%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 3.14s 1.32s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 12
% Syntax : Number of formulae : 113 ( 12 unt; 5 def)
% Number of atoms : 504 ( 146 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 636 ( 245 ~; 291 |; 69 &)
% ( 20 <=>; 9 =>; 0 <=; 2 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-2 aty)
% Number of variables : 134 ( 0 sgn 115 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_relat_1) ).
fof(f6,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(f15,axiom,
! [X0] : relation(identity_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k6_relat_1) ).
fof(f21,axiom,
! [X0] :
( relation(identity_relation(X0))
& function(identity_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_funct_1) ).
fof(f37,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t34_funct_1) ).
fof(f38,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = identity_relation(X0)
<=> ( relation_dom(X1) = X0
& ! [X2] :
( in(X2,X0)
=> apply(X1,X2) = X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f37]) ).
fof(f40,axiom,
! [X0] :
( relation_dom(identity_relation(X0)) = X0
& relation_rng(identity_relation(X0)) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f43,axiom,
! [X0,X1,X2] :
( ( relation(X2)
& function(X2) )
=> ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_funct_1) ).
fof(f49,plain,
! [X0,X1] :
( ( X1 = identity_relation(X0)
<=> ! [X2,X3] :
( in(ordered_pair(X2,X3),X1)
<=> ( in(X2,X0)
& X2 = X3 ) ) )
| ~ relation(X1) ),
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(ennf_transformation,[],[f6]) ).
fof(f51,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,[],[f50]) ).
fof(f61,plain,
? [X0,X1] :
( ( X1 = identity_relation(X0)
<~> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f62,plain,
? [X0,X1] :
( ( X1 = identity_relation(X0)
<~> ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) ) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f61]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(ennf_transformation,[],[f43]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ( in(ordered_pair(X0,X1),X2)
<=> ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f66]) ).
fof(f68,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f49]) ).
fof(f69,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
| ~ in(X2,X0)
| X2 != X3 )
& ( ( in(X2,X0)
& X2 = X3 )
| ~ in(ordered_pair(X2,X3),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f68]) ).
fof(f70,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ? [X2,X3] :
( ( ~ in(X2,X0)
| X2 != X3
| ~ in(ordered_pair(X2,X3),X1) )
& ( ( in(X2,X0)
& X2 = X3 )
| in(ordered_pair(X2,X3),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| ( ( ~ in(sK0(X0,X1),X0)
| sK0(X0,X1) != sK1(X0,X1)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( ( in(sK0(X0,X1),X0)
& sK0(X0,X1) = sK1(X0,X1) )
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ) ) )
& ( ! [X4,X5] :
( ( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5 )
& ( ( in(X4,X0)
& X4 = X5 )
| ~ in(ordered_pair(X4,X5),X1) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f70]) ).
fof(f72,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,[],[f51]) ).
fof(f80,plain,
? [X0,X1] :
( ( relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| identity_relation(X0) != X1 )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) )
& relation(X1)
& function(X1) ),
inference(nnf_transformation,[],[f62]) ).
fof(f81,plain,
? [X0,X1] :
( ( relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| identity_relation(X0) != X1 )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| X1 = identity_relation(X0) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
? [X0,X1] :
( ( relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) )
| identity_relation(X0) != X1 )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| X1 = identity_relation(X0) )
& relation(X1)
& function(X1) ),
inference(rectify,[],[f81]) ).
fof(f83,plain,
( ( sK9 != relation_dom(sK10)
| ( sK11 != apply(sK10,sK11)
& in(sK11,sK9) )
| sK10 != identity_relation(sK9) )
& ( ( sK9 = relation_dom(sK10)
& ! [X3] :
( apply(sK10,X3) = X3
| ~ in(X3,sK9) ) )
| sK10 = identity_relation(sK9) )
& relation(sK10)
& function(sK10) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11)],[f82]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1 )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(nnf_transformation,[],[f67]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( ( in(ordered_pair(X0,X1),X2)
| ~ in(X0,relation_dom(X2))
| apply(X2,X0) != X1 )
& ( ( in(X0,relation_dom(X2))
& X1 = apply(X2,X0) )
| ~ in(ordered_pair(X0,X1),X2) ) )
| ~ relation(X2)
| ~ function(X2) ),
inference(flattening,[],[f84]) ).
