%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:51:46 PM UTC 2026
% Result : Theorem 0.07s 0.35s
% Output : Refutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 14 unt; 4 def)
% Number of atoms : 391 ( 44 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 512 ( 217 ~; 212 |; 56 &)
% ( 13 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 110 ( 0 sgn 95 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f5,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f9,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t21_funct_1) ).
fof(f29,axiom,
! [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/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f30,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_rng(relation_composition(X2,X1)))
=> in(X0,relation_rng(X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t25_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_rng(relation_composition(X2,X1)))
=> in(X0,relation_rng(X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f46,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( X1 = relation_rng(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f48]) ).
fof(f52,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f53,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f52]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f65,plain,
! [X0,X1] :
( ! [X2] :
( ( in(X0,relation_dom(relation_composition(X2,X1)))
<=> ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f64]) ).
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,[],[f29]) ).
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(f68,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X0,relation_rng(X1))
& in(X0,relation_rng(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f31]) ).
fof(f69,plain,
? [X0,X1] :
( ? [X2] :
( ~ in(X0,relation_rng(X1))
& in(X0,relation_rng(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f68]) ).
fof(f79,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) )
& ( ? [X3] :
( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ? [X2] :
( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
| ~ in(X2,X1) )
& ( ? [X4] :
( in(X4,relation_dom(X0))
& apply(X0,X4) = X2 )
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ? [X7] :
( in(X7,relation_dom(X0))
& apply(X0,X7) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_rng(X0)
| ( ( ! [X3] :
( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != sK0(X0,X1) )
| ~ in(sK0(X0,X1),X1) )
& ( ( in(sK1(X0,X1),relation_dom(X0))
& sK0(X0,X1) = apply(X0,sK1(X0,X1)) )
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] :
( ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5 ) )
& ( ( in(sK2(X0,X5),relation_dom(X0))
& apply(X0,sK2(X0,X5)) = X5 )
| ~ in(X5,X1) ) )
| relation_rng(X0) != X1 ) )
| ~ relation(X0)
| ~ function(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))],[f80]) ).
fof(f91,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1)) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f65]) ).
fof(f92,plain,
! [X0,X1] :
( ! [X2] :
( ( ( in(X0,relation_dom(relation_composition(X2,X1)))
| ~ in(X0,relation_dom(X2))
| ~ in(apply(X2,X0),relation_dom(X1)) )
& ( ( in(X0,relation_dom(X2))
& in(apply(X2,X0),relation_dom(X1)) )
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ) )
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f91]) ).
fof(f93,plain,
( ~ in(sK12,relation_rng(sK13))
& in(sK12,relation_rng(relation_composition(sK14,sK13)))
& relation(sK14)
& function(sK14)
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13,sK14]),skolemize(X0,sK12),skolemize(X1,sK13),skolemize(X2,sK14)],[f69]) ).
fof(f97,plain,
! [X0,X1,X5] :
( apply(X0,sK2(X0,X5)) = X5
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f98,plain,
! [X0,X1,X5] :
( in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,X1)
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f99,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(X6,relation_dom(X0))
| apply(X0,X6) != X5
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f103,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f109,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f53]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| in(apply(X2,X0),relation_dom(X1))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0))
| ~ relation(X2)
| ~ function(X2)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f67]) ).
fof(f142,plain,
function(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f143,plain,
relation(sK13),
inference(cnf_transformation,[],[f93]) ).
fof(f144,plain,
function(sK14),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
relation(sK14),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
in(sK12,relation_rng(relation_composition(sK14,sK13))),
inference(cnf_transformation,[],[f93]) ).
fof(f147,plain,
~ in(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f93]) ).
fof(f155,plain,
! [X0,X1,X6] :
( in(apply(X0,X6),X1)
| ~ in(X6,relation_dom(X0))
| relation_rng(X0) != X1
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f156,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X0,X5] :
( in(sK2(X0,X5),relation_dom(X0))
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f158,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| apply(X0,sK2(X0,X5)) = X5
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f97]) ).
fof(f274,plain,
( sK12 = apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12))
| ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13)) ),
inference(resolution,[],[f158,f146]) ).
fof(f278,definition,
( spl15_3
<=> function(relation_composition(sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f279,plain,
( function(relation_composition(sK14,sK13))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f280,plain,
( ~ function(relation_composition(sK14,sK13))
| spl15_3 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f282,definition,
( spl15_4
<=> relation(relation_composition(sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f283,plain,
( relation(relation_composition(sK14,sK13))
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f284,plain,
( ~ relation(relation_composition(sK14,sK13))
| spl15_4 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f286,definition,
( spl15_5
<=> sK12 = apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) ),
introduced(definition,[new_symbols(definition,[spl15_5])],[avatar_definition]) ).
fof(f288,plain,
( sK12 = apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12))
| ~ spl15_5 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f289,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5 ),
inference(avatar_split_clause,[],[f274,f286,f282,f278]) ).
fof(f290,plain,
( ~ relation(sK14)
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| spl15_3 ),
inference(resolution,[],[f280,f109]) ).
fof(f291,plain,
( ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f290,f145]) ).
fof(f292,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f291,f144]) ).
fof(f293,plain,
( ~ function(sK13)
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f292,f143]) ).
fof(f294,plain,
( $false
| spl15_3 ),
inference(forward_subsumption_resolution,[],[f293,f142]) ).
fof(f295,plain,
spl15_3,
inference(avatar_contradiction_clause,[],[f294]) ).
