%------------------------------------------------------------------------------
% File : Vampire---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 THM
% Computer : n013.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 12:47:04 PM UTC 2026
% Result : Theorem 3.18s 1.31s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 11
% Syntax : Number of formulae : 108 ( 21 unt; 5 def)
% Number of atoms : 398 ( 65 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 510 ( 220 ~; 218 |; 48 &)
% ( 8 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 76 !; 8 ?)
% 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(f77,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) ) )
& ( ! [X1,X2] :
( X1 = X2
| ~ in(X1,relation_dom(X0))
| ~ in(X2,relation_dom(X0))
| apply(X0,X1) != apply(X0,X2) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f46]) ).
fof(f78,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) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK0(X0) != sK1(X0)
& in(sK0(X0),relation_dom(X0))
& in(sK1(X0),relation_dom(X0))
& apply(X0,sK0(X0)) = apply(X0,sK1(X0)) ) )
& ( ! [X3,X4] :
( X3 = X4
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4) )
| ~ one_to_one(X0) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X1,sK0(X0)),skolemize(X2,sK1(X0))],[f78]) ).
fof(f90,plain,
( ~ one_to_one(sK12)
& one_to_one(relation_composition(sK12,sK11))
& subset(relation_rng(sK12),relation_dom(sK11))
& relation(sK12)
& function(sK12)
& relation(sK11)
& function(sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK11,sK12]),skolemize(X0,sK11),skolemize(X1,sK12)],[f70]) ).
fof(f94,plain,
! [X3,X0,X4] :
( ~ one_to_one(X0)
| ~ in(X3,relation_dom(X0))
| ~ in(X4,relation_dom(X0))
| apply(X0,X3) != apply(X0,X4)
| X3 = X4
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f95,plain,
! [X0] :
( apply(X0,sK0(X0)) = apply(X0,sK1(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f96,plain,
! [X0] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f97,plain,
! [X0] :
( one_to_one(X0)
| in(sK0(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f98,plain,
! [X0] :
( sK0(X0) != sK1(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f99,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f48]) ).
fof(f105,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f134,plain,
! [X2,X0,X1] :
( 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(cnf_transformation,[],[f64]) ).
fof(f138,plain,
! [X0,X1] :
( ~ subset(relation_rng(X0),relation_dom(X1))
| relation_dom(X0) = relation_dom(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f139,plain,
function(sK11),
inference(cnf_transformation,[],[f90]) ).
fof(f140,plain,
relation(sK11),
inference(cnf_transformation,[],[f90]) ).
fof(f141,plain,
function(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f142,plain,
relation(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f143,plain,
subset(relation_rng(sK12),relation_dom(sK11)),
inference(cnf_transformation,[],[f90]) ).
fof(f144,plain,
one_to_one(relation_composition(sK12,sK11)),
inference(cnf_transformation,[],[f90]) ).
fof(f145,plain,
~ one_to_one(sK12),
inference(cnf_transformation,[],[f90]) ).
fof(f167,plain,
( in(sK1(sK12),relation_dom(sK12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f96,f145]) ).
fof(f168,plain,
( in(sK1(sK12),relation_dom(sK12))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f167,f142]) ).
fof(f169,plain,
in(sK1(sK12),relation_dom(sK12)),
inference(forward_subsumption_resolution,[],[f168,f141]) ).
fof(f172,plain,
( in(sK0(sK12),relation_dom(sK12))
| ~ relation(sK12)
| ~ function(sK12) ),
inference(resolution,[],[f97,f145]) ).
fof(f173,plain,
( in(sK0(sK12),relation_dom(sK12))
| ~ function(sK12) ),
inference(forward_subsumption_resolution,[],[f172,f142]) ).
fof(f174,plain,
in(sK0(sK12),relation_dom(sK12)),
inference(forward_subsumption_resolution,[],[f173,f141]) ).
fof(f178,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11))
| ~ relation(sK11)
| ~ relation(sK12) ),
inference(resolution,[],[f138,f143]) ).
fof(f180,plain,
( relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11))
| ~ relation(sK12) ),
inference(forward_subsumption_resolution,[],[f178,f140]) ).
