%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU014+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 : n019.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 4.96s 1.17s
% Output : Refutation 4.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 12
% Syntax : Number of formulae : 132 ( 30 unt; 6 def)
% Number of atoms : 442 ( 67 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 450 ( 140 ~; 255 |; 30 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 99 ( 0 sgn 95 !; 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(f28,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(X1))
=> apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f31,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ( subset(relation_rng(X0),relation_dom(X1))
=> relation_dom(relation_composition(X0,X1)) = relation_dom(X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_relat_1) ).
fof(f32,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(relation_composition(X1,X0))
& subset(relation_rng(X1),relation_dom(X0)) )
=> one_to_one(X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
fof(f33,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(relation_composition(X1,X0))
& subset(relation_rng(X1),relation_dom(X0)) )
=> one_to_one(X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
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(ennf_transformation,[],[f4]) ).
fof(f46,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,[],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f47]) ).
fof(f51,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(f52,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f51]) ).
fof(f63,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f28]) ).
fof(f64,plain,
! [X0,X1] :
( ! [X2] :
( apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0))
| ~ in(X0,relation_dom(X1))
| ~ relation(X2)
| ~ function(X2) )
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f63]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f68,plain,
! [X0] :
( ! [X1] :
( relation_dom(relation_composition(X0,X1)) = relation_dom(X0)
| ~ subset(relation_rng(X0),relation_dom(X1))
| ~ relation(X1) )
| ~ relation(X0) ),
inference(flattening,[],[f67]) ).
fof(f69,plain,
? [X0] :
( ? [X1] :
( ~ one_to_one(X1)
& one_to_one(relation_composition(X1,X0))
& subset(relation_rng(X1),relation_dom(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f70,plain,
? [X0] :
( ? [X1] :
( ~ one_to_one(X1)
& one_to_one(relation_composition(X1,X0))
& subset(relation_rng(X1),relation_dom(X0))
& relation(X1)
& function(X1) )
& relation(X0)
& function(X0) ),
inference(flattening,[],[f69]) ).
fof(f80,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) != apply(X0,X2)
| ~ in(X2,relation_dom(X0))
| ~ in(X1,relation_dom(X0))
| X1 = X2
| ~ one_to_one(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f81,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f82,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK1(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f83,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| in(sK0(X0),relation_dom(X0))
| one_to_one(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f84,plain,
! [X0] :
( ~ function(X0)
| ~ relation(X0)
| sK0(X0) != sK1(X0)
| one_to_one(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f85,plain,
! [X0,X1] :
( ~ relation(X1)
| ~ relation(X0)
| relation(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f91,plain,
! [X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| function(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f52]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ function(X1)
| ~ relation(X1)
| ~ function(X2)
| ~ relation(X2)
| ~ in(X0,relation_dom(X1))
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(cnf_transformation,[],[f64]) ).
fof(f124,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ relation(X1)
| ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(cnf_transformation,[],[f68]) ).
fof(f125,plain,
function(sK12),
inference(cnf_transformation,[],[f70]) ).
fof(f126,plain,
relation(sK12),
inference(cnf_transformation,[],[f70]) ).
fof(f127,plain,
subset(relation_rng(sK12),relation_dom(sK11)),
inference(cnf_transformation,[],[f70]) ).
fof(f128,plain,
one_to_one(relation_composition(sK12,sK11)),
inference(cnf_transformation,[],[f70]) ).
fof(f129,plain,
~ one_to_one(sK12),
inference(cnf_transformation,[],[f70]) ).
fof(f130,plain,
function(sK11),
inference(cnf_transformation,[],[f70]) ).
fof(f131,plain,
relation(sK11),
inference(cnf_transformation,[],[f70]) ).
fof(f140,plain,
! [X0] :
( sK0(X0) != sK1(X0)
| relation(X0)
| function(X0)
| one_to_one(X0) ),
inference(consistent_polarity_flipping,[],[f84]) ).
