conversion,[],[f2754]) ).
cnf(s39,plain,
~ spl23_31,
inference(sat_conversion,[],[f2768]) ).
cnf(s40,plain,
~ spl23_32,
inference(sat_conversion,[],[f2770]) ).
cnf(s41,plain,
( ~ spl23_14
| ~ spl23_22 ),
inference(rat,[],[s36,s40,s39]) ).
cnf(s42,plain,
~ spl23_13,
inference(rat,[],[s17,s18]) ).
cnf(s43,plain,
spl23_22,
inference(rat,[],[s27,s18,s42]) ).
cnf(s44,plain,
spl23_14,
inference(rat,[],[s19,s18,s42]) ).
cnf(s45,plain,
$false,
inference(rat,[],[s41,s43,s44]) ).
fof(f2771,plain,
$false,
inference(avatar_sat_refutation,[],[s45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU227+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n003.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 04:12:27 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.54 % (1179113)Will run a generic schedule for satisfiability detection.
% 0.18/0.54 % (1179119)% WARNING: option uhcvi not known.
% 0.18/0.54 % (1179119)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1378042296:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.54 % (1179122)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=205757514:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.54 % (1179118)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3699292632_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.54 % (1179120)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4159493106:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.54 % (1179123)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4067635491:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.54 % (1179121)dis+10_1_sil=32000:sp=arity:random_seed=2248376929:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.54 % TRYING [1]
% 0.18/0.54 % TRYING [2]
% 0.18/0.54 % TRYING [3]
% 0.18/0.54 % (1179124)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3977283967:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.54 % TRYING [4]
% 0.18/0.54 % (1179121)Instruction limit reached!
% 0.18/0.54 % (1179121)------------------------------
% 0.18/0.54 % (1179121)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (1179121)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (1179121)CaDiCaL version: 2.1.3
% 0.18/0.54 % (1179121)Termination reason: Instruction limit
% 0.18/0.54 % (1179121)Termination phase: Saturation
% 0.18/0.54 % (1179121)Time elapsed: 0.066 s
% 0.18/0.54 % (1179121)Peak memory usage: 12 MB
% 0.18/0.54 % (1179121)Instructions burned: 109 (million)
% 0.18/0.54 % (1179122)Instruction limit reached!
% 0.18/0.54 % (1179122)------------------------------
% 0.18/0.54 % (1179122)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.54 % (1179122)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.54 % (1179122)CaDiCaL version: 2.1.3
% 0.18/0.54 % (1179122)Termination reason: Instruction limit
% 0.18/0.54 % (1179122)Termination phase: Saturation
% 0.18/0.54 % (1179122)Time elapsed: 0.067 s
% 0.18/0.54 % (1179122)Peak memory usage: 13 MB
% 0.18/0.54 % (1179122)Instructions burned: 122 (million)
% 0.18/0.54 % (1179124) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1179113-1179124"...
% 0.18/0.54 % TRYING [5]
% 0.18/0.54 % (1179124)...printing done.
% 0.18/0.54 % (1179124)Refutation found. Thanks to Tanya!
% 0.18/0.54 % SZS status Theorem for theBenchmark
% 0.18/0.54 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.55 % (1179124)------------------------------
% 0.18/0.55 % (1179124)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.55 % (1179124)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.55 % (1179124)CaDiCaL version: 2.1.3
% 0.18/0.55 % (1179124)Termination reason: Refutation
% 0.18/0.55 % (1179124)Time elapsed: 0.052 s
% 0.18/0.55 % (1179124)Peak memory usage: 12 MB
% 0.18/0.55 % (1179124)Instructions burned: 51 (million)
% 0.18/0.55 % (1179113)Success in time 0.114 s
% 0.18/0.55 % Vampire exiting
%------------------------------------------------------------------------------