%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU220+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n009.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 12:47:49 PM UTC 2026
% Result : Theorem 4.72s 1.68s
% Output : Refutation 6.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 90 ( 15 unt; 6 def)
% Number of atoms : 418 ( 94 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 561 ( 233 ~; 231 |; 72 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 84 ( 0 sgn 74 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f50,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( relation(function_inverse(X0))
& function(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_funct_1) ).
fof(f160,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(f200,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ! [X1] :
( ( relation(X1)
& function(X1) )
=> ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
=> ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) ) )
& ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
=> ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f202,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f204,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f205,negated_conjecture,
~ ! [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) ) ) ),
inference(negated_conjecture,[status(cth)],[f204]) ).
fof(f288,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,[],[f160]) ).
fof(f289,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,[],[f288]) ).
fof(f322,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f200]) ).
fof(f323,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f322]) ).
fof(f326,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f202]) ).
fof(f327,plain,
! [X0] :
( ( relation_rng(X0) = relation_dom(function_inverse(X0))
& relation_dom(X0) = relation_rng(function_inverse(X0)) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f326]) ).
fof(f330,plain,
? [X0,X1] :
( ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f205]) ).
fof(f331,plain,
? [X0,X1] :
( ( apply(X1,apply(function_inverse(X1),X0)) != X0
| apply(relation_composition(function_inverse(X1),X1),X0) != X0 )
& one_to_one(X1)
& in(X0,relation_rng(X1))
& relation(X1)
& function(X1) ),
inference(flattening,[],[f330]) ).
fof(f414,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f415,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f414]) ).
fof(f439,definition,
! [X0,X2,X3,X1] :
( sP0(X0,X2,X3,X1)
<=> ( ( in(X2,relation_rng(X0))
& X3 = apply(X1,X2) )
| ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 ) ),
introduced(definition,[new_symbols(definition,[sP0])],[predicate_definition_introduction]) ).
fof(f440,plain,
! [X0] :
( ! [X1] :
( ( X1 = function_inverse(X0)
<=> ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_folding,[],[f323,f439]) ).
fof(f477,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f440]) ).
fof(f478,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X2,X3] :
( ( ( in(X3,relation_dom(X0))
& X2 = apply(X0,X3) )
| ~ in(X2,relation_rng(X0))
| apply(X1,X2) != X3 )
& sP0(X0,X2,X3,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f477]) ).
fof(f479,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ? [X2,X3] :
( ( ( ~ in(X3,relation_dom(X0))
| apply(X0,X3) != X2 )
& in(X2,relation_rng(X0))
& apply(X1,X2) = X3 )
| ~ sP0(X0,X2,X3,X1) ) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(rectify,[],[f478]) ).
fof(f480,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK9(X0,X1),relation_dom(X0))
| sK8(X0,X1) != apply(X0,sK9(X0,X1)) )
& in(sK8(X0,X1),relation_rng(X0))
& sK9(X0,X1) = apply(X1,sK8(X0,X1)) )
| ~ sP0(X0,sK8(X0,X1),sK9(X0,X1),X1) )
& ( ( relation_dom(X1) = relation_rng(X0)
& ! [X4,X5] :
( ( ( in(X5,relation_dom(X0))
& apply(X0,X5) = X4 )
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5 )
& sP0(X0,X4,X5,X1) ) )
| function_inverse(X0) != X1 ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9]),skolemize(X2,sK8(X0,X1)),skolemize(X3,sK9(X0,X1))],[f479]) ).
fof(f482,plain,
( ( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12) )
& one_to_one(sK13)
& in(sK12,relation_rng(sK13))
& relation(sK13)
& function(sK13) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK12,sK13]),skolemize(X0,sK12),skolemize(X1,sK13)],[f331]) ).
fof(f655,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,[],[f289]) ).
fof(f711,plain,
! [X0,X1,X4,X5] :
( apply(X0,X5) = X4
| ~ in(X4,relation_rng(X0))
| apply(X1,X4) != X5
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f480]) ).
fof(f719,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f721,plain,
function(sK13),
inference(cnf_transformation,[],[f482]) ).
fof(f722,plain,
relation(sK13),
inference(cnf_transformation,[],[f482]) ).