fof(f141,plain,
! [X0] :
( ~ in(sK0(X0),relation_dom(X0))
| relation(X0)
| function(X0)
| one_to_one(X0) ),
inference(consistent_polarity_flipping,[],[f83]) ).
fof(f142,plain,
! [X0] :
( ~ in(sK1(X0),relation_dom(X0))
| relation(X0)
| function(X0)
| one_to_one(X0) ),
inference(consistent_polarity_flipping,[],[f82]) ).
fof(f143,plain,
! [X0] :
( one_to_one(X0)
| relation(X0)
| apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| function(X0) ),
inference(consistent_polarity_flipping,[],[f81]) ).
fof(f144,plain,
! [X2,X0,X1] :
( apply(X0,X1) != apply(X0,X2)
| relation(X0)
| function(X0)
| in(X2,relation_dom(X0))
| in(X1,relation_dom(X0))
| X1 = X2
| ~ one_to_one(X0) ),
inference(consistent_polarity_flipping,[],[f80]) ).
fof(f145,plain,
! [X0,X1] :
( ~ relation(relation_composition(X0,X1))
| relation(X0)
| relation(X1) ),
inference(consistent_polarity_flipping,[],[f85]) ).
fof(f150,plain,
! [X0,X1] :
( ~ function(relation_composition(X0,X1))
| relation(X1)
| function(X0)
| relation(X0)
| function(X1) ),
inference(consistent_polarity_flipping,[],[f91]) ).
fof(f165,plain,
! [X2,X0,X1] :
( function(X2)
| in(X0,relation_dom(X1))
| function(X1)
| relation(X2)
| relation(X1)
| apply(relation_composition(X1,X2),X0) = apply(X2,apply(X1,X0)) ),
inference(consistent_polarity_flipping,[],[f120]) ).
fof(f169,plain,
! [X0,X1] :
( subset(relation_rng(X0),relation_dom(X1))
| relation(X1)
| relation(X0)
| relation_dom(X0) = relation_dom(relation_composition(X0,X1)) ),
inference(consistent_polarity_flipping,[],[f124]) ).
fof(f170,plain,
~ relation(sK11),
inference(consistent_polarity_flipping,[],[f131]) ).
fof(f171,plain,
~ function(sK11),
inference(consistent_polarity_flipping,[],[f130]) ).
fof(f172,plain,
~ subset(relation_rng(sK12),relation_dom(sK11)),
inference(consistent_polarity_flipping,[],[f127]) ).
fof(f173,plain,
~ relation(sK12),
inference(consistent_polarity_flipping,[],[f126]) ).
fof(f174,plain,
~ function(sK12),
inference(consistent_polarity_flipping,[],[f125]) ).
fof(f322,plain,
( relation(sK12)
| apply(sK12,sK0(sK12)) = apply(sK12,sK1(sK12))
| function(sK12) ),
inference(resolution,[],[f143,f129]) ).
fof(f323,plain,
( apply(sK12,sK0(sK12)) = apply(sK12,sK1(sK12))
| function(sK12) ),
inference(forward_subsumption_resolution,[],[f322,f173]) ).
fof(f324,plain,
apply(sK12,sK0(sK12)) = apply(sK12,sK1(sK12)),
inference(forward_subsumption_resolution,[],[f323,f174]) ).
fof(f325,plain,
( relation(sK11)
| relation(sK12)
| relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11)) ),
inference(resolution,[],[f169,f172]) ).
fof(f329,plain,
( relation(sK12)
| relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11)) ),
inference(forward_subsumption_resolution,[],[f325,f170]) ).
fof(f330,plain,
relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11)),
inference(forward_subsumption_resolution,[],[f329,f173]) ).
fof(f352,definition,
( spl13_8
<=> relation(relation_composition(sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_8])],[avatar_definition]) ).
fof(f353,plain,
( ~ relation(relation_composition(sK12,sK11))
| spl13_8 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f354,plain,
( relation(relation_composition(sK12,sK11))
| ~ spl13_8 ),
inference(avatar_component_clause,[],[f352]) ).