fof(f92,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ in(X4,X0)
| X4 != X5
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f93,plain,
! [X0,X1] :
( sK0(X0,X1) = sK1(X0,X1)
| identity_relation(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f94,plain,
! [X0,X1] :
( in(sK0(X0,X1),X0)
| identity_relation(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f95,plain,
! [X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f71]) ).
fof(f98,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,[],[f72]) ).
fof(f101,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[],[f15]) ).
fof(f107,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[],[f21]) ).
fof(f130,plain,
function(sK10),
inference(cnf_transformation,[],[f83]) ).
fof(f131,plain,
relation(sK10),
inference(cnf_transformation,[],[f83]) ).
fof(f132,plain,
! [X3] :
( apply(sK10,X3) = X3
| ~ in(X3,sK9)
| sK10 = identity_relation(sK9) ),
inference(cnf_transformation,[],[f83]) ).
fof(f133,plain,
( sK9 = relation_dom(sK10)
| sK10 = identity_relation(sK9) ),
inference(cnf_transformation,[],[f83]) ).
fof(f134,plain,
( sK9 != relation_dom(sK10)
| in(sK11,sK9)
| sK10 != identity_relation(sK9) ),
inference(cnf_transformation,[],[f83]) ).
fof(f135,plain,
( sK9 != relation_dom(sK10)
| sK11 != apply(sK10,sK11)
| sK10 != identity_relation(sK9) ),
inference(cnf_transformation,[],[f83]) ).
fof(f138,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[],[f40]) ).
fof(f141,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| apply(X2,X0) = X1
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X0,X1),X2)
| in(X0,relation_dom(X2))
| ~ relation(X2)
| ~ function(X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f144,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,X5),X1)
| ~ in(X5,X0)
| identity_relation(X0) != X1
| ~ relation(X1) ),
inference(equality_resolution,[],[f92]) ).
fof(f145,plain,
! [X0,X5] :
( in(ordered_pair(X5,X5),identity_relation(X0))
| ~ in(X5,X0)
| ~ relation(identity_relation(X0)) ),
inference(equality_resolution,[],[f144]) ).
fof(f148,plain,
! [X0,X1] :
( ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| in(ordered_pair(X1,apply(X0,X1)),X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f153,definition,
( spl12_1
<=> sK10 = identity_relation(sK9) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f154,plain,
( sK10 != identity_relation(sK9)
| spl12_1 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f155,plain,
( sK10 = identity_relation(sK9)
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f157,definition,
( spl12_2
<=> ! [X3] :
( apply(sK10,X3) = X3
| ~ in(X3,sK9) ) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f158,plain,
( ! [X3] :
( ~ in(X3,sK9)
| apply(sK10,X3) = X3 )
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f157]) ).
fof(f159,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f132,f157,f153]) ).
fof(f161,definition,
( spl12_3
<=> sK9 = relation_dom(sK10) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f163,plain,
( sK9 = relation_dom(sK10)
| ~ spl12_3 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,plain,
( spl12_1
| spl12_3 ),
inference(avatar_split_clause,[],[f133,f161,f153]) ).
fof(f166,definition,
( spl12_4
<=> in(sK11,sK9) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f168,plain,
( in(sK11,sK9)
| ~ spl12_4 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f169,plain,
( ~ spl12_1
| spl12_4
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f134,f161,f166,f153]) ).
fof(f171,definition,
( spl12_5
<=> sK11 = apply(sK10,sK11) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f174,plain,
( ~ spl12_1
| ~ spl12_5
| ~ spl12_3 ),
inference(avatar_split_clause,[],[f135,f161,f171,f153]) ).
fof(f238,plain,
! [X0,X5] :
( ~ in(X5,X0)
| in(ordered_pair(X5,X5),identity_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f145,f101]) ).
fof(f298,plain,
( sK9 = relation_dom(sK10)
| ~ spl12_1 ),
inference(superposition,[],[f138,f155]) ).
fof(f305,plain,
( spl12_3
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f298,f153,f161]) ).
fof(f314,plain,
( in(ordered_pair(sK11,sK11),identity_relation(sK9))
| ~ spl12_4 ),
inference(resolution,[],[f168,f238]) ).
