%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 12:51:49 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 152 ( 18 unt; 11 def)
% Number of atoms : 511 ( 117 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 621 ( 262 ~; 270 |; 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/sandbox2/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f6,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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] :
( ~ in(X0,relation_dom(X1))
| ~ one_to_one(X1)
| apply(relation_composition(X1,function_inverse(X1)),X0) = X0
| ~ 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(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(f374,definition,
( spl13_9
<=> relation(relation_composition(sK12,function_inverse(sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_9])],[avatar_definition]) ).
fof(f375,plain,
( relation(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_9 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f376,plain,
( ~ relation(relation_composition(sK12,function_inverse(sK12)))
| spl13_9 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f378,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12)))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f175,f181]) ).
fof(f383,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12)))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f378,f180]) ).
fof(f386,plain,
relation_dom(sK12) = relation_dom(relation_composition(sK12,function_inverse(sK12))),
inference(forward_subsumption_resolution,[],[f383,f179]) ).
fof(f392,definition,
( spl13_10
<=> relation(function_inverse(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f393,plain,
( relation(function_inverse(sK12))
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f394,plain,
( ~ relation(function_inverse(sK12))
| spl13_10 ),
inference(avatar_component_clause,[],[f392]) ).
fof(f409,plain,
( relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f177,f181]) ).
fof(f414,plain,
( relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f409,f180]) ).
fof(f417,plain,
relation_rng(sK12) = relation_dom(relation_composition(function_inverse(sK12),sK12)),
inference(forward_subsumption_resolution,[],[f414,f179]) ).
fof(f418,plain,
( ~ relation(sK12)
| ~ function(sK12)
| spl13_10 ),
inference(resolution,[],[f394,f118]) ).
fof(f419,plain,
( ~ function(sK12)
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f418,f180]) ).
fof(f420,plain,
( $false
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f419,f179]) ).
fof(f421,plain,
spl13_10,
inference(avatar_contradiction_clause,[],[f420]) ).
fof(f435,plain,
( ~ relation(sK12)
| ~ relation(function_inverse(sK12))
| spl13_9 ),
inference(resolution,[],[f376,f119]) ).
fof(f436,plain,
( ~ relation(function_inverse(sK12))
| spl13_9 ),
inference(forward_subsumption_resolution,[],[f435,f180]) ).
fof(f437,plain,
( $false
| spl13_9
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f436,f393]) ).
fof(f438,plain,
( spl13_9
| ~ spl13_10 ),
inference(avatar_contradiction_clause,[],[f437]) ).
fof(f455,definition,
( spl13_12
<=> function(relation_composition(sK12,function_inverse(sK12))) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f456,plain,
( function(relation_composition(sK12,function_inverse(sK12)))
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f457,plain,
( ~ function(relation_composition(sK12,function_inverse(sK12)))
| spl13_12 ),
inference(avatar_component_clause,[],[f455]) ).
fof(f466,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_12 ),
inference(resolution,[],[f457,f126]) ).
fof(f467,plain,
( ~ function(sK12)
| ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f466,f180]) ).
fof(f468,plain,
( ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f467,f179]) ).
fof(f469,plain,
( ~ function(function_inverse(sK12))
| ~ spl13_10
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f468,f393]) ).
fof(f471,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_10
| spl13_12 ),
inference(resolution,[],[f469,f117]) ).
fof(f472,plain,
( ~ function(sK12)
| ~ spl13_10
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f471,f180]) ).
fof(f473,plain,
( $false
| ~ spl13_10
| spl13_12 ),
inference(forward_subsumption_resolution,[],[f472,f179]) ).
fof(f474,plain,
( ~ spl13_10
| spl13_12 ),
inference(avatar_contradiction_clause,[],[f473]) ).
fof(f497,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,f386]) ).
fof(f498,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,f386]) ).
fof(f500,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_9 ),
inference(forward_subsumption_resolution,[],[f498,f375]) ).
fof(f501,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_9 ),
inference(forward_subsumption_resolution,[],[f497,f375]) ).
fof(f504,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_9
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f500,f456]) ).
fof(f505,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_9
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f501,f456]) ).
fof(f509,definition,
( spl13_18
<=> in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_18])],[avatar_definition]) ).
fof(f511,plain,
( in(sK11(relation_dom(sK12),relation_composition(sK12,function_inverse(sK12))),relation_dom(sK12))
| ~ spl13_18 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f512,plain,
( spl13_2
| spl13_18
| ~ spl13_9
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f504,f455,f374,f509,f195]) ).