fof(f367,plain,
! [X0,X1] :
( function(X1)
| function(X0)
| relation(X1)
| relation(X0)
| apply(relation_composition(X0,X1),sK0(X0)) = apply(X1,apply(X0,sK0(X0)))
| relation(X0)
| function(X0)
| one_to_one(X0) ),
inference(resolution,[],[f165,f141]) ).
fof(f368,plain,
! [X0,X1] :
( function(X1)
| function(X0)
| relation(X1)
| relation(X0)
| apply(relation_composition(X0,X1),sK1(X0)) = apply(X1,apply(X0,sK1(X0)))
| relation(X0)
| function(X0)
| one_to_one(X0) ),
inference(resolution,[],[f165,f142]) ).
fof(f371,plain,
! [X0,X1] :
( function(X1)
| one_to_one(X0)
| relation(X1)
| relation(X0)
| apply(relation_composition(X0,X1),sK1(X0)) = apply(X1,apply(X0,sK1(X0)))
| function(X0) ),
inference(duplicate_literal_removal,[],[f368]) ).
fof(f372,plain,
! [X0,X1] :
( function(X1)
| one_to_one(X0)
| relation(X1)
| relation(X0)
| apply(relation_composition(X0,X1),sK0(X0)) = apply(X1,apply(X0,sK0(X0)))
| function(X0) ),
inference(duplicate_literal_removal,[],[f367]) ).
fof(f374,definition,
( spl13_10
<=> function(relation_composition(sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_10])],[avatar_definition]) ).
fof(f375,plain,
( ~ function(relation_composition(sK12,sK11))
| spl13_10 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f376,plain,
( function(relation_composition(sK12,sK11))
| ~ spl13_10 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f389,plain,
( relation(sK12)
| relation(sK11)
| ~ spl13_8 ),
inference(resolution,[],[f354,f145]) ).
fof(f391,plain,
( relation(sK11)
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f389,f173]) ).
fof(f392,plain,
( $false
| ~ spl13_8 ),
inference(forward_subsumption_resolution,[],[f391,f170]) ).
fof(f393,plain,
~ spl13_8,
inference(avatar_contradiction_clause,[],[f392]) ).
fof(f433,plain,
( relation(sK11)
| function(sK12)
| relation(sK12)
| function(sK11)
| ~ spl13_10 ),
inference(resolution,[],[f376,f150]) ).
fof(f435,plain,
( function(sK12)
| relation(sK12)
| function(sK11)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f433,f170]) ).
fof(f436,plain,
( relation(sK12)
| function(sK11)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f435,f174]) ).
fof(f437,plain,
( function(sK11)
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f436,f173]) ).
fof(f438,plain,
( $false
| ~ spl13_10 ),
inference(forward_subsumption_resolution,[],[f437,f171]) ).
fof(f439,plain,
~ spl13_10,
inference(avatar_contradiction_clause,[],[f438]) ).
fof(f559,plain,
! [X0] :
( function(X0)
| relation(X0)
| relation(sK12)
| apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK1(sK12)))
| function(sK12) ),
inference(resolution,[],[f371,f129]) ).
fof(f560,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK1(sK12)))
| function(sK12) ),
inference(forward_subsumption_resolution,[],[f559,f173]) ).
fof(f564,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK1(sK12))) ),
inference(forward_subsumption_resolution,[],[f560,f174]) ).
fof(f565,plain,
! [X0] :
( function(X0)
| apply(relation_composition(sK12,X0),sK1(sK12)) = apply(X0,apply(sK12,sK0(sK12)))
| relation(X0) ),
inference(forward_demodulation,[],[f564,f324]) ).
fof(f569,plain,
! [X0] :
( function(X0)
| relation(X0)
| relation(sK12)
| apply(X0,apply(sK12,sK0(sK12))) = apply(relation_composition(sK12,X0),sK0(sK12))
| function(sK12) ),
inference(resolution,[],[f372,f129]) ).
fof(f570,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(X0,apply(sK12,sK0(sK12))) = apply(relation_composition(sK12,X0),sK0(sK12))
| function(sK12) ),
inference(forward_subsumption_resolution,[],[f569,f173]) ).