fof(f337,plain,
( sK11 = apply(identity_relation(sK9),sK11)
| ~ relation(identity_relation(sK9))
| ~ function(identity_relation(sK9))
| ~ spl12_4 ),
inference(resolution,[],[f314,f141]) ).
fof(f343,plain,
( sK11 = apply(identity_relation(sK9),sK11)
| ~ function(identity_relation(sK9))
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f337,f101]) ).
fof(f345,plain,
( sK11 = apply(identity_relation(sK9),sK11)
| ~ spl12_4 ),
inference(forward_subsumption_resolution,[],[f343,f107]) ).
fof(f350,plain,
! [X0] :
( ~ in(X0,relation_dom(sK10))
| ~ relation(sK10)
| in(ordered_pair(X0,apply(sK10,X0)),sK10) ),
inference(resolution,[],[f148,f130]) ).
fof(f351,plain,
! [X0] :
( ~ in(X0,relation_dom(sK10))
| in(ordered_pair(X0,apply(sK10,X0)),sK10) ),
inference(forward_subsumption_resolution,[],[f350,f131]) ).
fof(f355,plain,
( ! [X0] :
( ~ in(X0,sK9)
| in(ordered_pair(X0,apply(sK10,X0)),sK10) )
| ~ spl12_3 ),
inference(forward_demodulation,[],[f351,f163]) ).
fof(f367,plain,
( ! [X0] :
( sK0(sK9,X0) = apply(sK10,sK0(sK9,X0))
| in(ordered_pair(sK0(sK9,X0),sK1(sK9,X0)),X0)
| ~ relation(X0)
| identity_relation(sK9) = X0 )
| ~ spl12_2 ),
inference(resolution,[],[f94,f158]) ).
fof(f391,plain,
! [X0,X1] :
( sK0(X0,X1) != sK0(X0,X1)
| ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X1)
| ~ relation(X1)
| identity_relation(X0) = X1
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1)
| ~ relation(X1) ),
inference(superposition,[],[f95,f93]) ).
fof(f392,plain,
! [X0,X1] :
( sK0(X0,X1) != sK0(X0,X1)
| ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X1)
| ~ relation(X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ),
inference(duplicate_literal_removal,[],[f391]) ).
fof(f393,plain,
! [X0,X1] :
( ~ in(sK0(X0,X1),X0)
| identity_relation(X0) = X1
| ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X1)
| ~ relation(X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ),
inference(trivial_inequality_removal,[],[f392]) ).
fof(f394,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK0(X0,X1),sK0(X0,X1)),X1)
| identity_relation(X0) = X1
| ~ relation(X1)
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) ),
inference(forward_subsumption_resolution,[],[f393,f94]) ).
fof(f395,plain,
( ! [X0] :
( in(ordered_pair(sK0(sK9,X0),apply(sK10,sK0(sK9,X0))),sK10)
| identity_relation(sK9) = X0
| in(ordered_pair(sK0(sK9,X0),sK1(sK9,X0)),X0)
| ~ relation(X0) )
| ~ spl12_3 ),
inference(resolution,[],[f355,f94]) ).
fof(f572,plain,
( ! [X0] :
( in(ordered_pair(sK0(sK9,X0),sK0(sK9,X0)),sK10)
| identity_relation(sK9) = X0
| in(ordered_pair(sK0(sK9,X0),sK1(sK9,X0)),X0)
| ~ relation(X0)
| in(ordered_pair(sK0(sK9,X0),sK1(sK9,X0)),X0)
| ~ relation(X0)
| identity_relation(sK9) = X0 )
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f395,f367]) ).
fof(f574,plain,
( ! [X0] :
( in(ordered_pair(sK0(sK9,X0),sK0(sK9,X0)),sK10)
| identity_relation(sK9) = X0
| in(ordered_pair(sK0(sK9,X0),sK1(sK9,X0)),X0)
| ~ relation(X0) )
| ~ spl12_2
| ~ spl12_3 ),
inference(duplicate_literal_removal,[],[f572]) ).
fof(f797,plain,
( sK10 = identity_relation(sK9)
| in(ordered_pair(sK0(sK9,sK10),sK1(sK9,sK10)),sK10)
| ~ relation(sK10)
| sK10 = identity_relation(sK9)
| ~ relation(sK10)
| in(ordered_pair(sK0(sK9,sK10),sK1(sK9,sK10)),sK10)
| ~ spl12_2
| ~ spl12_3 ),
inference(resolution,[],[f574,f394]) ).
