%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU013+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n008.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 12:51:47 PM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : Refutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 133 ( 16 unt; 5 def)
% Number of atoms : 506 ( 56 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 689 ( 316 ~; 312 |; 35 &)
% ( 11 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 11 ( 9 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 0 sgn 78 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(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(f26,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(f27,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] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& one_to_one(X1) )
=> one_to_one(relation_composition(X0,X1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_funct_1) ).
fof(f31,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X0)
& one_to_one(X1) )
=> one_to_one(relation_composition(X0,X1)) ) ) ),
inference(negated_conjecture,[status(cth)],[f30]) ).
fof(f44,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,[],[f4]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f47,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f46]) ).
fof(f50,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(f51,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f50]) ).
fof(f59,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,[],[f26]) ).
fof(f60,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,[],[f59]) ).
fof(f61,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,[],[f27]) ).
fof(f62,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,[],[f61]) ).
fof(f66,plain,
? [X0] :
( ? [X1] :
( ~ one_to_one(relation_composition(X0,X1))
& one_to_one(X0)
& one_to_one(X1)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f67,plain,
? [X0] :
( ? [X1] :
( ~ one_to_one(relation_composition(X0,X1))
& one_to_one(X0)
& one_to_one(X1)
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f66]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ one_to_one(X0)
| ~ relation(X0)
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f78,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f79,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f80,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f81,plain,
! [X0] :
( one_to_one(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f82,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f114,plain,
! [X2,X0,X1] :
( in(apply(X2,X0),relation_dom(X1))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| ~ in(X0,relation_dom(relation_composition(X2,X1))) ),
inference(cnf_transformation,[],[f60]) ).
fof(f115,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| in(X0,relation_dom(X2))
| ~ function(X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f117,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X2,X1)))
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ function(X1)
| apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f120,plain,
function(sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f121,plain,
relation(sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f122,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f67]) ).
fof(f123,plain,
one_to_one(sK11),
inference(cnf_transformation,[],[f67]) ).
fof(f124,plain,
~ one_to_one(relation_composition(sK11,sK12)),
inference(cnf_transformation,[],[f67]) ).
fof(f125,plain,
function(sK11),
inference(cnf_transformation,[],[f67]) ).
fof(f126,plain,
relation(sK11),
inference(cnf_transformation,[],[f67]) ).
fof(f293,plain,
( ~ relation(relation_composition(sK11,sK12))
| in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| ~ function(relation_composition(sK11,sK12)) ),
inference(resolution,[],[f79,f124]) ).
fof(f295,definition,
( spl13_3
<=> function(relation_composition(sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f296,plain,
( function(relation_composition(sK11,sK12))
| ~ spl13_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f297,plain,
( ~ function(relation_composition(sK11,sK12))
| spl13_3 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f299,definition,
( spl13_4
<=> in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_4])],[avatar_definition]) ).
fof(f301,plain,
( in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| ~ spl13_4 ),
inference(avatar_component_clause,[],[f299]) ).
fof(f303,definition,
( spl13_5
<=> relation(relation_composition(sK11,sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f304,plain,
( relation(relation_composition(sK11,sK12))
| ~ spl13_5 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f305,plain,
( ~ relation(relation_composition(sK11,sK12))
| spl13_5 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f306,plain,
( ~ spl13_3
| spl13_4
| ~ spl13_5 ),
inference(avatar_split_clause,[],[f293,f303,f299,f295]) ).
fof(f308,plain,
( ~ relation(relation_composition(sK11,sK12))
| in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| ~ function(relation_composition(sK11,sK12)) ),
inference(resolution,[],[f80,f124]) ).
fof(f313,plain,
( ~ relation(relation_composition(sK11,sK12))
| sK0(relation_composition(sK11,sK12)) != sK1(relation_composition(sK11,sK12))
| ~ function(relation_composition(sK11,sK12)) ),
inference(resolution,[],[f81,f124]) ).
fof(f314,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| spl13_3 ),
inference(resolution,[],[f88,f297]) ).
fof(f315,plain,
( ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f314,f121]) ).
fof(f316,plain,
( ~ relation(sK11)
| ~ function(sK12)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f315,f125]) ).
fof(f317,plain,
( ~ function(sK12)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f316,f126]) ).
fof(f318,plain,
( $false
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f317,f120]) ).