fof(f181,plain,
relation_dom(sK12) = relation_dom(relation_composition(sK12,sK11)),
inference(forward_subsumption_resolution,[],[f180,f142]) ).
fof(f197,definition,
( spl13_3
<=> relation(relation_composition(sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_3])],[avatar_definition]) ).
fof(f199,plain,
( ~ relation(relation_composition(sK12,sK11))
| spl13_3 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f214,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(relation_composition(sK12,sK11)))
| ~ in(X1,relation_dom(relation_composition(sK12,sK11)))
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),X1)
| X0 = X1
| ~ relation(relation_composition(sK12,sK11))
| ~ function(relation_composition(sK12,sK11)) ),
inference(resolution,[],[f94,f144]) ).
fof(f219,plain,
! [X0,X1] :
( ~ in(X0,relation_dom(sK12))
| ~ in(X1,relation_dom(relation_composition(sK12,sK11)))
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),X1)
| X0 = X1
| ~ relation(relation_composition(sK12,sK11))
| ~ function(relation_composition(sK12,sK11)) ),
inference(forward_demodulation,[],[f214,f181]) ).
fof(f220,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(sK12))
| ~ in(X0,relation_dom(sK12))
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),X1)
| X0 = X1
| ~ relation(relation_composition(sK12,sK11))
| ~ function(relation_composition(sK12,sK11)) ),
inference(forward_demodulation,[],[f219,f181]) ).
fof(f222,definition,
( spl13_5
<=> function(relation_composition(sK12,sK11)) ),
introduced(definition,[new_symbols(definition,[spl13_5])],[avatar_definition]) ).
fof(f224,plain,
( ~ function(relation_composition(sK12,sK11))
| spl13_5 ),
inference(avatar_component_clause,[],[f222]) ).
fof(f226,definition,
( spl13_6
<=> ! [X0,X1] :
( ~ in(X1,relation_dom(sK12))
| X0 = X1
| ~ in(X0,relation_dom(sK12))
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),X1) ) ),
introduced(definition,[new_symbols(definition,[spl13_6])],[avatar_definition]) ).
fof(f227,plain,
( ! [X0,X1] :
( ~ in(X1,relation_dom(sK12))
| X0 = X1
| ~ in(X0,relation_dom(sK12))
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),X1) )
| ~ spl13_6 ),
inference(avatar_component_clause,[],[f226]) ).
fof(f228,plain,
( ~ spl13_5
| ~ spl13_3
| spl13_6 ),
inference(avatar_split_clause,[],[f220,f226,f197,f222]) ).
fof(f231,plain,
( ~ relation(sK12)
| ~ relation(sK11)
| spl13_3 ),
inference(resolution,[],[f199,f99]) ).
fof(f233,plain,
( ~ relation(sK11)
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f231,f142]) ).
fof(f234,plain,
( $false
| spl13_3 ),
inference(forward_subsumption_resolution,[],[f233,f140]) ).
fof(f235,plain,
spl13_3,
inference(avatar_contradiction_clause,[],[f234]) ).
fof(f236,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ relation(sK11)
| ~ function(sK11)
| spl13_5 ),
inference(resolution,[],[f224,f105]) ).
fof(f238,plain,
( ~ function(sK12)
| ~ relation(sK11)
| ~ function(sK11)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f236,f142]) ).
fof(f239,plain,
( ~ relation(sK11)
| ~ function(sK11)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f238,f141]) ).
fof(f240,plain,
( ~ function(sK11)
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f239,f140]) ).
fof(f241,plain,
( $false
| spl13_5 ),
inference(forward_subsumption_resolution,[],[f240,f139]) ).
fof(f242,plain,
spl13_5,
inference(avatar_contradiction_clause,[],[f241]) ).
fof(f244,plain,
( ! [X0] :
( ~ in(X0,relation_dom(sK12))
| sK0(sK12) = X0
| apply(relation_composition(sK12,sK11),X0) != apply(relation_composition(sK12,sK11),sK0(sK12)) )
| ~ spl13_6 ),
inference(resolution,[],[f227,f174]) ).