fof(f574,plain,
! [X0] :
( function(X0)
| relation(X0)
| apply(X0,apply(sK12,sK0(sK12))) = apply(relation_composition(sK12,X0),sK0(sK12)) ),
inference(forward_subsumption_resolution,[],[f570,f174]) ).
fof(f686,plain,
( apply(relation_composition(sK12,sK11),sK1(sK12)) = apply(sK11,apply(sK12,sK0(sK12)))
| relation(sK11) ),
inference(resolution,[],[f565,f171]) ).
fof(f689,plain,
apply(relation_composition(sK12,sK11),sK1(sK12)) = apply(sK11,apply(sK12,sK0(sK12))),
inference(forward_subsumption_resolution,[],[f686,f170]) ).
fof(f699,plain,
( relation(sK11)
| apply(sK11,apply(sK12,sK0(sK12))) = apply(relation_composition(sK12,sK11),sK0(sK12)) ),
inference(resolution,[],[f574,f171]) ).
fof(f702,plain,
apply(sK11,apply(sK12,sK0(sK12))) = apply(relation_composition(sK12,sK11),sK0(sK12)),
inference(forward_subsumption_resolution,[],[f699,f170]) ).
fof(f1961,definition,
( spl13_54
<=> in(sK1(sK12),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_54])],[avatar_definition]) ).
fof(f1963,plain,
( in(sK1(sK12),relation_dom(sK12))
| ~ spl13_54 ),
inference(avatar_component_clause,[],[f1961]) ).
fof(f2008,plain,
! [X0] :
( apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| relation(relation_composition(sK12,sK11))
| function(relation_composition(sK12,sK11))
| in(sK0(sK12),relation_dom(relation_composition(sK12,sK11)))
| in(X0,relation_dom(relation_composition(sK12,sK11)))
| sK0(sK12) = X0
| ~ one_to_one(relation_composition(sK12,sK11)) ),
inference(superposition,[],[f144,f702]) ).
fof(f2011,plain,
( ! [X0] :
( apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| function(relation_composition(sK12,sK11))
| in(sK0(sK12),relation_dom(relation_composition(sK12,sK11)))
| in(X0,relation_dom(relation_composition(sK12,sK11)))
| sK0(sK12) = X0
| ~ one_to_one(relation_composition(sK12,sK11)) )
| spl13_8 ),
inference(forward_subsumption_resolution,[],[f2008,f353]) ).
fof(f2013,plain,
( ! [X0] :
( apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| in(sK0(sK12),relation_dom(relation_composition(sK12,sK11)))
| in(X0,relation_dom(relation_composition(sK12,sK11)))
| sK0(sK12) = X0
| ~ one_to_one(relation_composition(sK12,sK11)) )
| spl13_8
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f2011,f375]) ).
fof(f2015,plain,
( ! [X0] :
( apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| in(sK0(sK12),relation_dom(relation_composition(sK12,sK11)))
| in(X0,relation_dom(relation_composition(sK12,sK11)))
| sK0(sK12) = X0 )
| spl13_8
| spl13_10 ),
inference(forward_subsumption_resolution,[],[f2013,f128]) ).
fof(f2017,plain,
( ! [X0] :
( in(sK0(sK12),relation_dom(sK12))
| apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| in(X0,relation_dom(relation_composition(sK12,sK11)))
| sK0(sK12) = X0 )
| spl13_8
| spl13_10 ),
inference(forward_demodulation,[],[f2015,f330]) ).
fof(f2019,plain,
( ! [X0] :
( in(X0,relation_dom(sK12))
| in(sK0(sK12),relation_dom(sK12))
| apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| sK0(sK12) = X0 )
| spl13_8
| spl13_10 ),
inference(forward_demodulation,[],[f2017,f330]) ).
fof(f2021,definition,
( spl13_62
<=> ! [X0] :
( in(X0,relation_dom(sK12))
| sK0(sK12) = X0
| apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12))) ) ),
introduced(definition,[new_symbols(definition,[spl13_62])],[avatar_definition]) ).