fof(f514,definition,
( spl13_19
<=> 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_19])],[avatar_definition]) ).
fof(f517,plain,
( spl13_2
| ~ spl13_19
| ~ spl13_9
| ~ spl13_12 ),
inference(avatar_split_clause,[],[f505,f455,f374,f514,f195]) ).
fof(f564,definition,
( spl13_26
<=> relation(relation_composition(function_inverse(sK12),sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_26])],[avatar_definition]) ).
fof(f565,plain,
( relation(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_26 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f566,plain,
( ~ relation(relation_composition(function_inverse(sK12),sK12))
| spl13_26 ),
inference(avatar_component_clause,[],[f564]) ).
fof(f569,definition,
( spl13_27
<=> function(relation_composition(function_inverse(sK12),sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_27])],[avatar_definition]) ).
fof(f570,plain,
( function(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f571,plain,
( ~ function(relation_composition(function_inverse(sK12),sK12))
| spl13_27 ),
inference(avatar_component_clause,[],[f569]) ).
fof(f589,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,f417]) ).
fof(f590,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,f417]) ).
fof(f607,definition,
( spl13_33
<=> in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_33])],[avatar_definition]) ).
fof(f609,plain,
( in(sK11(relation_rng(sK12),relation_composition(function_inverse(sK12),sK12)),relation_rng(sK12))
| ~ spl13_33 ),
inference(avatar_component_clause,[],[f607]) ).
fof(f612,definition,
( spl13_34
<=> 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_34])],[avatar_definition]) ).
fof(f636,plain,
( ~ relation(function_inverse(sK12))
| ~ relation(sK12)
| spl13_26 ),
inference(resolution,[],[f566,f119]) ).
fof(f637,plain,
( ~ relation(sK12)
| ~ spl13_10
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f636,f393]) ).
fof(f638,plain,
( $false
| ~ spl13_10
| spl13_26 ),
inference(forward_subsumption_resolution,[],[f637,f180]) ).
fof(f639,plain,
( ~ spl13_10
| spl13_26 ),
inference(avatar_contradiction_clause,[],[f638]) ).
fof(f655,plain,
( ~ relation(function_inverse(sK12))
| ~ function(function_inverse(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_27 ),
inference(resolution,[],[f571,f126]) ).
fof(f656,plain,
( ~ function(function_inverse(sK12))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_27 ),
inference(forward_subsumption_resolution,[],[f655,f118]) ).
fof(f657,plain,
( ~ relation(sK12)
| ~ function(sK12)
| spl13_27 ),
inference(forward_subsumption_resolution,[],[f656,f117]) ).
fof(f658,plain,
( ~ function(sK12)
| spl13_27 ),
inference(forward_subsumption_resolution,[],[f657,f180]) ).
fof(f659,plain,
( $false
| spl13_27 ),
inference(forward_subsumption_resolution,[],[f658,f179]) ).
fof(f660,plain,
spl13_27,
inference(avatar_contradiction_clause,[],[f659]) ).
fof(f702,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_33 ),
inference(resolution,[],[f609,f172]) ).
fof(f707,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_33 ),
inference(forward_subsumption_resolution,[],[f702,f181]) ).
fof(f709,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_33 ),
inference(forward_subsumption_resolution,[],[f707,f180]) ).
fof(f711,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_33 ),
inference(forward_subsumption_resolution,[],[f709,f179]) ).
fof(f713,plain,
( spl13_34
| ~ spl13_33 ),
inference(avatar_split_clause,[],[f711,f607,f612]) ).
fof(f714,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))
| ~ function(relation_composition(function_inverse(sK12),sK12))
| ~ spl13_26 ),
inference(forward_subsumption_resolution,[],[f590,f565]) ).
fof(f715,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_26 ),
inference(forward_subsumption_resolution,[],[f589,f565]) ).
fof(f716,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))
| ~ spl13_26
| ~ spl13_27 ),
inference(forward_subsumption_resolution,[],[f714,f570]) ).
fof(f717,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_26
| ~ spl13_27 ),
inference(forward_subsumption_resolution,[],[f715,f570]) ).
fof(f718,plain,
( spl13_1
| spl13_33
| ~ spl13_26
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f716,f569,f564,f607,f191]) ).
fof(f719,plain,
( spl13_1
| ~ spl13_34
| ~ spl13_26
| ~ spl13_27 ),
inference(avatar_split_clause,[],[f717,f569,f564,f612,f191]) ).