fof(f325,definition,
( spl13_11
<=> apply(relation_composition(sK12,sK11),sK1(sK12)) = apply(relation_composition(sK12,sK11),sK0(sK12)) ),
introduced(definition,[new_symbols(definition,[spl13_11])],[avatar_definition]) ).
fof(f327,plain,
( apply(relation_composition(sK12,sK11),sK1(sK12)) != apply(relation_composition(sK12,sK11),sK0(sK12))
| spl13_11 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f329,definition,
( spl13_12
<=> sK1(sK12) = sK0(sK12) ),
introduced(definition,[new_symbols(definition,[spl13_12])],[avatar_definition]) ).
fof(f331,plain,
( sK1(sK12) = sK0(sK12)
| ~ spl13_12 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f334,plain,
( sK1(sK12) = sK0(sK12)
| apply(relation_composition(sK12,sK11),sK1(sK12)) != apply(relation_composition(sK12,sK11),sK0(sK12))
| ~ spl13_6 ),
inference(resolution,[],[f244,f169]) ).
fof(f338,plain,
( ~ spl13_11
| spl13_12
| ~ spl13_6 ),
inference(avatar_split_clause,[],[f334,f226,f329,f325]) ).
fof(f499,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| ~ in(sK1(sK12),relation_dom(sK12))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(superposition,[],[f327,f134]) ).
fof(f500,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f499,f169]) ).
fof(f501,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f500,f140]) ).
fof(f502,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f501,f139]) ).
fof(f503,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f502,f142]) ).
fof(f504,plain,
( apply(relation_composition(sK12,sK11),sK0(sK12)) != apply(sK11,apply(sK12,sK1(sK12)))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f503,f141]) ).
fof(f555,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| ~ in(sK0(sK12),relation_dom(sK12))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(superposition,[],[f504,f134]) ).
fof(f556,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| ~ relation(sK11)
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f555,f174]) ).
fof(f557,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| ~ function(sK11)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f556,f140]) ).
fof(f558,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f557,f139]) ).
fof(f559,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f558,f142]) ).
fof(f560,plain,
( apply(sK11,apply(sK12,sK1(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f559,f141]) ).
fof(f606,plain,
( apply(sK11,apply(sK12,sK0(sK12))) != apply(sK11,apply(sK12,sK0(sK12)))
| one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(superposition,[],[f560,f95]) ).
fof(f607,plain,
( one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(trivial_inequality_removal,[],[f606]) ).
fof(f608,plain,
( ~ relation(sK12)
| ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f607,f145]) ).
fof(f609,plain,
( ~ function(sK12)
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f608,f142]) ).
fof(f610,plain,
( $false
| spl13_11 ),
inference(forward_subsumption_resolution,[],[f609,f141]) ).
fof(f611,plain,
spl13_11,
inference(avatar_contradiction_clause,[],[f610]) ).
fof(f621,plain,
( sK0(sK12) != sK0(sK12)
| one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_12 ),
inference(superposition,[],[f98,f331]) ).
fof(f622,plain,
( one_to_one(sK12)
| ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_12 ),
inference(trivial_inequality_removal,[],[f621]) ).
fof(f623,plain,
( ~ relation(sK12)
| ~ function(sK12)
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f622,f145]) ).
fof(f624,plain,
( ~ function(sK12)
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f623,f142]) ).
fof(f625,plain,
( $false
| ~ spl13_12 ),
inference(forward_subsumption_resolution,[],[f624,f141]) ).
fof(f626,plain,
~ spl13_12,
inference(avatar_contradiction_clause,[],[f625]) ).
cnf(s4,plain,
( ~ spl13_3
| ~ spl13_5
| spl13_6 ),
inference(sat_conversion,[],[f228]) ).
cnf(s5,plain,
spl13_3,
inference(sat_conversion,[],[f235]) ).
cnf(s6,plain,
spl13_5,
inference(sat_conversion,[],[f242]) ).
cnf(s10,plain,
( ~ spl13_6
| ~ spl13_11
| spl13_12 ),
inference(sat_conversion,[],[f338]) ).
cnf(s20,plain,
spl13_11,
inference(sat_conversion,[],[f611]) ).
cnf(s21,plain,
~ spl13_12,
inference(sat_conversion,[],[f626]) ).
cnf(s22,plain,
~ spl13_6,
inference(rat,[],[s10,s21,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s4,s22,s6,s5]) ).
fof(f627,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % 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 THM
% 0.10/0.36 % Computer : n013.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 03:21:36 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.18/1.31 % (775341)Detected formulas, will run a generic FOF schedule.
