%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU072+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 12:47:11 PM UTC 2026
% Result : Theorem 3.34s 1.37s
% Output : Refutation 4.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 107 ( 16 unt; 6 def)
% Number of atoms : 378 ( 83 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 466 ( 195 ~; 191 |; 51 &)
% ( 18 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 2 con; 0-2 aty)
% Number of variables : 111 ( 0 sgn 96 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f6,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
<=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) )
=> X1 = X2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8_funct_1) ).
fof(f28,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( in(X0,relation_dom(X1))
=> relation_image(X1,singleton(X0)) = singleton(apply(X1,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t117_funct_1) ).
fof(f29,axiom,
! [X0,X1] :
( relation(X1)
=> ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t142_funct_1) ).
fof(f30,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t153_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
=> one_to_one(X0) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f34,axiom,
! [X0,X1] :
( subset(X0,singleton(X1))
<=> ( X0 = empty_set
| X0 = singleton(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t39_zfmisc_1) ).
fof(f39,axiom,
! [X0,X1] :
( subset(singleton(X0),singleton(X1))
=> X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_zfmisc_1) ).
fof(f50,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,[],[f5]) ).
fof(f51,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,[],[f50]) ).
fof(f52,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f53,plain,
! [X0] :
( ( one_to_one(X0)
<=> ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f52]) ).
fof(f61,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f62,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1] :
( ( in(X0,relation_rng(X1))
<=> relation_inverse_image(X1,singleton(X0)) != empty_set )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f29]) ).
fof(f64,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f65,plain,
? [X0] :
( ~ one_to_one(X0)
& ! [X1] : subset(relation_inverse_image(X0,relation_image(X0,X1)),X1)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f64]) ).
fof(f73,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(singleton(X0),singleton(X1)) ),
inference(ennf_transformation,[],[f39]) ).
fof(f76,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,[],[f51]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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))],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f80,plain,
! [X0] :
( ( ( one_to_one(X0)
| ? [X1,X2] :
( X1 != X2
& in(X1,relation_dom(X0))
& in(X2,relation_dom(X0))
& apply(X0,X1) = apply(X0,X2) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f79]) ).
fof(f81,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK3(X0) != sK4(X0)
& in(sK3(X0),relation_dom(X0))
& in(sK4(X0),relation_dom(X0))
& apply(X0,sK3(X0)) = apply(X0,sK4(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X1,sK3(X0)),skolemize(X2,sK4(X0))],[f80]) ).
fof(f93,plain,
! [X0,X1] :
( ( ( in(X0,relation_rng(X1))
| empty_set = relation_inverse_image(X1,singleton(X0)) )
& ( relation_inverse_image(X1,singleton(X0)) != empty_set
| ~ in(X0,relation_rng(X1)) ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f63]) ).
fof(f94,plain,
( ~ one_to_one(sK16)
& ! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1)
& relation(sK16)
& function(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f65]) ).
fof(f95,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(nnf_transformation,[],[f34]) ).
fof(f96,plain,
! [X0,X1] :
( ( subset(X0,singleton(X1))
| ( empty_set != X0
& singleton(X1) != X0 ) )
& ( X0 = empty_set
| X0 = singleton(X1)
| ~ subset(X0,singleton(X1)) ) ),
inference(flattening,[],[f95]) ).
fof(f106,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,[],[f78]) ).
fof(f111,plain,
! [X0] :
( one_to_one(X0)
| apply(X0,sK3(X0)) = apply(X0,sK4(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f112,plain,
! [X0] :
( in(sK4(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f113,plain,
! [X0] :
( in(sK3(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f114,plain,
! [X0] :
( sK3(X0) != sK4(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f81]) ).
fof(f149,plain,
! [X0,X1] :
( relation_image(X1,singleton(X0)) = singleton(apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f150,plain,
! [X0,X1] :
( empty_set != relation_inverse_image(X1,singleton(X0))
| ~ in(X0,relation_rng(X1))
| ~ relation(X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f152,plain,
function(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f153,plain,
relation(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f154,plain,
! [X1] : subset(relation_inverse_image(sK16,relation_image(sK16,X1)),X1),
inference(cnf_transformation,[],[f94]) ).
fof(f155,plain,
~ one_to_one(sK16),
inference(cnf_transformation,[],[f94]) ).
fof(f158,plain,
! [X0,X1] :
( ~ subset(X0,singleton(X1))
| singleton(X1) = X0
| empty_set = X0 ),
inference(cnf_transformation,[],[f96]) ).
fof(f166,plain,
! [X0,X1] :
( ~ subset(singleton(X0),singleton(X1))
| X0 = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f169,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,[],[f106]) ).
fof(f170,plain,
! [X0,X6] :
( in(apply(X0,X6),relation_rng(X0))
| ~ in(X6,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f169]) ).
fof(f215,plain,
( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f111,f155]) ).
fof(f216,plain,
( apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f215,f153]) ).
fof(f217,plain,
apply(sK16,sK3(sK16)) = apply(sK16,sK4(sK16)),
inference(forward_subsumption_resolution,[],[f216,f152]) ).
fof(f218,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(superposition,[],[f170,f217]) ).