fof(f804,plain,
( sK10 = identity_relation(sK9)
| in(ordered_pair(sK0(sK9,sK10),sK1(sK9,sK10)),sK10)
| ~ relation(sK10)
| ~ spl12_2
| ~ spl12_3 ),
inference(duplicate_literal_removal,[],[f797]) ).
fof(f806,plain,
( in(ordered_pair(sK0(sK9,sK10),sK1(sK9,sK10)),sK10)
| ~ relation(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f804,f154]) ).
fof(f808,plain,
( in(ordered_pair(sK0(sK9,sK10),sK1(sK9,sK10)),sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f806,f131]) ).
fof(f810,plain,
( sK1(sK9,sK10) = apply(sK10,sK0(sK9,sK10))
| ~ relation(sK10)
| ~ function(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(resolution,[],[f808,f141]) ).
fof(f811,plain,
( in(sK0(sK9,sK10),relation_dom(sK10))
| ~ relation(sK10)
| ~ function(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(resolution,[],[f808,f142]) ).
fof(f818,plain,
( in(sK0(sK9,sK10),relation_dom(sK10))
| ~ function(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f811,f131]) ).
fof(f819,plain,
( sK1(sK9,sK10) = apply(sK10,sK0(sK9,sK10))
| ~ function(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f810,f131]) ).
fof(f820,plain,
( in(sK0(sK9,sK10),relation_dom(sK10))
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f818,f130]) ).
fof(f821,plain,
( sK1(sK9,sK10) = apply(sK10,sK0(sK9,sK10))
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f819,f130]) ).
fof(f822,plain,
( in(sK0(sK9,sK10),sK9)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_demodulation,[],[f820,f163]) ).
fof(f824,plain,
( sK0(sK9,sK10) = apply(sK10,sK0(sK9,sK10))
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(resolution,[],[f822,f158]) ).
fof(f1094,plain,
( sK0(sK9,sK10) = sK1(sK9,sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f824,f821]) ).
fof(f1114,plain,
( in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f808,f1094]) ).
fof(f1115,plain,
( sK0(sK9,sK10) != sK0(sK9,sK10)
| ~ in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| ~ in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| ~ relation(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(superposition,[],[f95,f1094]) ).
fof(f1116,plain,
( ~ in(sK0(sK9,sK10),sK9)
| sK10 = identity_relation(sK9)
| ~ in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| ~ relation(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(trivial_inequality_removal,[],[f1115]) ).
fof(f1117,plain,
( sK10 = identity_relation(sK9)
| ~ in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| ~ relation(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1116,f822]) ).
fof(f1118,plain,
( ~ in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| ~ relation(sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1117,f154]) ).
fof(f1119,plain,
( ~ in(ordered_pair(sK0(sK9,sK10),sK0(sK9,sK10)),sK10)
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1118,f131]) ).
fof(f1384,plain,
( $false
| spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(forward_subsumption_resolution,[],[f1119,f1114]) ).
fof(f1385,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(avatar_contradiction_clause,[],[f1384]) ).
fof(f1407,plain,
( sK11 = apply(sK10,sK11)
| ~ spl12_1
| ~ spl12_4 ),
inference(superposition,[],[f345,f155]) ).
fof(f1439,plain,
( spl12_5
| ~ spl12_1
| ~ spl12_4 ),
inference(avatar_split_clause,[],[f1407,f166,f153,f171]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f159]) ).
cnf(s2,plain,
( spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f164]) ).
cnf(s3,plain,
( ~ spl12_1
| ~ spl12_3
| spl12_4 ),
inference(sat_conversion,[],[f169]) ).
cnf(s4,plain,
( ~ spl12_1
| ~ spl12_3
| ~ spl12_5 ),
inference(sat_conversion,[],[f174]) ).
cnf(s9,plain,
( ~ spl12_1
| spl12_3 ),
inference(sat_conversion,[],[f305]) ).
cnf(s46,plain,
( spl12_1
| ~ spl12_2
| ~ spl12_3 ),
inference(sat_conversion,[],[f1385]) ).
cnf(s49,plain,
( ~ spl12_1
| ~ spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f1439]) ).
cnf(s50,plain,
spl12_1,
inference(rat,[],[s46,s1,s2]) ).
cnf(s51,plain,
spl12_3,
inference(rat,[],[s9,s50]) ).
cnf(s52,plain,
~ spl12_5,
inference(rat,[],[s4,s50,s51]) ).
cnf(s53,plain,
spl12_4,
inference(rat,[],[s3,s50,s51]) ).
cnf(s54,plain,
$false,
inference(rat,[],[s49,s50,s52,s53]) ).
fof(f1440,plain,
$false,
inference(avatar_sat_refutation,[],[s54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU216+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n004.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 04:05:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 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
% 3.14/1.32 % (4138820)Detected formulas, will run a generic FOF schedule.
