%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU214+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 12:47:47 PM UTC 2026
% Result : Theorem 2.01s 1.30s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 9
% Syntax : Number of formulae : 85 ( 15 unt; 3 def)
% Number of atoms : 361 ( 47 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 461 ( 185 ~; 185 |; 59 &)
% ( 17 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 154 ( 0 sgn 130 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,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(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f13,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f33,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f34,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f33]) ).
fof(f49,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f50,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f49]) ).
fof(f51,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f57]) ).
fof(f66,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f67,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f66]) ).
fof(f77,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f78,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,[],[f51]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f52]) ).
fof(f82,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK4(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0)
& in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1) )
| in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X10,sK6(X0,X1,X7,X8))],[f82]) ).
fof(f93,plain,
( apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16))
& in(sK16,relation_dom(relation_composition(sK18,sK17)))
& relation(sK18)
& function(sK18)
& relation(sK17)
& function(sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X0,sK16),skolemize(X1,sK17),skolemize(X2,sK18)],[f67]) ).
fof(f100,plain,
! [X2,X0,X1] :
( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f101,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f103,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f107,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f108,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f83]) ).
fof(f113,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f119,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f148,plain,
function(sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
relation(sK17),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
function(sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
relation(sK18),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
in(sK16,relation_dom(relation_composition(sK18,sK17))),
inference(cnf_transformation,[],[f93]) ).
fof(f153,plain,
apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16)),
inference(cnf_transformation,[],[f93]) ).
fof(f161,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,apply(X0,X1)),X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f100]) ).
fof(f164,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f103]) ).
fof(f167,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f108]) ).
fof(f168,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f107]) ).
fof(f217,definition,
( spl19_1
<=> relation(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f219,plain,
( ~ relation(relation_composition(sK18,sK17))
| spl19_1 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f227,plain,
( ~ relation(sK18)
| ~ relation(sK17)
| spl19_1 ),
inference(resolution,[],[f219,f113]) ).
fof(f229,plain,
( ~ relation(sK17)
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f227,f151]) ).
fof(f230,plain,
( $false
| spl19_1 ),
inference(forward_subsumption_resolution,[],[f229,f149]) ).
fof(f231,plain,
spl19_1,
inference(avatar_contradiction_clause,[],[f230]) ).
fof(f232,plain,
( in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| ~ function(relation_composition(sK18,sK17)) ),
inference(resolution,[],[f161,f152]) ).
fof(f234,definition,
( spl19_3
<=> function(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f236,plain,
( ~ function(relation_composition(sK18,sK17))
| spl19_3 ),
inference(avatar_component_clause,[],[f234]) ).
fof(f238,definition,
( spl19_4
<=> in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f240,plain,
( in(ordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16)),relation_composition(sK18,sK17))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f241,plain,
( ~ spl19_3
| ~ spl19_1
| spl19_4 ),
inference(avatar_split_clause,[],[f232,f238,f217,f234]) ).
fof(f242,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f101,f164]) ).
fof(f243,plain,
( ~ relation(sK18)
| ~ function(sK18)
| ~ relation(sK17)
| ~ function(sK17)
| spl19_3 ),
inference(resolution,[],[f236,f119]) ).
fof(f245,plain,
( ~ function(sK18)
| ~ relation(sK17)
| ~ function(sK17)
| spl19_3 ),
inference(forward_subsumption_resolution,[],[f243,f151]) ).
fof(f246,plain,
( ~ relation(sK17)
| ~ function(sK17)
| spl19_3 ),
inference(forward_subsumption_resolution,[],[f245,f150]) ).
fof(f247,plain,
( ~ function(sK17)
| spl19_3 ),
inference(forward_subsumption_resolution,[],[f246,f149]) ).
fof(f248,plain,
( $false
| spl19_3 ),
inference(forward_subsumption_resolution,[],[f247,f148]) ).
fof(f249,plain,
spl19_3,
inference(avatar_contradiction_clause,[],[f248]) ).
fof(f267,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f167,f113]) ).
fof(f271,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ spl19_4 ),
inference(resolution,[],[f240,f267]) ).
fof(f279,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ relation(sK18)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f271,f149]) ).
fof(f280,plain,
( in(ordered_pair(sK16,sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),sK18)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f279,f151]) ).
fof(f281,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f168,f113]) ).
fof(f283,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ relation(sK17)
| ~ relation(sK18)
| ~ spl19_4 ),
inference(resolution,[],[f281,f240]) ).
fof(f284,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ relation(sK18)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f283,f149]) ).
fof(f286,plain,
( in(ordered_pair(sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f284,f151]) ).
fof(f335,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ relation(sK18)
| ~ function(sK18)
| ~ spl19_4 ),
inference(resolution,[],[f280,f242]) ).
fof(f343,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ function(sK18)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f335,f151]) ).
fof(f345,plain,
( apply(sK18,sK16) = sK6(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f343,f150]) ).
fof(f598,plain,
( in(ordered_pair(apply(sK18,sK16),apply(relation_composition(sK18,sK17),sK16)),sK17)
| ~ spl19_4 ),
inference(forward_demodulation,[],[f286,f345]) ).
