%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU028+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 12:47:05 PM UTC 2026
% Result : Theorem 3.63s 1.30s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 156 ( 18 unt; 11 def)
% Number of atoms : 525 ( 114 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 640 ( 271 ~; 280 |; 58 &)
% ( 14 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 17 ( 15 usr; 12 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 74 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f11,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(f34,axiom,
! [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(f37,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_dom(X1)) )
=> ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t56_funct_1) ).
fof(f38,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f39,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t58_funct_1) ).
fof(f40,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t59_funct_1) ).
fof(f42,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t61_funct_1) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_composition(X0,function_inverse(X0)) = identity_relation(relation_dom(X0))
& relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f56,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f57,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f56]) ).
fof(f58,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f59,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f58]) ).
fof(f62,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f63,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f62]) ).
fof(f76,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,[],[f34]) ).
fof(f77,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,[],[f76]) ).
fof(f81,plain,
! [X0,X1] :
( ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f82,plain,
! [X0,X1] :
( ( X0 = apply(function_inverse(X1),apply(X1,X0))
& X0 = apply(relation_composition(X1,function_inverse(X1)),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f81]) ).
fof(f83,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f38]) ).
fof(f84,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f83]) ).
fof(f85,plain,
! [X0] :
( ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f86,plain,
! [X0] :
( ( relation_dom(relation_composition(X0,function_inverse(X0))) = relation_dom(X0)
& relation_rng(relation_composition(X0,function_inverse(X0))) = relation_dom(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f85]) ).
fof(f87,plain,
! [X0] :
( ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f88,plain,
! [X0] :
( ( relation_dom(relation_composition(function_inverse(X0),X0)) = relation_rng(X0)
& relation_rng(relation_composition(function_inverse(X0),X0)) = relation_rng(X0) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f87]) ).
fof(f90,plain,
? [X0] :
( ( relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0))
| relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f91,plain,
? [X0] :
( ( relation_composition(X0,function_inverse(X0)) != identity_relation(relation_dom(X0))
| relation_composition(function_inverse(X0),X0) != identity_relation(relation_rng(X0)) )
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f90]) ).
fof(f106,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f107,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X2] :
( apply(X1,X2) = X2
| ~ in(X2,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f106]) ).
fof(f108,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ? [X2] :
( apply(X1,X2) != X2
& in(X2,X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(rectify,[],[f107]) ).
fof(f109,plain,
! [X0,X1] :
( ( ( X1 = identity_relation(X0)
| relation_dom(X1) != X0
| ( sK11(X0,X1) != apply(X1,sK11(X0,X1))
& in(sK11(X0,X1),X0) ) )
& ( ( relation_dom(X1) = X0
& ! [X3] :
( apply(X1,X3) = X3
| ~ in(X3,X0) ) )
| identity_relation(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(X2,sK11(X0,X1))],[f108]) ).
fof(f110,plain,
( ( relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12))
| relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12)) )
& one_to_one(sK12)
& relation(sK12)
& function(sK12) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(X0,sK12)],[f91]) ).
fof(f117,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f118,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f119,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f126,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f166,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| relation_dom(X1) != X0
| in(sK11(X0,X1),X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f167,plain,
! [X0,X1] :
( identity_relation(X0) = X1
| relation_dom(X1) != X0
| sK11(X0,X1) != apply(X1,sK11(X0,X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f109]) ).
fof(f170,plain,
! [X0,X1] :
( apply(relation_composition(X1,function_inverse(X1)),X0) = X0
| ~ one_to_one(X1)
| ~ in(X0,relation_dom(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f172,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(relation_composition(function_inverse(X1),X1),X0) = X0
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f175,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,function_inverse(X0)))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f177,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(relation_composition(function_inverse(X0),X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f88]) ).
fof(f179,plain,
function(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f180,plain,
relation(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f181,plain,
one_to_one(sK12),
inference(cnf_transformation,[],[f110]) ).
fof(f182,plain,
( relation_composition(sK12,function_inverse(sK12)) != identity_relation(relation_dom(sK12))
| relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12)) ),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
! [X1] :
( sK11(relation_dom(X1),X1) != apply(X1,sK11(relation_dom(X1),X1))
| identity_relation(relation_dom(X1)) = X1
| ~ relation(X1)
| ~ function(X1) ),
inference(equality_resolution,[],[f167]) ).