fof(f2022,plain,
( ! [X0] :
( apply(relation_composition(sK12,sK11),X0) != apply(sK11,apply(sK12,sK0(sK12)))
| sK0(sK12) = X0
| in(X0,relation_dom(sK12)) )
| ~ spl13_62 ),
inference(avatar_component_clause,[],[f2021]) ).
fof(f2024,definition,
( spl13_63
<=> in(sK0(sK12),relation_dom(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_63])],[avatar_definition]) ).
fof(f2026,plain,
( in(sK0(sK12),relation_dom(sK12))
| ~ spl13_63 ),
inference(avatar_component_clause,[],[f2024]) ).
fof(f2028,plain,
( spl13_63
| spl13_62
| spl13_8
| spl13_10 ),
inference(avatar_split_clause,[],[f2019,f374,f352,f2021,f2024]) ).
fof(f25125,definition,
( spl13_859
<=> sK0(sK12) = sK1(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_859])],[avatar_definition]) ).
fof(f25127,plain,
( sK0(sK12) = sK1(sK12)
| ~ spl13_859 ),
inference(avatar_component_clause,[],[f25125]) ).
fof(f25129,plain,
( apply(sK11,apply(sK12,sK0(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| sK0(sK12) = sK1(sK12)
| in(sK1(sK12),relation_dom(sK12))
| ~ spl13_62 ),
inference(superposition,[],[f2022,f689]) ).
fof(f25131,plain,
( sK0(sK12) = sK1(sK12)
| in(sK1(sK12),relation_dom(sK12))
| ~ spl13_62 ),
inference(trivial_inequality_removal,[],[f25129]) ).
fof(f25137,plain,
( spl13_54
| spl13_859
| ~ spl13_62 ),
inference(avatar_split_clause,[],[f25131,f2021,f25125,f1961]) ).
fof(f25153,plain,
( sK0(sK12) != sK0(sK12)
| relation(sK12)
| function(sK12)
| one_to_one(sK12)
| ~ spl13_859 ),
inference(superposition,[],[f140,f25127]) ).
fof(f25166,plain,
( relation(sK12)
| function(sK12)
| one_to_one(sK12)
| ~ spl13_859 ),
inference(trivial_inequality_removal,[],[f25153]) ).
fof(f25167,plain,
( function(sK12)
| one_to_one(sK12)
| ~ spl13_859 ),
inference(forward_subsumption_resolution,[],[f25166,f173]) ).
fof(f25169,plain,
( one_to_one(sK12)
| ~ spl13_859 ),
inference(forward_subsumption_resolution,[],[f25167,f174]) ).
fof(f25170,plain,
( $false
| ~ spl13_859 ),
inference(forward_subsumption_resolution,[],[f25169,f129]) ).
fof(f25171,plain,
~ spl13_859,
inference(avatar_contradiction_clause,[],[f25170]) ).
fof(f25172,plain,
( relation(sK12)
| function(sK12)
| one_to_one(sK12)
| ~ spl13_54 ),
inference(resolution,[],[f1963,f142]) ).
fof(f25175,plain,
( function(sK12)
| one_to_one(sK12)
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f25172,f173]) ).
fof(f25176,plain,
( one_to_one(sK12)
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f25175,f174]) ).
fof(f25177,plain,
( $false
| ~ spl13_54 ),
inference(forward_subsumption_resolution,[],[f25176,f129]) ).
fof(f25178,plain,
~ spl13_54,
inference(avatar_contradiction_clause,[],[f25177]) ).
fof(f25323,plain,
( relation(sK12)
| function(sK12)
| one_to_one(sK12)
| ~ spl13_63 ),
inference(resolution,[],[f2026,f141]) ).
fof(f25326,plain,
( function(sK12)
| one_to_one(sK12)
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f25323,f173]) ).
fof(f25327,plain,
( one_to_one(sK12)
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f25326,f174]) ).