fof(f319,plain,
spl13_3,
inference(avatar_contradiction_clause,[],[f318]) ).
fof(f334,plain,
( ~ relation(sK11)
| ~ relation(sK12)
| spl13_5 ),
inference(resolution,[],[f305,f82]) ).
fof(f335,plain,
( ~ relation(sK12)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f334,f126]) ).
fof(f336,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f335,f121]) ).
fof(f337,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f336]) ).
fof(f338,plain,
( in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| ~ function(relation_composition(sK11,sK12))
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f308,f304]) ).
fof(f339,plain,
( sK0(relation_composition(sK11,sK12)) != sK1(relation_composition(sK11,sK12))
| ~ function(relation_composition(sK11,sK12))
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f313,f304]) ).
fof(f340,plain,
( in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f338,f296]) ).
fof(f341,plain,
( sK0(relation_composition(sK11,sK12)) != sK1(relation_composition(sK11,sK12))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f339,f296]) ).
fof(f342,plain,
( ~ relation(relation_composition(sK11,sK12))
| apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12)))
| ~ function(relation_composition(sK11,sK12)) ),
inference(resolution,[],[f78,f124]) ).
fof(f343,plain,
( apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12)))
| ~ function(relation_composition(sK11,sK12))
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f342,f304]) ).
fof(f344,plain,
( apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12)))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f343,f296]) ).
fof(f345,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| in(sK1(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_4 ),
inference(resolution,[],[f301,f115]) ).
fof(f349,plain,
( ~ function(sK11)
| ~ relation(sK11)
| in(sK1(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f345,f121]) ).
fof(f350,plain,
( ~ relation(sK11)
| in(sK1(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f349,f125]) ).
fof(f351,plain,
( in(sK1(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f350,f126]) ).
fof(f352,plain,
( in(sK1(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f351,f120]) ).
fof(f371,plain,
! [X0,X1] :
( ~ relation(sK12)
| apply(sK12,X0) != apply(sK12,X1)
| ~ in(X1,relation_dom(sK12))
| ~ in(X0,relation_dom(sK12))
| X0 = X1
| ~ function(sK12) ),
inference(resolution,[],[f77,f122]) ).
fof(f372,plain,
! [X0,X1] :
( ~ relation(sK11)
| apply(sK11,X0) != apply(sK11,X1)
| ~ in(X1,relation_dom(sK11))
| ~ in(X0,relation_dom(sK11))
| X0 = X1
| ~ function(sK11) ),
inference(resolution,[],[f77,f123]) ).
fof(f381,plain,
! [X0,X1] :
( apply(sK11,X0) != apply(sK11,X1)
| ~ in(X1,relation_dom(sK11))
| ~ in(X0,relation_dom(sK11))
| X0 = X1
| ~ function(sK11) ),
inference(forward_subsumption_resolution,[],[f372,f126]) ).
fof(f382,plain,
! [X0,X1] :
( apply(sK12,X0) != apply(sK12,X1)
| ~ in(X1,relation_dom(sK12))
| ~ in(X0,relation_dom(sK12))
| X0 = X1
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f371,f121]) ).
fof(f383,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sK11))
| ~ in(X0,relation_dom(sK11))
| apply(sK11,X0) != apply(sK11,X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f381,f125]) ).
fof(f384,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sK12))
| ~ in(X0,relation_dom(sK12))
| apply(sK12,X0) != apply(sK12,X1)
| X0 = X1 ),
inference(forward_subsumption_resolution,[],[f382,f120]) ).
fof(f392,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_4 ),
inference(resolution,[],[f117,f301]) ).
fof(f395,plain,
( ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f392,f121]) ).
fof(f397,plain,
( ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f395,f125]) ).
fof(f398,plain,
( ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f397,f126]) ).
fof(f399,plain,
( apply(relation_composition(sK11,sK12),sK1(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_4 ),
inference(forward_subsumption_resolution,[],[f398,f120]) ).
fof(f400,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_5 ),
inference(resolution,[],[f340,f117]) ).
fof(f401,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| in(sK0(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_3
| ~ spl13_5 ),
inference(resolution,[],[f340,f115]) ).
fof(f405,plain,
( ~ function(sK11)
| ~ relation(sK11)
| in(sK0(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f401,f121]) ).
fof(f406,plain,
( ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f400,f121]) ).
fof(f407,plain,
( ~ relation(sK11)
| in(sK0(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f405,f125]) ).