fof(f187,plain,
! [X1] :
( in(sK11(relation_dom(X1),X1),relation_dom(X1))
| identity_relation(relation_dom(X1)) = X1
| ~ relation(X1)
| ~ function(X1) ),
inference(equality_resolution,[],[f166]) ).
fof(f191,definition,
( spl13_1
<=> relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_1])],[avatar_definition]) ).
fof(f193,plain,
( relation_composition(function_inverse(sK12),sK12) != identity_relation(relation_rng(sK12))
| spl13_1 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f195,definition,
( spl13_2
<=> relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_2])],[avatar_definition]) ).
fof(f198,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(avatar_split_clause,[],[f182,f195,f191]) ).
fof(f268,definition,
( spl13_6
<=> relation(relation_composition(sK12,function_inverse(sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f269,plain,
( relation(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f270,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| spl13_6 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f272,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f175,f181]) ).
fof(f277,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12)))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f272,f180]) ).
fof(f280,plain,
relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12))),
inference(forward_subsumption_resolution,[],[f277,f179]) ).
fof(f285,definition,
( spl13_7
<=> relation(function_inverse(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_7])],[avatar_definition]) ).
fof(f286,plain,
( relation(function_inverse(sK12))
| ~ spl13_7 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f287,plain,
( ~ relation(function_inverse(sK12))
| spl13_7 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f302,plain,
( relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f177,f181]) ).
fof(f307,plain,
( relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f302,f180]) ).
fof(f310,plain,
relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12)),
inference(forward_subsumption_resolution,[],[f307,f179]) ).
fof(f311,plain,
( ~ relation(sK12)
| ~ function(sK12)
| spl13_7 ),
inference(resolution,[],[f287,f118]) ).
fof(f313,plain,
( ~ function(sK12)
| spl13_7 ),
inference(forward_subsumption_resolution,[],[f311,f180]) ).
fof(f314,plain,
( $false
| spl13_7 ),
inference(forward_subsumption_resolution,[],[f313,f179]) ).
fof(f315,plain,
spl13_7,
inference(avatar_contradiction_clause,[],[f314]) ).
fof(f323,plain,
( ~ relation(sK12)
| ~ relation(function_inverse(sK12))
| spl13_6 ),
inference(resolution,[],[f270,f119]) ).
fof(f325,plain,
( ~ relation(function_inverse(sK12))
| spl13_6 ),
inference(forward_subsumption_resolution,[],[f323,f180]) ).
fof(f326,plain,
( $false
| spl13_6
| ~ spl13_7 ),
inference(forward_subsumption_resolution,[],[f325,f286]) ).
fof(f327,plain,
( spl13_6
| ~ spl13_7 ),
inference(avatar_contradiction_clause,[],[f326]) ).
fof(f336,definition,
( spl13_9
<=> function(relation_composition(sK12,function_inverse(sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f337,plain,
( function(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f338,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| spl13_9 ),
inference(avatar_component_clause,[],[f336]) ).
fof(f347,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_9 ),
inference(resolution,[],[f338,f126]) ).
fof(f349,plain,
( ~ function(sK12)
| ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f347,f180]) ).
fof(f350,plain,
( ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f349,f179]) ).
fof(f351,plain,
( ~ function(function_inverse(sK12))
| ~ spl13_7
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f350,f286]) ).
fof(f353,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_7
| spl13_9 ),
inference(resolution,[],[f351,f117]) ).
fof(f355,plain,
( ~ function(sK12)
| ~ spl13_7
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f353,f180]) ).
fof(f356,plain,
( $false
| ~ spl13_7
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f355,f179]) ).
fof(f357,plain,
( ~ spl13_7
| spl13_9 ),
inference(avatar_contradiction_clause,[],[f356]) ).
fof(f365,plain,
( sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) != apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| ~ function(relation_composition(sK12,function_inverse(sK12))) ),
inference(superposition,[],[f186,f280]) ).
fof(f366,plain,
( in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ relation(relation_composition(sK12,function_inverse(sK12)))
| ~ function(relation_composition(sK12,function_inverse(sK12))) ),
inference(superposition,[],[f187,f280]) ).
fof(f370,plain,
( in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f366,f269]) ).