fof(f25328,plain,
( $false
| ~ spl13_63 ),
inference(forward_subsumption_resolution,[],[f25327,f129]) ).
fof(f25329,plain,
~ spl13_63,
inference(avatar_contradiction_clause,[],[f25328]) ).
cnf(s15,plain,
~ spl13_8,
inference(sat_conversion,[],[f393]) ).
cnf(s16,plain,
~ spl13_10,
inference(sat_conversion,[],[f439]) ).
cnf(s62,plain,
( spl13_8
| spl13_10
| spl13_62
| spl13_63 ),
inference(sat_conversion,[],[f2028]) ).
cnf(s900,plain,
( spl13_54
| ~ spl13_62
| spl13_859 ),
inference(sat_conversion,[],[f25137]) ).
cnf(s902,plain,
~ spl13_859,
inference(sat_conversion,[],[f25171]) ).
cnf(s903,plain,
~ spl13_54,
inference(sat_conversion,[],[f25178]) ).
cnf(s907,plain,
~ spl13_63,
inference(sat_conversion,[],[f25329]) ).
cnf(s911,plain,
~ spl13_62,
inference(rat,[],[s900,s902,s903]) ).
cnf(s948,plain,
( spl13_8
| spl13_10 ),
inference(rat,[],[s62,s907,s911]) ).
cnf(s974,plain,
spl13_8,
inference(rat,[],[s948,s16]) ).
cnf(s975,plain,
$false,
inference(rat,[],[s15,s974]) ).
fof(f25330,plain,
$false,
inference(avatar_sat_refutation,[],[s975]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU014+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 28 03:22:19 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.40 Running first-order model finding
% 0.14/0.40 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
% 4.96/1.17 % (3631734)Will run a generic schedule for satisfiability detection.
% 4.96/1.17 % (3631742)dis+10_1_sil=32000:sp=arity:random_seed=1498680199:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 4.96/1.17 % (3631740)% WARNING: option uhcvi not known.
% 4.96/1.17 % (3631739)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1838043472_2999 on theBenchmark for (2999ds/0Mi)
% 4.96/1.17 % (3631740)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1489056450:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 4.96/1.17 % (3631741)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2547408945:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 4.96/1.17 % (3631743)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2020296026:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 4.96/1.17 % (3631745)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3327823329:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 4.96/1.17 % (3631744)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1798423568:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 4.96/1.17 % TRYING [1]
% 4.96/1.17 % TRYING [2]
% 4.96/1.17 % TRYING [3]
% 4.96/1.17 % TRYING [4]
% 4.96/1.17 % TRYING [5]
% 4.96/1.17 % (3631742)Instruction limit reached!
% 4.96/1.17 % (3631742)------------------------------
% 4.96/1.17 % (3631742)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631742)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631742)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631742)Termination reason: Instruction limit
% 4.96/1.17 % (3631742)Termination phase: Saturation
% 4.96/1.17 % (3631742)Time elapsed: 0.033 s
% 4.96/1.17 % (3631742)Peak memory usage: 12 MB
% 4.96/1.17 % (3631742)Instructions burned: 107 (million)
% 4.96/1.17 % TRYING [6]
% 4.96/1.17 % (3631753)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=2163829662:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 4.96/1.17 % TRYING [1]
% 4.96/1.17 % TRYING [2]
% 4.96/1.17 % TRYING [3]
% 4.96/1.17 % TRYING [4]
% 4.96/1.17 % TRYING [5]
% 4.96/1.17 % TRYING [6]
% 4.96/1.17 % (3631743)Instruction limit reached!
% 4.96/1.17 % (3631743)------------------------------
% 4.96/1.17 % (3631743)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631743)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631743)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631743)Termination reason: Instruction limit
% 4.96/1.17 % (3631743)Termination phase: Saturation
% 4.96/1.17 % (3631743)Time elapsed: 0.063 s
% 4.96/1.17 % (3631743)Peak memory usage: 13 MB
% 4.96/1.17 % (3631743)Instructions burned: 118 (million)
% 4.96/1.17 % TRYING [7]
% 4.96/1.17 % (3631744)Instruction limit reached!