fof(f723,plain,
in(sK12,relation_rng(sK13)),
inference(cnf_transformation,[],[f482]) ).
fof(f724,plain,
one_to_one(sK13),
inference(cnf_transformation,[],[f482]) ).
fof(f725,plain,
( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12) ),
inference(cnf_transformation,[],[f482]) ).
fof(f963,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f415]) ).
fof(f964,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f415]) ).
fof(f1150,plain,
! [X0,X1,X4] :
( apply(X0,apply(X1,X4)) = X4
| ~ in(X4,relation_rng(X0))
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f711]) ).
fof(f1151,plain,
! [X0,X4] :
( apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ in(X4,relation_rng(X0))
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f1150]) ).
fof(f1272,definition,
( spl78_1
<=> sK12 = apply(relation_composition(function_inverse(sK13),sK13),sK12) ),
introduced(definition,[new_symbols(definition,[spl78_1])],[avatar_definition]) ).
fof(f1274,plain,
( sK12 != apply(relation_composition(function_inverse(sK13),sK13),sK12)
| spl78_1 ),
inference(avatar_component_clause,[],[f1272]) ).
fof(f1276,definition,
( spl78_2
<=> sK12 = apply(sK13,apply(function_inverse(sK13),sK12)) ),
introduced(definition,[new_symbols(definition,[spl78_2])],[avatar_definition]) ).
fof(f1277,plain,
( sK12 = apply(sK13,apply(function_inverse(sK13),sK12))
| ~ spl78_2 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1278,plain,
( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| spl78_2 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1279,plain,
( ~ spl78_1
| ~ spl78_2 ),
inference(avatar_split_clause,[],[f725,f1276,f1272]) ).
fof(f1282,plain,
! [X0,X4] :
( apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ in(X4,relation_rng(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f1151,f964]) ).
fof(f1303,plain,
! [X0,X4] :
( apply(X0,apply(function_inverse(X0),X4)) = X4
| ~ in(X4,relation_rng(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f1282,f963]) ).
fof(f1333,definition,
( spl78_7
<=> function(function_inverse(sK13)) ),
introduced(definition,[new_symbols(definition,[spl78_7])],[avatar_definition]) ).
fof(f1334,plain,
( function(function_inverse(sK13))
| ~ spl78_7 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f1335,plain,
( ~ function(function_inverse(sK13))
| spl78_7 ),
inference(avatar_component_clause,[],[f1333]) ).
fof(f1337,definition,
( spl78_8
<=> relation(function_inverse(sK13)) ),
introduced(definition,[new_symbols(definition,[spl78_8])],[avatar_definition]) ).
fof(f1338,plain,
( relation(function_inverse(sK13))
| ~ spl78_8 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f1339,plain,
( ~ relation(function_inverse(sK13))
| spl78_8 ),
inference(avatar_component_clause,[],[f1337]) ).
fof(f1341,definition,
( spl78_9
<=> in(sK12,relation_dom(function_inverse(sK13))) ),
introduced(definition,[new_symbols(definition,[spl78_9])],[avatar_definition]) ).
fof(f1342,plain,
( ~ in(sK12,relation_dom(function_inverse(sK13)))
| spl78_9 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1343,plain,
( in(sK12,relation_dom(function_inverse(sK13)))
| ~ spl78_9 ),
inference(avatar_component_clause,[],[f1341]) ).
fof(f1354,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl78_7 ),
inference(resolution,[],[f1335,f963]) ).
fof(f1356,plain,
( ~ function(sK13)
| spl78_7 ),
inference(forward_subsumption_resolution,[],[f1354,f722]) ).
fof(f1357,plain,
( $false
| spl78_7 ),
inference(forward_subsumption_resolution,[],[f1356,f721]) ).
fof(f1358,plain,
spl78_7,
inference(avatar_contradiction_clause,[],[f1357]) ).
fof(f1366,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl78_8 ),
inference(resolution,[],[f1339,f964]) ).
fof(f1368,plain,
( ~ function(sK13)
| spl78_8 ),
inference(forward_subsumption_resolution,[],[f1366,f722]) ).
fof(f1369,plain,
( $false
| spl78_8 ),
inference(forward_subsumption_resolution,[],[f1368,f721]) ).