fof(f408,plain,
( ~ relation(sK11)
| ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f406,f125]) ).
fof(f409,plain,
( in(sK0(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ function(sK12)
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f407,f126]) ).
fof(f410,plain,
( ~ function(sK12)
| apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f408,f126]) ).
fof(f411,plain,
( in(sK0(relation_composition(sK11,sK12)),relation_dom(sK11))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f409,f120]) ).
fof(f412,plain,
( apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f410,f120]) ).
fof(f433,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK11))
| apply(sK11,X0) != apply(sK11,sK0(relation_composition(sK11,sK12)))
| sK0(relation_composition(sK11,sK12)) = X0 )
| ~ spl13_3
| ~ spl13_5 ),
inference(resolution,[],[f383,f411]) ).
fof(f464,plain,
( apply(relation_composition(sK11,sK12),sK0(relation_composition(sK11,sK12))) = apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5 ),
inference(superposition,[],[f344,f399]) ).
fof(f469,plain,
( apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12)))) = apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5 ),
inference(forward_demodulation,[],[f464,f412]) ).
fof(f518,definition,
( spl13_8
<=> in(apply(sK11,sK1(relation_composition(sK11,sK12))),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f519,plain,
( in(apply(sK11,sK1(relation_composition(sK11,sK12))),relation_dom(sK12))
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f520,plain,
( ~ in(apply(sK11,sK1(relation_composition(sK11,sK12))),relation_dom(sK12))
| spl13_8 ),
inference(avatar_component_clause,[],[f518]) ).
fof(f539,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_8 ),
inference(resolution,[],[f520,f114]) ).
fof(f540,plain,
( ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f539,f121]) ).
fof(f541,plain,
( ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f540,f125]) ).
fof(f542,plain,
( ~ function(sK12)
| ~ in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f541,f126]) ).
fof(f543,plain,
( ~ in(sK1(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f542,f120]) ).
fof(f544,plain,
( $false
| ~ spl13_4
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f543,f301]) ).
fof(f545,plain,
( ~ spl13_4
| spl13_8 ),
inference(avatar_contradiction_clause,[],[f544]) ).
fof(f558,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK12))
| apply(sK12,X0) != apply(sK12,apply(sK11,sK1(relation_composition(sK11,sK12))))
| apply(sK11,sK1(relation_composition(sK11,sK12))) = X0 )
| ~ spl13_8 ),
inference(resolution,[],[f519,f384]) ).
fof(f562,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK12))
| apply(sK12,X0) != apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| apply(sK11,sK1(relation_composition(sK11,sK12))) = X0 )
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8 ),
inference(forward_demodulation,[],[f558,f469]) ).
fof(f737,plain,
( apply(sK11,sK1(relation_composition(sK11,sK12))) != apply(sK11,sK0(relation_composition(sK11,sK12)))
| sK0(relation_composition(sK11,sK12)) = sK1(relation_composition(sK11,sK12))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5 ),
inference(resolution,[],[f433,f352]) ).
fof(f739,plain,
( apply(sK11,sK1(relation_composition(sK11,sK12))) != apply(sK11,sK0(relation_composition(sK11,sK12)))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5 ),
inference(forward_subsumption_resolution,[],[f737,f341]) ).
fof(f938,definition,
( spl13_30
<=> in(apply(sK11,sK0(relation_composition(sK11,sK12))),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_30])],[avatar_definition]) ).
fof(f939,plain,
( in(apply(sK11,sK0(relation_composition(sK11,sK12))),relation_dom(sK12))
| ~ spl13_30 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f940,plain,
( ~ in(apply(sK11,sK0(relation_composition(sK11,sK12))),relation_dom(sK12))
| spl13_30 ),
inference(avatar_component_clause,[],[f938]) ).
fof(f983,plain,
( ~ relation(sK12)
| ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_30 ),
inference(resolution,[],[f940,f114]) ).
fof(f984,plain,
( ~ function(sK11)
| ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f983,f121]) ).
fof(f985,plain,
( ~ relation(sK11)
| ~ function(sK12)
| ~ in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f984,f125]) ).
fof(f986,plain,
( ~ function(sK12)
| ~ in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f985,f126]) ).
fof(f987,plain,
( ~ in(sK0(relation_composition(sK11,sK12)),relation_dom(relation_composition(sK11,sK12)))
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f986,f120]) ).