% 4.96/1.17 % (3631744)------------------------------
% 4.96/1.17 % (3631744)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631744)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631744)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631744)Termination reason: Instruction limit
% 4.96/1.17 % (3631744)Termination phase: Saturation
% 4.96/1.17 % (3631744)Time elapsed: 0.075 s
% 4.96/1.17 % (3631744)Peak memory usage: 14 MB
% 4.96/1.17 % (3631744)Instructions burned: 131 (million)
% 4.96/1.17 % TRYING [7]
% 4.96/1.17 % (3631755)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3966803998:i=131:bd=preordered:fsd=on_2998 on theBenchmark for (2998ds/131Mi)
% 4.96/1.17 % (3631745)Instruction limit reached!
% 4.96/1.17 % (3631745)------------------------------
% 4.96/1.17 % (3631745)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631745)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631745)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631745)Termination reason: Instruction limit
% 4.96/1.17 % (3631745)Termination phase: Saturation
% 4.96/1.17 % (3631745)Time elapsed: 0.097 s
% 4.96/1.17 % (3631745)Peak memory usage: 13 MB
% 4.96/1.17 % (3631745)Instructions burned: 160 (million)
% 4.96/1.17 % (3631756)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=2682332151:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2998 on theBenchmark for (2998ds/684Mi)
% 4.96/1.17 % (3631759)ott-21_1_sil=16000:fs=off:random_seed=3322432192:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 4.96/1.17 % (3631755)Instruction limit reached!
% 4.96/1.17 % (3631755)------------------------------
% 4.96/1.17 % (3631755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631755)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631755)Termination reason: Instruction limit
% 4.96/1.17 % (3631755)Termination phase: Saturation
% 4.96/1.17 % (3631755)Time elapsed: 0.083 s
% 4.96/1.17 % (3631755)Peak memory usage: 14 MB
% 4.96/1.17 % (3631755)Instructions burned: 132 (million)
% 4.96/1.17 % (3631761)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=2541187840:i=477:bd=all_2997 on theBenchmark for (2997ds/477Mi)
% 4.96/1.17 % (3631759)Instruction limit reached!
% 4.96/1.17 % (3631759)------------------------------
% 4.96/1.17 % (3631759)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631759)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631759)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631759)Termination reason: Instruction limit
% 4.96/1.17 % (3631759)Termination phase: Saturation
% 4.96/1.17 % (3631759)Time elapsed: 0.079 s
% 4.96/1.17 % (3631759)Peak memory usage: 12 MB
% 4.96/1.17 % (3631759)Instructions burned: 182 (million)
% 4.96/1.17 % (3631753)Instruction limit reached!
% 4.96/1.17 % (3631753)------------------------------
% 4.96/1.17 % (3631753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631753)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631753)Termination reason: Instruction limit
% 4.96/1.17 % (3631753)Termination phase: Finite model building SAT solving
% 4.96/1.17 % (3631753)Time elapsed: 0.179 s
% 4.96/1.17 % (3631753)Peak memory usage: 29 MB
% 4.96/1.17 % (3631753)Instructions burned: 716 (million)
% 4.96/1.17 % (3631763)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=1852273549:fmbsr=1.3:i=865:ins=25_2997 on theBenchmark for (2997ds/865Mi)
% 4.96/1.17 % TRYING [1]
% 4.96/1.17 % TRYING [2]
% 4.96/1.17 % TRYING [3]
% 4.96/1.17 % (3631764)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=710199129:i=1179_2997 on theBenchmark for (2997ds/1179Mi)
% 4.96/1.17 % TRYING [4]
% 4.96/1.17 % TRYING [5]
% 4.96/1.17 % TRYING [8]
% 4.96/1.17 % TRYING [6]
% 4.96/1.17 % TRYING [7]
% 4.96/1.17 % (3631756)Instruction limit reached!