fof(f605,plain,
( apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16))
| ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_4 ),
inference(resolution,[],[f598,f242]) ).
fof(f614,plain,
( ~ relation(sK17)
| ~ function(sK17)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f605,f153]) ).
fof(f616,plain,
( ~ function(sK17)
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f614,f149]) ).
fof(f617,plain,
( $false
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f616,f148]) ).
fof(f618,plain,
~ spl19_4,
inference(avatar_contradiction_clause,[],[f617]) ).
cnf(s2,plain,
spl19_1,
inference(sat_conversion,[],[f231]) ).
cnf(s3,plain,
( ~ spl19_1
| ~ spl19_3
| spl19_4 ),
inference(sat_conversion,[],[f241]) ).
cnf(s4,plain,
spl19_3,
inference(sat_conversion,[],[f249]) ).
cnf(s8,plain,
~ spl19_4,
inference(sat_conversion,[],[f618]) ).
cnf(s9,plain,
~ spl19_1,
inference(rat,[],[s3,s8,s4]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s2,s9]) ).
fof(f619,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU214+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n010.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:05:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.01/1.30 % (1545480)Detected formulas, will run a generic FOF schedule.
% 2.01/1.30 % (1545491)dis-21_1_sil=8000:lcm=predicate:random_seed=179502864: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)
% 2.01/1.30 % (1545488)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3286926646:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.01/1.30 % (1545488)Refutation not found, incomplete strategy
% 2.01/1.30 % (1545488)------------------------------
% 2.01/1.30 % (1545488)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1545488)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1545488)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1545488)Termination reason: Refutation not found, incomplete strategy
% 2.01/1.30 % (1545488)Time elapsed: 0.003 s
% 2.01/1.30 % (1545488)Peak memory usage: 88 MB
% 2.01/1.30 % (1545488)Instructions burned: 3 (million)
% 2.01/1.30 % (1545485)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=1371734667:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.01/1.30 % (1545486)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=3435644785:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.01/1.30 % (1545487)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=1241072733:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.01/1.30 % (1545489)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=457501969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.01/1.30 % (1545490)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=798494862:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.01/1.30 % (1545491)Instruction limit reached!
% 2.01/1.30 % (1545491)------------------------------
% 2.01/1.30 % (1545491)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1545491)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1545491)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1545491)Termination reason: Instruction limit
% 2.01/1.30 % (1545491)Termination phase: Saturation
% 2.01/1.30 % (1545491)Time elapsed: 0.049 s
% 2.01/1.30 % (1545491)Peak memory usage: 90 MB
% 2.01/1.30 % (1545491)Instructions burned: 131 (million)
% 2.01/1.30 % (1545490)First to succeed.
% 2.01/1.30 % (1545490)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1545480"
% 2.01/1.30 % (1545489)Instruction limit reached!
% 2.01/1.30 % (1545489)------------------------------
% 2.01/1.30 % (1545489)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1545489)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1545489)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1545489)Termination reason: Instruction limit
% 2.01/1.30 % (1545489)Termination phase: Saturation
% 2.01/1.30 % (1545489)Time elapsed: 0.066 s
% 2.01/1.30 % (1545489)Peak memory usage: 88 MB
% 2.01/1.30 % (1545489)Instructions burned: 120 (million)
% 2.01/1.30 % (1545499)lrs+10_1_sil=8000:sp=occurrence:random_seed=3374757692:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.01/1.30 % (1545499)Instruction limit reached!
% 2.01/1.30 % (1545499)------------------------------
% 2.01/1.30 % (1545499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.01/1.30 % (1545499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.01/1.30 % (1545499)CaDiCaL version: 2.1.3
% 2.01/1.30 % (1545499)Termination reason: Instruction limit
% 2.01/1.30 % (1545499)Termination phase: Saturation
% 2.01/1.30 % (1545499)Time elapsed: 0.089 s
% 2.01/1.30 % (1545499)Peak memory usage: 91 MB
% 2.01/1.30 % (1545499)Instructions burned: 285 (million)
% 2.01/1.30 % (1545500)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3584637418:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.01/1.30 % (1545488)------------------------------
% 2.01/1.30 % (1545488)------------------------------
% 2.01/1.30 % (1545490)Refutation found. Thanks to Tanya!
% 2.01/1.30 % SZS status Theorem for theBenchmark
% 2.01/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.50 % (1545490)------------------------------
% 0.17/1.50 % (1545490)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.50 % (1545490)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.50 % (1545490)CaDiCaL version: 2.1.3
% 0.17/1.50 % (1545490)Termination reason: Refutation
% 0.17/1.50 % (1545490)Time elapsed: 0.022 s
% 0.17/1.50 % (1545490)Peak memory usage: 90 MB
% 0.17/1.50 % (1545490)Instructions burned: 28 (million)
% 0.17/1.50 % (1545490)------------------------------
% 0.17/1.50 % (1545490)------------------------------
% 0.17/1.50 % (1545480)Success in time 0.437 s
% 0.17/1.50 % Vampire exiting
%------------------------------------------------------------------------------