fof(f988,plain,
( $false
| ~ spl13_3
| ~ spl13_5
| spl13_30 ),
inference(forward_subsumption_resolution,[],[f987,f340]) ).
fof(f989,plain,
( ~ spl13_3
| ~ spl13_5
| spl13_30 ),
inference(avatar_contradiction_clause,[],[f988]) ).
fof(f1029,plain,
( apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12)))) != apply(sK12,apply(sK11,sK0(relation_composition(sK11,sK12))))
| apply(sK11,sK1(relation_composition(sK11,sK12))) = apply(sK11,sK0(relation_composition(sK11,sK12)))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_30 ),
inference(resolution,[],[f939,f562]) ).
fof(f1037,plain,
( apply(sK11,sK1(relation_composition(sK11,sK12))) = apply(sK11,sK0(relation_composition(sK11,sK12)))
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_30 ),
inference(trivial_inequality_removal,[],[f1029]) ).
fof(f1038,plain,
( $false
| ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_30 ),
inference(forward_subsumption_resolution,[],[f1037,f739]) ).
fof(f1039,plain,
( ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_30 ),
inference(avatar_contradiction_clause,[],[f1038]) ).
cnf(s7,plain,
( ~ spl13_3
| spl13_4
| ~ spl13_5 ),
inference(sat_conversion,[],[f306]) ).
cnf(s8,plain,
spl13_3,
inference(sat_conversion,[],[f319]) ).
cnf(s9,plain,
spl13_5,
inference(sat_conversion,[],[f337]) ).
cnf(s12,plain,
( ~ spl13_4
| spl13_8 ),
inference(sat_conversion,[],[f545]) ).
cnf(s27,plain,
( ~ spl13_3
| ~ spl13_5
| spl13_30 ),
inference(sat_conversion,[],[f989]) ).
cnf(s28,plain,
( ~ spl13_3
| ~ spl13_4
| ~ spl13_5
| ~ spl13_8
| ~ spl13_30 ),
inference(sat_conversion,[],[f1039]) ).
cnf(s30,plain,
spl13_30,
inference(rat,[],[s27,s9,s8]) ).
cnf(s32,plain,
spl13_4,
inference(rat,[],[s7,s9,s8]) ).
cnf(s33,plain,
~ spl13_8,
inference(rat,[],[s28,s30,s8,s9,s32]) ).
cnf(s34,plain,
$false,
inference(rat,[],[s12,s33,s32]) ).
fof(f1040,plain,
$false,
inference(avatar_sat_refutation,[],[s34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU013+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n008.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 03:22:55 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.41 Running first-order model finding
% 0.12/0.41 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.48 % (1837847)Will run a generic schedule for satisfiability detection.
% 0.12/0.48 % (1837853)% WARNING: option uhcvi not known.
% 0.12/0.48 % (1837853)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1531352429:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.48 % (1837857)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3639884275:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.48 % (1837856)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=234843764:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.48 % (1837852)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3777292036_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.48 % (1837854)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2850174822:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.48 % (1837855)dis+10_1_sil=32000:sp=arity:random_seed=3938068108:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.48 % (1837858)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2177754559:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.48 % TRYING [1]
% 0.12/0.48 % TRYING [2]
% 0.12/0.48 % TRYING [3]
% 0.12/0.48 % TRYING [4]
% 0.12/0.48 % TRYING [5]
% 0.12/0.48 % (1837856) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1837847-1837856"...
% 0.12/0.48 % (1837856)...printing done.
% 0.12/0.48 % (1837856)Refutation found. Thanks to Tanya!
% 0.12/0.48 % SZS status Theorem for theBenchmark
% 0.12/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.25/0.48 % (1837856)------------------------------
% 0.25/0.48 % (1837856)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.25/0.48 % (1837856)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.25/0.48 % (1837856)CaDiCaL version: 2.1.3
% 0.25/0.48 % (1837856)Termination reason: Refutation
% 0.25/0.48 % (1837856)Time elapsed: 0.026 s
% 0.25/0.48 % (1837856)Peak memory usage: 13 MB
% 0.25/0.48 % (1837856)Instructions burned: 37 (million)
% 0.25/0.48 % (1837847)Success in time 0.06 s
% 0.25/0.48 % Vampire exiting
%------------------------------------------------------------------------------