% 3.18/1.31 % (775349)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1263857885:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.18/1.31 % (775349)Refutation not found, incomplete strategy
% 3.18/1.31 % (775349)------------------------------
% 3.18/1.31 % (775349)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.31 % (775349)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.31 % (775349)CaDiCaL version: 2.1.3
% 3.18/1.31 % (775349)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.31 % (775349)Time elapsed: 0.001 s
% 3.18/1.31 % (775349)Peak memory usage: 88 MB
% 3.18/1.31 % (775349)Instructions burned: 1 (million)
% 3.18/1.31 % (775348)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=70309234:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.18/1.31 % (775352)dis-21_1_sil=8000:lcm=predicate:random_seed=897846450:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.18/1.31 % (775350)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1028155699:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.18/1.31 % (775346)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=163274769:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.18/1.31 % (775347)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=1509434708:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.18/1.31 % (775351)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3623667233:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.18/1.31 % (775351)First to succeed.
% 3.18/1.31 % (775351)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-775341"
% 3.18/1.31 % (775350)Instruction limit reached!
% 3.18/1.31 % (775350)------------------------------
% 3.18/1.31 % (775350)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.31 % (775350)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.31 % (775350)CaDiCaL version: 2.1.3
% 3.18/1.31 % (775350)Termination reason: Instruction limit
% 3.18/1.31 % (775350)Termination phase: Saturation
% 3.18/1.31 % (775350)Time elapsed: 0.068 s
% 3.18/1.31 % (775350)Peak memory usage: 88 MB
% 3.18/1.31 % (775350)Instructions burned: 119 (million)
% 3.18/1.31 % (775352)Instruction limit reached!
% 3.18/1.31 % (775352)------------------------------
% 3.18/1.31 % (775352)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.31 % (775352)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.31 % (775352)CaDiCaL version: 2.1.3
% 3.18/1.31 % (775352)Termination reason: Instruction limit
% 3.18/1.31 % (775352)Termination phase: Saturation
% 3.18/1.31 % (775352)Time elapsed: 0.077 s
% 3.18/1.31 % (775352)Peak memory usage: 90 MB
% 3.18/1.31 % (775352)Instructions burned: 130 (million)
% 3.18/1.31 % (775349)------------------------------
% 3.18/1.31 % (775349)------------------------------
% 3.18/1.31 % (775360)lrs+10_1_sil=8000:sp=occurrence:random_seed=4008875981:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.18/1.31 % (775361)lrs+10_1_sil=32000:urr=on:br=off:random_seed=350271425:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.18/1.31 % (775362)lrs+1011_1_sil=32000:sp=occurrence:random_seed=354007445:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 3.18/1.31 % (775362)Also succeeded, but the first one will report.
% 3.18/1.31 % (775351)Refutation found. Thanks to Tanya!
% 3.18/1.31 % SZS status Theorem for theBenchmark
% 3.18/1.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/1.50 % (775351)------------------------------
% 0.15/1.50 % (775351)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.15/1.50 % (775351)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/1.50 % (775351)CaDiCaL version: 2.1.3
% 0.15/1.50 % (775351)Termination reason: Refutation
% 0.15/1.50 % (775351)Time elapsed: 0.020 s
% 0.15/1.50 % (775351)Peak memory usage: 89 MB
% 0.15/1.50 % (775351)Instructions burned: 25 (million)
% 0.15/1.50 % (775351)------------------------------
% 0.15/1.50 % (775351)------------------------------
% 0.15/1.50 % (775341)Success in time 0.456 s
% 0.15/1.50 % Vampire exiting
%------------------------------------------------------------------------------