fof(f371,plain,
( sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) != apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ function(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_6 ),
inference(forward_subsumption_resolution,[],[f365,f269]) ).
fof(f372,plain,
( in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ spl13_6
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f370,f337]) ).
fof(f373,plain,
( sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) != apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))))
| relation_composition(sK12,function_inverse(sK12)) = identity_relation(relation_dom(sK12))
| ~ spl13_6
| ~ spl13_9 ),
inference(forward_subsumption_resolution,[],[f371,f337]) ).
fof(f375,definition,
( spl13_13
<=> in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_13])],[avatar_definition]) ).
fof(f377,plain,
( in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| ~ spl13_13 ),
inference(avatar_component_clause,[],[f375]) ).
fof(f378,plain,
( spl13_2
| spl13_13
| ~ spl13_6
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f372,f336,f268,f375,f195]) ).
fof(f380,definition,
( spl13_14
<=> sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) = apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))) ),
introduced(definition,[new_symbols(definition,[spl13_14])],[avatar_definition]) ).
fof(f382,plain,
( sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) != apply(relation_composition(sK12,function_inverse(sK12)),sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))))
| spl13_14 ),
inference(avatar_component_clause,[],[f380]) ).
fof(f383,plain,
( spl13_2
| ~ spl13_14
| ~ spl13_6
| ~ spl13_9 ),
inference(avatar_split_clause,[],[f373,f336,f268,f380,f195]) ).
fof(f405,definition,
( spl13_18
<=> relation(relation_composition(function_inverse(sK12),sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f406,plain,
( relation(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f407,plain,
( ~ relation(relation_composition(function_inverse(sK12),sK12))
| spl13_18 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f410,definition,
( spl13_19
<=> function(relation_composition(function_inverse(sK12),sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_19])],[avatar_definition]) ).
fof(f411,plain,
( function(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_19 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f412,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| spl13_19 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f427,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) != apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12)) ),
inference(superposition,[],[f186,f310]) ).
fof(f428,plain,
( in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12)) ),
inference(superposition,[],[f187,f310]) ).
fof(f433,plain,
( in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12))
| ~ relation(relation_composition(function_inverse(sK12),sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12))
| spl13_1 ),
inference(forward_subsumption_resolution,[],[f428,f193]) ).
fof(f437,definition,
( spl13_23
<=> in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_23])],[avatar_definition]) ).
fof(f439,plain,
( in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12))
| ~ spl13_23 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f440,plain,
( ~ spl13_19
| ~ spl13_18
| spl13_23
| spl13_1 ),
inference(avatar_split_clause,[],[f433,f191,f437,f405,f410]) ).
fof(f442,definition,
( spl13_24
<=> sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) = apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_24])],[avatar_definition]) ).
fof(f448,plain,
( ~ relation(function_inverse(sK12))
| ~ relation(sK12)
| spl13_18 ),
inference(resolution,[],[f407,f119]) ).
fof(f450,plain,
( ~ relation(sK12)
| ~ spl13_7
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f448,f286]) ).
fof(f451,plain,
( $false
| ~ spl13_7
| spl13_18 ),
inference(forward_subsumption_resolution,[],[f450,f180]) ).
fof(f452,plain,
( ~ spl13_7
| spl13_18 ),
inference(avatar_contradiction_clause,[],[f451]) ).
fof(f473,plain,
( ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_19 ),
inference(resolution,[],[f412,f126]) ).
fof(f475,plain,
( ~ function(function_inverse(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_19 ),
inference(forward_subsumption_resolution,[],[f473,f118]) ).
fof(f476,plain,
( ~ relation(sK12)
| ~ function(sK12)
| spl13_19 ),
inference(forward_subsumption_resolution,[],[f475,f117]) ).
fof(f477,plain,
( ~ function(sK12)
| spl13_19 ),
inference(forward_subsumption_resolution,[],[f476,f180]) ).
fof(f478,plain,
( $false
| spl13_19 ),
inference(forward_subsumption_resolution,[],[f477,f179]) ).
fof(f479,plain,
spl13_19,
inference(avatar_contradiction_clause,[],[f478]) ).
fof(f520,plain,
( ~ one_to_one(sK12)
| sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) = apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_23 ),
inference(resolution,[],[f439,f172]) ).