fof(f312,plain,
( ~ relation(sK14)
| ~ relation(sK13)
| spl15_4 ),
inference(resolution,[],[f284,f103]) ).
fof(f313,plain,
( ~ relation(sK13)
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f312,f145]) ).
fof(f314,plain,
( $false
| spl15_4 ),
inference(forward_subsumption_resolution,[],[f313,f143]) ).
fof(f315,plain,
spl15_4,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f335,definition,
( spl15_6
<=> in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13))) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f336,plain,
( in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13)))
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f337,plain,
( ~ in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13)))
| spl15_6 ),
inference(avatar_component_clause,[],[f335]) ).
fof(f342,plain,
( ~ in(sK12,relation_rng(relation_composition(sK14,sK13)))
| ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13))
| spl15_6 ),
inference(resolution,[],[f337,f157]) ).
fof(f343,plain,
( ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13))
| spl15_6 ),
inference(forward_subsumption_resolution,[],[f342,f146]) ).
fof(f344,plain,
( ~ function(relation_composition(sK14,sK13))
| ~ spl15_4
| spl15_6 ),
inference(forward_subsumption_resolution,[],[f343,f283]) ).
fof(f345,plain,
( $false
| ~ spl15_3
| ~ spl15_4
| spl15_6 ),
inference(forward_subsumption_resolution,[],[f344,f279]) ).
fof(f346,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_6 ),
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f354,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK14)
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(resolution,[],[f336,f138]) ).
fof(f360,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f354,f145]) ).
fof(f362,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f360,f144]) ).
fof(f364,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f362,f143]) ).
fof(f366,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f364,f142]) ).
fof(f371,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ relation(sK14)
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(resolution,[],[f141,f336]) ).
fof(f372,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f371,f145]) ).
fof(f375,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f372,f144]) ).
fof(f378,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ function(sK13)
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f375,f143]) ).
fof(f379,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f378,f142]) ).
fof(f380,plain,
( sK12 = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ spl15_5
| ~ spl15_6 ),
inference(forward_demodulation,[],[f379,f288]) ).
fof(f454,plain,
( in(sK12,relation_rng(sK13))
| ~ in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_5
| ~ spl15_6 ),
inference(superposition,[],[f156,f380]) ).
fof(f455,plain,
( ~ in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_5
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f454,f147]) ).
fof(f458,plain,
( ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_5
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f455,f366]) ).
fof(f461,plain,
( ~ function(sK13)
| ~ spl15_5
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f458,f143]) ).
fof(f464,plain,
( $false
| ~ spl15_5
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f461,f142]) ).
fof(f465,plain,
( ~ spl15_5
| ~ spl15_6 ),
inference(avatar_contradiction_clause,[],[f464]) ).
cnf(s3,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_5 ),
inference(sat_conversion,[],[f289]) ).
cnf(s4,plain,
spl15_3,
inference(sat_conversion,[],[f295]) ).
cnf(s5,plain,
spl15_4,
inference(sat_conversion,[],[f315]) ).
cnf(s7,plain,
( ~ spl15_3
| ~ spl15_4
| spl15_6 ),
inference(sat_conversion,[],[f346]) ).
cnf(s9,plain,
( ~ spl15_5
| ~ spl15_6 ),
inference(sat_conversion,[],[f465]) ).
cnf(s10,plain,
spl15_6,
inference(rat,[],[s7,s5,s4]) ).
cnf(s11,plain,
~ spl15_5,
inference(rat,[],[s9,s10]) ).
cnf(s12,plain,
$false,
inference(rat,[],[s3,s11,s5,s4]) ).
fof(f466,plain,
$false,
inference(avatar_sat_refutation,[],[s12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Mon Sep 28 03:21:49 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.03/0.32 Running first-order model finding
% 0.03/0.32 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % (2986996)Will run a generic schedule for satisfiability detection.
% 0.07/0.35 % (2987002)% WARNING: option uhcvi not known.
% 0.07/0.35 % (2987002)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=980879014:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.07/0.35 % (2987004)dis+10_1_sil=32000:sp=arity:random_seed=541623840:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.07/0.35 % (2987001)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3567839844_2999 on theBenchmark for (2999ds/0Mi)
% 0.07/0.35 % (2987007)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2871554120:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.07/0.35 % (2987003)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1945316527:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.07/0.35 % (2987006)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3084244611:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.07/0.35 % (2987005)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3295894877:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.07/0.35 % TRYING [1]
% 0.07/0.35 % TRYING [2]
% 0.07/0.35 % TRYING [3]
% 0.07/0.35 % TRYING [4]
% 0.07/0.35 % (2987004) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2986996-2987004"...
% 0.07/0.35 % (2987004)...printing done.
% 0.07/0.35 % (2987004)Refutation found. Thanks to Tanya!
% 0.07/0.35 % SZS status Theorem for theBenchmark
% 0.07/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.07/0.35 % (2987004)------------------------------
% 0.07/0.35 % (2987004)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.07/0.35 % (2987004)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.07/0.35 % (2987004)CaDiCaL version: 2.1.3
% 0.07/0.35 % (2987004)Termination reason: Refutation
% 0.07/0.35 % (2987004)Time elapsed: 0.007 s
% 0.07/0.35 % (2987004)Peak memory usage: 12 MB
% 0.07/0.35 % (2987004)Instructions burned: 16 (million)
% 0.07/0.35 % (2986996)Success in time 0.03 s
% 0.07/0.35 % Vampire exiting
%------------------------------------------------------------------------------