fof(f219,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f218,f153]) ).
fof(f220,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ in(sK4(sK16),relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[],[f219,f152]) ).
fof(f222,definition,
( spl17_1
<=> in(sK4(sK16),relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f223,plain,
( in(sK4(sK16),relation_dom(sK16))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f224,plain,
( ~ in(sK4(sK16),relation_dom(sK16))
| spl17_1 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl17_2
<=> in(apply(sK16,sK3(sK16)),relation_rng(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_2])],[avatar_definition]) ).
fof(f228,plain,
( in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ spl17_2 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f229,plain,
( ~ spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f220,f226,f222]) ).
fof(f232,plain,
( one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| spl17_1 ),
inference(resolution,[],[f224,f112]) ).
fof(f233,plain,
( ~ relation(sK16)
| ~ function(sK16)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f232,f155]) ).
fof(f234,plain,
( ~ function(sK16)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f233,f153]) ).
fof(f235,plain,
( $false
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f234,f152]) ).
fof(f236,plain,
spl17_1,
inference(avatar_contradiction_clause,[],[f235]) ).
fof(f238,plain,
! [X0] :
( subset(relation_inverse_image(sK16,singleton(apply(sK16,X0))),singleton(X0))
| ~ in(X0,relation_dom(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(superposition,[],[f154,f149]) ).
fof(f239,plain,
! [X0] :
( subset(relation_inverse_image(sK16,singleton(apply(sK16,X0))),singleton(X0))
| ~ in(X0,relation_dom(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f238,f153]) ).
fof(f241,plain,
! [X0] :
( subset(relation_inverse_image(sK16,singleton(apply(sK16,X0))),singleton(X0))
| ~ in(X0,relation_dom(sK16)) ),
inference(forward_subsumption_resolution,[],[f239,f152]) ).
fof(f265,plain,
( subset(relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))),singleton(sK4(sK16)))
| ~ in(sK4(sK16),relation_dom(sK16)) ),
inference(superposition,[],[f241,f217]) ).
fof(f270,plain,
( subset(relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))),singleton(sK4(sK16)))
| ~ spl17_1 ),
inference(forward_subsumption_resolution,[],[f265,f223]) ).
fof(f275,plain,
( singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_1 ),
inference(resolution,[],[f270,f158]) ).
fof(f277,definition,
( spl17_3
<=> empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f279,plain,
( empty_set = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f281,definition,
( spl17_4
<=> singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16)))) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f283,plain,
( singleton(sK4(sK16)) = relation_inverse_image(sK16,singleton(apply(sK16,sK3(sK16))))
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f284,plain,
( spl17_3
| spl17_4
| ~ spl17_1 ),
inference(avatar_split_clause,[],[f275,f222,f281,f277]) ).
fof(f286,plain,
( subset(singleton(sK4(sK16)),singleton(sK3(sK16)))
| ~ in(sK3(sK16),relation_dom(sK16))
| ~ spl17_4 ),
inference(superposition,[],[f241,f283]) ).
fof(f290,definition,
( spl17_5
<=> in(sK3(sK16),relation_dom(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f292,plain,
( ~ in(sK3(sK16),relation_dom(sK16))
| spl17_5 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f294,definition,
( spl17_6
<=> subset(singleton(sK4(sK16)),singleton(sK3(sK16))) ),
introduced(definition,[new_symbols(definition,[spl17_6])],[avatar_definition]) ).
fof(f296,plain,
( subset(singleton(sK4(sK16)),singleton(sK3(sK16)))
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f294]) ).
fof(f297,plain,
( ~ spl17_5
| spl17_6
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f286,f281,f294,f290]) ).
fof(f311,plain,
( one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| spl17_5 ),
inference(resolution,[],[f292,f113]) ).
fof(f312,plain,
( ~ relation(sK16)
| ~ function(sK16)
| spl17_5 ),
inference(forward_subsumption_resolution,[],[f311,f155]) ).
fof(f313,plain,
( ~ function(sK16)
| spl17_5 ),
inference(forward_subsumption_resolution,[],[f312,f153]) ).
fof(f314,plain,
( $false
| spl17_5 ),
inference(forward_subsumption_resolution,[],[f313,f152]) ).
fof(f315,plain,
spl17_5,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f350,plain,
( sK3(sK16) = sK4(sK16)
| ~ spl17_6 ),
inference(resolution,[],[f296,f166]) ).
fof(f366,plain,
( sK3(sK16) != sK3(sK16)
| one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_6 ),
inference(superposition,[],[f114,f350]) ).
fof(f368,plain,
( one_to_one(sK16)
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_6 ),
inference(trivial_inequality_removal,[],[f366]) ).
fof(f369,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f368,f155]) ).
fof(f371,plain,
( ~ function(sK16)
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f369,f153]) ).
fof(f372,plain,
( $false
| ~ spl17_6 ),
inference(forward_subsumption_resolution,[],[f371,f152]) ).
fof(f373,plain,
~ spl17_6,
inference(avatar_contradiction_clause,[],[f372]) ).