fof(f524,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) = apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_23 ),
inference(forward_subsumption_resolution,[],[f520,f181]) ).
fof(f526,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) = apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| ~ function(sK12)
| ~ spl13_23 ),
inference(forward_subsumption_resolution,[],[f524,f180]) ).
fof(f528,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) = apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| ~ spl13_23 ),
inference(forward_subsumption_resolution,[],[f526,f179]) ).
fof(f530,plain,
( spl13_24
| ~ spl13_23 ),
inference(avatar_split_clause,[],[f528,f437,f442]) ).
fof(f531,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) != apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
| ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f427,f406]) ).
fof(f532,plain,
( sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)) != apply(relation_composition(function_inverse(sK12),sK12),sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)))
| relation_composition(function_inverse(sK12),sK12) = identity_relation(relation_rng(sK12))
| ~ spl13_18
| ~ spl13_19 ),
inference(forward_subsumption_resolution,[],[f531,f411]) ).
fof(f533,plain,
( spl13_1
| ~ spl13_24
| ~ spl13_18
| ~ spl13_19 ),
inference(avatar_split_clause,[],[f532,f410,f405,f442,f191]) ).
fof(f806,plain,
( sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))) != sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12)))
| ~ one_to_one(sK12)
| ~ in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_14 ),
inference(superposition,[],[f382,f170]) ).
fof(f807,plain,
( ~ one_to_one(sK12)
| ~ in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_14 ),
inference(trivial_inequality_removal,[],[f806]) ).
fof(f808,plain,
( ~ in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_14 ),
inference(forward_subsumption_resolution,[],[f807,f181]) ).
fof(f809,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_13
| spl13_14 ),
inference(forward_subsumption_resolution,[],[f808,f377]) ).
fof(f810,plain,
( ~ function(sK12)
| ~ spl13_13
| spl13_14 ),
inference(forward_subsumption_resolution,[],[f809,f180]) ).
fof(f811,plain,
( $false
| ~ spl13_13
| spl13_14 ),
inference(forward_subsumption_resolution,[],[f810,f179]) ).
fof(f812,plain,
( ~ spl13_13
| spl13_14 ),
inference(avatar_contradiction_clause,[],[f811]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f198]) ).
cnf(s6,plain,
spl13_7,
inference(sat_conversion,[],[f315]) ).
cnf(s7,plain,
( spl13_6
| ~ spl13_7 ),
inference(sat_conversion,[],[f327]) ).
cnf(s9,plain,
( ~ spl13_7
| spl13_9 ),
inference(sat_conversion,[],[f357]) ).
cnf(s11,plain,
( spl13_2
| ~ spl13_6
| ~ spl13_9
| spl13_13 ),
inference(sat_conversion,[],[f378]) ).
cnf(s12,plain,
( spl13_2
| ~ spl13_6
| ~ spl13_9
| ~ spl13_14 ),
inference(sat_conversion,[],[f383]) ).
cnf(s19,plain,
( spl13_1
| ~ spl13_18
| ~ spl13_19
| spl13_23 ),
inference(sat_conversion,[],[f440]) ).
cnf(s21,plain,
( ~ spl13_7
| spl13_18 ),
inference(sat_conversion,[],[f452]) ).
cnf(s22,plain,
spl13_19,
inference(sat_conversion,[],[f479]) ).
cnf(s23,plain,
( ~ spl13_23
| spl13_24 ),
inference(sat_conversion,[],[f530]) ).
cnf(s24,plain,
( spl13_1
| ~ spl13_18
| ~ spl13_19
| ~ spl13_24 ),
inference(sat_conversion,[],[f533]) ).
cnf(s47,plain,
( ~ spl13_13
| spl13_14 ),
inference(sat_conversion,[],[f812]) ).
cnf(s49,plain,
( spl13_1
| ~ spl13_18
| spl13_23 ),
inference(rat,[],[s19,s22]) ).
cnf(s52,plain,
spl13_18,
inference(rat,[],[s21,s6]) ).
cnf(s53,plain,
spl13_9,
inference(rat,[],[s9,s6]) ).
cnf(s54,plain,
spl13_6,
inference(rat,[],[s7,s6]) ).
cnf(s57,plain,
spl13_1,
inference(rat,[],[s23,s49,s24,s52,s22]) ).
cnf(s58,plain,
~ spl13_2,
inference(rat,[],[s1,s57]) ).
cnf(s59,plain,
~ spl13_14,
inference(rat,[],[s12,s54,s53,s58]) ).
cnf(s60,plain,
spl13_13,
inference(rat,[],[s11,s54,s53,s58]) ).
cnf(s61,plain,
$false,
inference(rat,[],[s47,s59,s60]) ).
fof(f813,plain,
$false,
inference(avatar_sat_refutation,[],[s61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 03:24:34 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 2.72/1.30 % (3997258)Detected formulas, will run a generic FOF schedule.