% 3.14/1.32 % (4138826)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=3051800742:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.14/1.32 % (4138831)dis-21_1_sil=8000:lcm=predicate:random_seed=3743714620: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)
% 3.14/1.32 % (4138828)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3461981757:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.14/1.32 % (4138825)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=876884514:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.14/1.32 % (4138829)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1683200616:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.14/1.32 % (4138827)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=4151448092:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.14/1.32 % (4138830)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2282558473:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.14/1.32 % (4138828)Refutation not found, incomplete strategy
% 3.14/1.32 % (4138828)------------------------------
% 3.14/1.32 % (4138828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.32 % (4138828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.32 % (4138828)CaDiCaL version: 2.1.3
% 3.14/1.32 % (4138828)Termination reason: Refutation not found, incomplete strategy
% 3.14/1.32 % (4138828)Time elapsed: 0.004 s
% 3.14/1.32 % (4138828)Peak memory usage: 88 MB
% 3.14/1.32 % (4138828)Instructions burned: 4 (million)
% 3.14/1.32 % (4138830)First to succeed.
% 3.14/1.32 % (4138830)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4138820"
% 3.14/1.32 % (4138829)Instruction limit reached!
% 3.14/1.32 % (4138829)------------------------------
% 3.14/1.32 % (4138829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.32 % (4138829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.32 % (4138829)CaDiCaL version: 2.1.3
% 3.14/1.32 % (4138829)Termination reason: Instruction limit
% 3.14/1.32 % (4138829)Termination phase: Saturation
% 3.14/1.32 % (4138829)Time elapsed: 0.066 s
% 3.14/1.32 % (4138829)Peak memory usage: 88 MB
% 3.14/1.32 % (4138829)Instructions burned: 120 (million)
% 3.14/1.32 % (4138831)Instruction limit reached!
% 3.14/1.32 % (4138831)------------------------------
% 3.14/1.32 % (4138831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.14/1.32 % (4138831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.14/1.32 % (4138831)CaDiCaL version: 2.1.3
% 3.14/1.32 % (4138831)Termination reason: Instruction limit
% 3.14/1.32 % (4138831)Termination phase: Saturation
% 3.14/1.32 % (4138831)Time elapsed: 0.068 s
% 3.14/1.32 % (4138831)Peak memory usage: 90 MB
% 3.14/1.32 % (4138831)Instructions burned: 129 (million)
% 3.14/1.32 % (4138840)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1143498912:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.14/1.32 % (4138839)lrs+10_1_sil=8000:sp=occurrence:random_seed=921738751:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.14/1.32 % (4138828)------------------------------
% 3.14/1.32 % (4138828)------------------------------
% 3.14/1.32 % (4138839)Also succeeded, but the first one will report.
% 3.14/1.32 % (4138830)Refutation found. Thanks to Tanya!
% 3.14/1.32 % SZS status Theorem for theBenchmark
% 3.14/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.91/1.51 % (4138830)------------------------------
% 3.91/1.51 % (4138830)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.91/1.51 % (4138830)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.91/1.51 % (4138830)CaDiCaL version: 2.1.3
% 3.91/1.51 % (4138830)Termination reason: Refutation
% 3.91/1.51 % (4138830)Time elapsed: 0.035 s
% 3.91/1.51 % (4138830)Peak memory usage: 90 MB
% 3.91/1.51 % (4138830)Instructions burned: 49 (million)
% 3.91/1.51 % (4138830)------------------------------
% 3.91/1.51 % (4138830)------------------------------
% 3.91/1.51 % (4138820)Success in time 0.462 s
% 3.91/1.51 % Vampire exiting
%------------------------------------------------------------------------------