fof(f749,plain,
( ~ one_to_one(sK12)
| 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(sK12)
| ~ function(sK12)
| ~ spl13_18 ),
inference(resolution,[],[f511,f170]) ).
fof(f754,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(sK12)
| ~ function(sK12)
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f749,f181]) ).
fof(f756,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))))
| ~ function(sK12)
| ~ spl13_18 ),
inference(forward_subsumption_resolution,[],[f754,f180]) ).
fof(f758,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_18 ),
inference(forward_subsumption_resolution,[],[f756,f179]) ).
fof(f760,plain,
( spl13_19
| ~ spl13_18 ),
inference(avatar_split_clause,[],[f758,f509,f514]) ).
cnf(s1,plain,
( ~ spl13_1
| ~ spl13_2 ),
inference(sat_conversion,[],[f198]) ).
cnf(s14,plain,
spl13_10,
inference(sat_conversion,[],[f421]) ).
cnf(s15,plain,
( spl13_9
| ~ spl13_10 ),
inference(sat_conversion,[],[f438]) ).
cnf(s17,plain,
( ~ spl13_10
| spl13_12 ),
inference(sat_conversion,[],[f474]) ).
cnf(s20,plain,
( spl13_2
| ~ spl13_9
| ~ spl13_12
| spl13_18 ),
inference(sat_conversion,[],[f512]) ).
cnf(s21,plain,
( spl13_2
| ~ spl13_9
| ~ spl13_12
| ~ spl13_19 ),
inference(sat_conversion,[],[f517]) ).
cnf(s38,plain,
( ~ spl13_10
| spl13_26 ),
inference(sat_conversion,[],[f639]) ).
cnf(s39,plain,
spl13_27,
inference(sat_conversion,[],[f660]) ).
cnf(s40,plain,
( ~ spl13_33
| spl13_34 ),
inference(sat_conversion,[],[f713]) ).
cnf(s41,plain,
( spl13_1
| ~ spl13_26
| ~ spl13_27
| spl13_33 ),
inference(sat_conversion,[],[f718]) ).
cnf(s42,plain,
( spl13_1
| ~ spl13_26
| ~ spl13_27
| ~ spl13_34 ),
inference(sat_conversion,[],[f719]) ).
cnf(s43,plain,
( ~ spl13_18
| spl13_19 ),
inference(sat_conversion,[],[f760]) ).
cnf(s50,plain,
spl13_26,
inference(rat,[],[s38,s14]) ).
cnf(s51,plain,
spl13_12,
inference(rat,[],[s17,s14]) ).
cnf(s52,plain,
spl13_9,
inference(rat,[],[s15,s14]) ).
cnf(s56,plain,
spl13_1,
inference(rat,[],[s40,s41,s42,s39,s50]) ).
cnf(s57,plain,
~ spl13_2,
inference(rat,[],[s1,s56]) ).
cnf(s58,plain,
~ spl13_19,
inference(rat,[],[s21,s52,s51,s57]) ).
cnf(s59,plain,
spl13_18,
inference(rat,[],[s20,s52,s51,s57]) ).
cnf(s60,plain,
$false,
inference(rat,[],[s43,s58,s59]) ).
fof(f761,plain,
$false,
inference(avatar_sat_refutation,[],[s60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU028+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 03:25:47 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (406138)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (406148)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2862841030:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.48 % (406144)% WARNING: option uhcvi not known.
% 0.17/0.48 % (406143)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1161989977_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.48 % (406147)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=783108514:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.48 % (406144)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=936577030:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.48 % (406145)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3658664260:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (406146)dis+10_1_sil=32000:sp=arity:random_seed=2787704463:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.48 % (406149)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=557962134:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.48 % TRYING [1]
% 0.17/0.48 % TRYING [2]
% 0.17/0.48 % TRYING [3]
% 0.17/0.48 % TRYING [4]
% 0.17/0.48 % (406146) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-406138-406146"...
% 0.17/0.48 % (406147) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-406138-406147"...
% 0.17/0.48 % TRYING [5]
% 0.17/0.48 % (406146)...printing done.
% 0.17/0.48 % (406146)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (406146)------------------------------
% 0.17/0.48 % (406146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (406146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (406146)CaDiCaL version: 2.1.3
% 0.17/0.48 % (406146)Termination reason: Refutation
% 0.17/0.48 % (406146)Time elapsed: 0.015 s
% 0.17/0.48 % (406146)Peak memory usage: 12 MB
% 0.17/0.48 % (406146)Instructions burned: 21 (million)
% 0.17/0.48 % (406138)Success in time 0.054 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------