%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU002+1 : 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 : n020.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 12:47:02 PM UTC 2026
% Result : Theorem 2.86s 1.27s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 89 ( 13 unt; 3 def)
% Number of atoms : 376 ( 44 equ)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 495 ( 208 ~; 205 |; 56 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 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/sandbox/benchmark/theBenchmark.p',d5_funct_1) ).
fof(f5,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(X6,relation_dom(X0))
| in(apply(X0,X6),relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f155]) ).
fof(f157,plain,
! [X0,X5] :
( ~ in(X5,relation_rng(X0))
| in(sK2(X0,X5),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f158,plain,
! [X0,X5] :
( apply(X0,sK2(X0,X5)) = X5
| ~ in(X5,relation_rng(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f97]) ).
fof(f188,plain,
( in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13)))
| ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13)) ),
inference(resolution,[],[f157,f146]) ).
fof(f190,definition,
( spl15_1
<=> function(relation_composition(sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f191,plain,
( function(relation_composition(sK14,sK13))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f192,plain,
( ~ function(relation_composition(sK14,sK13))
| spl15_1 ),
inference(avatar_component_clause,[],[f190]) ).
fof(f194,definition,
( spl15_2
<=> relation(relation_composition(sK14,sK13)) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f195,plain,
( relation(relation_composition(sK14,sK13))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f196,plain,
( ~ relation(relation_composition(sK14,sK13))
| spl15_2 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f198,definition,
( spl15_3
<=> in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13))) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f200,plain,
( in(sK2(relation_composition(sK14,sK13),sK12),relation_dom(relation_composition(sK14,sK13)))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f201,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f188,f198,f194,f190]) ).
fof(f202,plain,
( ~ relation(sK14)
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| spl15_1 ),
inference(resolution,[],[f192,f109]) ).
fof(f204,plain,
( ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f202,f145]) ).
fof(f205,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f204,f144]) ).
fof(f206,plain,
( ~ function(sK13)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f205,f143]) ).
fof(f207,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f206,f142]) ).
fof(f208,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f211,plain,
( ~ relation(sK14)
| ~ relation(sK13)
| spl15_2 ),
inference(resolution,[],[f196,f103]) ).
fof(f213,plain,
( ~ relation(sK13)
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f211,f145]) ).
fof(f214,plain,
( $false
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f213,f143]) ).
fof(f215,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f214]) ).
fof(f228,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK14)
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_3 ),
inference(resolution,[],[f200,f138]) ).
fof(f237,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ function(sK14)
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f228,f145]) ).
fof(f240,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f237,f144]) ).
fof(f242,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ function(sK13)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f240,f143]) ).
fof(f244,plain,
( in(apply(sK14,sK2(relation_composition(sK14,sK13),sK12)),relation_dom(sK13))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f242,f142]) ).
fof(f262,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_3 ),
inference(resolution,[],[f141,f200]) ).
fof(f263,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_3 ),
inference(forward_subsumption_resolution,[],[f262,f145]) ).
fof(f265,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_3 ),
inference(forward_subsumption_resolution,[],[f263,f144]) ).
fof(f267,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_3 ),
inference(forward_subsumption_resolution,[],[f265,f143]) ).
fof(f268,plain,
( apply(relation_composition(sK14,sK13),sK2(relation_composition(sK14,sK13),sK12)) = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f267,f142]) ).
fof(f290,plain,
( in(apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12))),relation_rng(sK13))
| ~ relation(sK13)
| ~ function(sK13)
| ~ spl15_3 ),
inference(resolution,[],[f244,f156]) ).
fof(f295,plain,
( in(apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12))),relation_rng(sK13))
| ~ function(sK13)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f290,f143]) ).
fof(f296,plain,
( in(apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12))),relation_rng(sK13))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f295,f142]) ).
fof(f384,plain,
( sK12 = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ in(sK12,relation_rng(relation_composition(sK14,sK13)))
| ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13))
| ~ spl15_3 ),
inference(superposition,[],[f158,f268]) ).
fof(f387,plain,
( sK12 = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ relation(relation_composition(sK14,sK13))
| ~ function(relation_composition(sK14,sK13))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f384,f146]) ).
fof(f390,plain,
( sK12 = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ function(relation_composition(sK14,sK13))
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f387,f195]) ).