% 4.96/1.17 % (3631756)------------------------------
% 4.96/1.17 % (3631756)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631756)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631756)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631756)Termination reason: Instruction limit
% 4.96/1.17 % (3631756)Termination phase: Saturation
% 4.96/1.17 % (3631756)Time elapsed: 0.354 s
% 4.96/1.17 % (3631756)Peak memory usage: 19 MB
% 4.96/1.17 % (3631756)Instructions burned: 685 (million)
% 4.96/1.17 % (3631767)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=2740190318:i=889:ins=1_2995 on theBenchmark for (2995ds/889Mi)
% 4.96/1.17 % (3631761)Instruction limit reached!
% 4.96/1.17 % (3631761)------------------------------
% 4.96/1.17 % (3631761)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631761)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631761)Termination reason: Instruction limit
% 4.96/1.17 % (3631761)Termination phase: Saturation
% 4.96/1.17 % (3631761)Time elapsed: 0.308 s
% 4.96/1.17 % (3631761)Peak memory usage: 15 MB
% 4.96/1.17 % (3631761)Instructions burned: 478 (million)
% 4.96/1.17 % TRYING [14]
% 4.96/1.17 % (3631769)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3072356054:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2994 on theBenchmark for (2994ds/692Mi)
% 4.96/1.17 % (3631763)Instruction limit reached!
% 4.96/1.17 % (3631763)------------------------------
% 4.96/1.17 % (3631763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631763)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631763)Termination reason: Instruction limit
% 4.96/1.17 % (3631763)Termination phase: Finite model building SAT solving
% 4.96/1.17 % (3631763)Time elapsed: 0.310 s
% 4.96/1.17 % (3631763)Peak memory usage: 20 MB
% 4.96/1.17 % (3631763)Instructions burned: 865 (million)
% 4.96/1.17 % (3631771)dis-10_1_anc=none:sil=64000:spb=goal:newcnf=on:cn=on:random_seed=3022109055:i=879:kws=inv_precedence:fsr=off_2994 on theBenchmark for (2994ds/879Mi)
% 4.96/1.17 % (3631764)Instruction limit reached!
% 4.96/1.17 % (3631764)------------------------------
% 4.96/1.17 % (3631764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.17 % (3631764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.17 % (3631764)CaDiCaL version: 2.1.3
% 4.96/1.17 % (3631764)Termination reason: Instruction limit
% 4.96/1.17 % (3631764)Termination phase: Saturation
% 4.96/1.17 % (3631764)Time elapsed: 0.331 s
% 4.96/1.17 % (3631764)Peak memory usage: 25 MB
% 4.96/1.17 % (3631764)Instructions burned: 1179 (million)
% 4.96/1.17 % (3631773)fmb+10_1_sil=64000:random_seed=3292690135:i=22061:nm=2:gsp=on_2994 on theBenchmark for (2994ds/22061Mi)
% 4.96/1.17 % TRYING [1]
% 4.96/1.17 % TRYING [2]
% 4.96/1.17 % TRYING [3]
% 4.96/1.17 % TRYING [4]
% 4.96/1.17 % TRYING [5]
% 4.96/1.17 % TRYING [6]
% 4.96/1.17 % TRYING [7]
% 4.96/1.17 % (3631740) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3631734-3631740"...
% 4.96/1.17 % (3631740)...printing done.
% 4.96/1.17 % (3631740)Refutation found. Thanks to Tanya!
% 4.96/1.17 % SZS status Theorem for theBenchmark
% 4.96/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 4.96/1.18 % (3631740)------------------------------
% 4.96/1.18 % (3631740)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 4.96/1.18 % (3631740)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.96/1.18 % (3631740)CaDiCaL version: 2.1.3
% 4.96/1.18 % (3631740)Termination reason: Refutation
% 4.96/1.18 % (3631740)Time elapsed: 0.717 s
% 4.96/1.18 % (3631740)Peak memory usage: 22 MB
% 4.96/1.18 % (3631740)Instructions burned: 1305 (million)
% 4.96/1.18 % (3631734)Success in time 0.766 s
% 4.96/1.18 % Vampire exiting
%------------------------------------------------------------------------------