% 2.72/1.30 % (3997267)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2045338630:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.72/1.30 % (3997267)Refutation not found, incomplete strategy
% 2.72/1.30 % (3997267)------------------------------
% 2.72/1.30 % (3997267)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.72/1.30 % (3997267)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.72/1.30 % (3997267)CaDiCaL version: 2.1.3
% 2.72/1.30 % (3997267)Termination reason: Refutation not found, incomplete strategy
% 2.72/1.30 % (3997267)Time elapsed: 0.002 s
% 2.72/1.30 % (3997267)Peak memory usage: 88 MB
% 2.72/1.30 % (3997267)Instructions burned: 5 (million)
% 2.72/1.30 % (3997269)dis-21_1_sil=8000:lcm=predicate:random_seed=1801337339: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)
% 2.72/1.30 % (3997268)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2926348595:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.63/1.30 % (3997263)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=4144851408:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.63/1.30 % (3997264)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=2112577281:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.63/1.30 % (3997265)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=516497714:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.63/1.30 % (3997266)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2056200257:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.63/1.30 % (3997266)Refutation not found, incomplete strategy
% 3.63/1.30 % (3997266)------------------------------
% 3.63/1.30 % (3997266)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.30 % (3997266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.30 % (3997266)CaDiCaL version: 2.1.3
% 3.63/1.30 % (3997266)Termination reason: Refutation not found, incomplete strategy
% 3.63/1.30 % (3997266)Time elapsed: 0.002 s
% 3.63/1.30 % (3997266)Peak memory usage: 88 MB
% 3.63/1.30 % (3997266)Instructions burned: 2 (million)
% 3.63/1.30 % (3997268)First to succeed.
% 3.63/1.30 % (3997268)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3997258"
% 3.63/1.30 % (3997269)Instruction limit reached!
% 3.63/1.30 % (3997269)------------------------------
% 3.63/1.30 % (3997269)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.63/1.30 % (3997269)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.63/1.30 % (3997269)CaDiCaL version: 2.1.3
% 3.63/1.30 % (3997269)Termination reason: Instruction limit
% 3.63/1.30 % (3997269)Termination phase: Saturation
% 3.63/1.30 % (3997269)Time elapsed: 0.074 s
% 3.63/1.30 % (3997269)Peak memory usage: 90 MB
% 3.63/1.30 % (3997269)Instructions burned: 130 (million)
% 3.63/1.30 % (3997267)------------------------------
% 3.63/1.30 % (3997267)------------------------------
% 3.63/1.30 % (3997277)lrs+10_1_sil=8000:sp=occurrence:random_seed=2598418364:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.63/1.30 % (3997278)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1299248753:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.63/1.30 % (3997266)------------------------------
% 3.63/1.30 % (3997266)------------------------------
% 3.63/1.30 % (3997277)Also succeeded, but the first one will report.
% 3.63/1.30 % (3997268)Refutation found. Thanks to Tanya!
% 3.63/1.30 % SZS status Theorem for theBenchmark
% 3.63/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.40 % (3997268)------------------------------
% 0.15/1.40 % (3997268)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.40 % (3997268)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.40 % (3997268)CaDiCaL version: 2.1.3
% 0.15/1.40 % (3997268)Termination reason: Refutation
% 0.15/1.40 % (3997268)Time elapsed: 0.018 s
% 0.15/1.40 % (3997268)Peak memory usage: 90 MB
% 0.15/1.40 % (3997268)Instructions burned: 24 (million)
% 0.15/1.40 % (3997268)------------------------------
% 0.15/1.40 % (3997268)------------------------------
% 0.15/1.40 % (3997258)Success in time 0.449 s
% 0.15/1.40 % Vampire exiting
%------------------------------------------------------------------------------