fof(f393,plain,
( sK12 = apply(sK13,apply(sK14,sK2(relation_composition(sK14,sK13),sK12)))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f390,f191]) ).
fof(f406,plain,
( in(sK12,relation_rng(sK13))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_demodulation,[],[f296,f393]) ).
fof(f407,plain,
( $false
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f406,f147]) ).
fof(f408,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(avatar_contradiction_clause,[],[f407]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f201]) ).
cnf(s2,plain,
spl15_1,
inference(sat_conversion,[],[f208]) ).
cnf(s3,plain,
spl15_2,
inference(sat_conversion,[],[f215]) ).
cnf(s4,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(sat_conversion,[],[f408]) ).
cnf(s5,plain,
~ spl15_3,
inference(rat,[],[s4,s3,s2]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s5,s3,s2]) ).
fof(f409,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU002+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n020.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 28 03:23:04 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 2.86/1.27 % (3996379)Detected formulas, will run a generic FOF schedule.
% 2.86/1.27 % (3996386)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=2383622136:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/1.27 % (3996390)dis-21_1_sil=8000:lcm=predicate:random_seed=3912643086: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)
% 2.86/1.27 % (3996387)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=393337823:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/1.27 % (3996385)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=238069567:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/1.27 % (3996388)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3941719063:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/1.27 % (3996384)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=1947636187:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/1.27 % (3996389)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2779435489:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/1.27 % (3996388)Refutation not found, incomplete strategy
% 2.86/1.27 % (3996388)------------------------------
% 2.86/1.27 % (3996388)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.27 % (3996387)Refutation not found, incomplete strategy
% 2.86/1.27 % (3996387)------------------------------
% 2.86/1.27 % (3996387)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.27 % (3996388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.27 % (3996388)CaDiCaL version: 2.1.3
% 2.86/1.27 % (3996387)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.27 % (3996388)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.27 % (3996388)Time elapsed: 0.002 s
% 2.86/1.27 % (3996388)Peak memory usage: 87 MB
% 2.86/1.27 % (3996387)CaDiCaL version: 2.1.3
% 2.86/1.27 % (3996388)Instructions burned: 1 (million)
% 2.86/1.27 % (3996387)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.27 % (3996387)Time elapsed: 0.002 s
% 2.86/1.27 % (3996387)Peak memory usage: 88 MB
% 2.86/1.27 % (3996387)Instructions burned: 1 (million)
% 2.86/1.27 % (3996389)First to succeed.
% 2.86/1.27 % (3996389)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3996379"
% 2.86/1.27 % (3996390)Instruction limit reached!
% 2.86/1.27 % (3996390)------------------------------
% 2.86/1.27 % (3996390)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.27 % (3996390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.27 % (3996390)CaDiCaL version: 2.1.3
% 2.86/1.27 % (3996390)Termination reason: Instruction limit
% 2.86/1.27 % (3996390)Termination phase: Saturation
% 2.86/1.27 % (3996390)Time elapsed: 0.080 s
% 2.86/1.27 % (3996390)Peak memory usage: 90 MB
% 2.86/1.27 % (3996390)Instructions burned: 130 (million)
% 2.86/1.27 % (3996387)------------------------------
% 2.86/1.27 % (3996387)------------------------------
% 2.86/1.27 % (3996388)------------------------------
% 2.86/1.27 % (3996388)------------------------------
% 2.86/1.27 % (3996398)lrs+10_1_sil=8000:sp=occurrence:random_seed=67727089:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.86/1.27 % (3996389)Refutation found. Thanks to Tanya!
% 2.86/1.27 % SZS status Theorem for theBenchmark
% 2.86/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.46 % (3996389)------------------------------
% 3.64/1.46 % (3996389)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.46 % (3996389)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.46 % (3996389)CaDiCaL version: 2.1.3
% 3.64/1.46 % (3996389)Termination reason: Refutation
% 3.64/1.46 % (3996389)Time elapsed: 0.015 s
% 3.64/1.46 % (3996389)Peak memory usage: 89 MB
% 3.64/1.46 % (3996389)Instructions burned: 19 (million)
% 3.64/1.46 % (3996389)------------------------------
% 3.64/1.46 % (3996389)------------------------------
% 3.64/1.46 % (3996379)Success in time 0.434 s
% 3.64/1.46 % Vampire exiting
%------------------------------------------------------------------------------