fof(f404,plain,
( empty_set != empty_set
| ~ in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ relation(sK16)
| ~ spl17_3 ),
inference(superposition,[],[f150,f279]) ).
fof(f405,plain,
( ~ in(apply(sK16,sK3(sK16)),relation_rng(sK16))
| ~ relation(sK16)
| ~ spl17_3 ),
inference(trivial_inequality_removal,[],[f404]) ).
fof(f406,plain,
( ~ relation(sK16)
| ~ spl17_2
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f405,f228]) ).
fof(f407,plain,
( $false
| ~ spl17_2
| ~ spl17_3 ),
inference(forward_subsumption_resolution,[],[f406,f153]) ).
fof(f408,plain,
( ~ spl17_2
| ~ spl17_3 ),
inference(avatar_contradiction_clause,[],[f407]) ).
cnf(s1,plain,
( ~ spl17_1
| spl17_2 ),
inference(sat_conversion,[],[f229]) ).
cnf(s2,plain,
spl17_1,
inference(sat_conversion,[],[f236]) ).
cnf(s3,plain,
( ~ spl17_1
| spl17_3
| spl17_4 ),
inference(sat_conversion,[],[f284]) ).
cnf(s4,plain,
( ~ spl17_4
| ~ spl17_5
| spl17_6 ),
inference(sat_conversion,[],[f297]) ).
cnf(s5,plain,
spl17_5,
inference(sat_conversion,[],[f315]) ).
cnf(s8,plain,
~ spl17_6,
inference(sat_conversion,[],[f373]) ).
cnf(s9,plain,
( ~ spl17_2
| ~ spl17_3 ),
inference(sat_conversion,[],[f408]) ).
cnf(s10,plain,
~ spl17_4,
inference(rat,[],[s4,s8,s5]) ).
cnf(s11,plain,
( ~ spl17_1
| spl17_3 ),
inference(rat,[],[s3,s10]) ).
cnf(s12,plain,
spl17_3,
inference(rat,[],[s11,s2]) ).
cnf(s13,plain,
~ spl17_2,
inference(rat,[],[s9,s12]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s1,s13,s2]) ).
fof(f409,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU072+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n020.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 03:30:49 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 3.34/1.37 % (3999697)Detected formulas, will run a generic FOF schedule.
% 3.34/1.37 % (3999798)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=3716298705:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.34/1.37 % (3999797)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=3468687994:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.34/1.37 % (3999796)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=1017251708:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.34/1.37 % (3999799)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2710312367:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.34/1.37 % (3999800)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2430947707:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.34/1.37 % (3999799)Refutation not found, incomplete strategy
% 3.34/1.37 % (3999799)------------------------------
% 3.34/1.37 % (3999799)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.37 % (3999799)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.37 % (3999799)CaDiCaL version: 2.1.3
% 3.34/1.37 % (3999799)Termination reason: Refutation not found, incomplete strategy
% 3.34/1.37 % (3999799)Time elapsed: 0.003 s
% 3.34/1.37 % (3999799)Peak memory usage: 88 MB
% 3.34/1.37 % (3999799)Instructions burned: 2 (million)
% 3.34/1.37 % (3999802)dis-21_1_sil=8000:lcm=predicate:random_seed=4229952695: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)
% 3.34/1.37 % (3999801)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=654042403:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.34/1.37 % (3999801)First to succeed.
% 3.34/1.37 % (3999801)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3999697"
% 3.34/1.37 % (3999800)Also succeeded, but the first one will report.
% 3.34/1.37 % (3999802)Instruction limit reached!
% 3.34/1.37 % (3999802)------------------------------
% 3.34/1.37 % (3999802)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.34/1.37 % (3999802)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.34/1.37 % (3999802)CaDiCaL version: 2.1.3
% 3.34/1.37 % (3999802)Termination reason: Instruction limit
% 3.34/1.37 % (3999802)Termination phase: Saturation
% 3.34/1.37 % (3999802)Time elapsed: 0.094 s
% 3.34/1.37 % (3999802)Peak memory usage: 90 MB
% 3.34/1.37 % (3999802)Instructions burned: 129 (million)
% 3.34/1.37 % (3999799)------------------------------
% 3.34/1.37 % (3999799)------------------------------
% 3.34/1.37 % (3999801)Refutation found. Thanks to Tanya!
% 3.34/1.37 % SZS status Theorem for theBenchmark
% 3.34/1.37 % SZS output start Proof for theBenchmark
% See solution above
% 4.13/1.57 % (3999801)------------------------------
% 4.13/1.57 % (3999801)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.13/1.57 % (3999801)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.13/1.57 % (3999801)CaDiCaL version: 2.1.3
% 4.13/1.57 % (3999801)Termination reason: Refutation
% 4.13/1.57 % (3999801)Time elapsed: 0.013 s
% 4.13/1.57 % (3999801)Peak memory usage: 89 MB
% 4.13/1.57 % (3999801)Instructions burned: 16 (million)
% 4.13/1.57 % (3999801)------------------------------
% 4.13/1.57 % (3999801)------------------------------
% 4.13/1.57 % (3999697)Success in time 0.498 s
% 4.13/1.57 % Vampire exiting
%------------------------------------------------------------------------------