fof(f1370,plain,
spl78_8,
inference(avatar_contradiction_clause,[],[f1369]) ).
fof(f3229,plain,
( ~ in(sK12,relation_rng(sK13))
| ~ one_to_one(sK13)
| ~ relation(sK13)
| ~ function(sK13)
| spl78_9 ),
inference(superposition,[],[f1342,f719]) ).
fof(f3250,plain,
( ~ one_to_one(sK13)
| ~ relation(sK13)
| ~ function(sK13)
| spl78_9 ),
inference(forward_subsumption_resolution,[],[f3229,f723]) ).
fof(f3252,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl78_9 ),
inference(forward_subsumption_resolution,[],[f3250,f724]) ).
fof(f3253,plain,
( ~ function(sK13)
| spl78_9 ),
inference(forward_subsumption_resolution,[],[f3252,f722]) ).
fof(f3254,plain,
( $false
| spl78_9 ),
inference(forward_subsumption_resolution,[],[f3253,f721]) ).
fof(f3255,plain,
spl78_9,
inference(avatar_contradiction_clause,[],[f3254]) ).
fof(f4821,plain,
( sK12 != sK12
| ~ in(sK12,relation_rng(sK13))
| ~ one_to_one(sK13)
| ~ relation(sK13)
| ~ function(sK13)
| spl78_2 ),
inference(superposition,[],[f1278,f1303]) ).
fof(f4822,plain,
( ~ in(sK12,relation_rng(sK13))
| ~ one_to_one(sK13)
| ~ relation(sK13)
| ~ function(sK13)
| spl78_2 ),
inference(trivial_inequality_removal,[],[f4821]) ).
fof(f4827,plain,
( ~ one_to_one(sK13)
| ~ relation(sK13)
| ~ function(sK13)
| spl78_2 ),
inference(forward_subsumption_resolution,[],[f4822,f723]) ).
fof(f4835,plain,
( ~ relation(sK13)
| ~ function(sK13)
| spl78_2 ),
inference(forward_subsumption_resolution,[],[f4827,f724]) ).
fof(f4842,plain,
( ~ function(sK13)
| spl78_2 ),
inference(forward_subsumption_resolution,[],[f4835,f722]) ).
fof(f4847,plain,
( $false
| spl78_2 ),
inference(forward_subsumption_resolution,[],[f4842,f721]) ).
fof(f4848,plain,
spl78_2,
inference(avatar_contradiction_clause,[],[f4847]) ).
fof(f5666,plain,
( sK12 != apply(sK13,apply(function_inverse(sK13),sK12))
| ~ in(sK12,relation_dom(function_inverse(sK13)))
| ~ relation(sK13)
| ~ function(sK13)
| ~ relation(function_inverse(sK13))
| ~ function(function_inverse(sK13))
| spl78_1 ),
inference(superposition,[],[f1274,f655]) ).
fof(f5684,plain,
( ~ in(sK12,relation_dom(function_inverse(sK13)))
| ~ relation(sK13)
| ~ function(sK13)
| ~ relation(function_inverse(sK13))
| ~ function(function_inverse(sK13))
| spl78_1
| ~ spl78_2 ),
inference(forward_subsumption_resolution,[],[f5666,f1277]) ).
fof(f5694,plain,
( ~ relation(sK13)
| ~ function(sK13)
| ~ relation(function_inverse(sK13))
| ~ function(function_inverse(sK13))
| spl78_1
| ~ spl78_2
| ~ spl78_9 ),
inference(forward_subsumption_resolution,[],[f5684,f1343]) ).
fof(f5701,plain,
( ~ function(sK13)
| ~ relation(function_inverse(sK13))
| ~ function(function_inverse(sK13))
| spl78_1
| ~ spl78_2
| ~ spl78_9 ),
inference(forward_subsumption_resolution,[],[f5694,f722]) ).
fof(f5703,plain,
( ~ relation(function_inverse(sK13))
| ~ function(function_inverse(sK13))
| spl78_1
| ~ spl78_2
| ~ spl78_9 ),
inference(forward_subsumption_resolution,[],[f5701,f721]) ).
fof(f5704,plain,
( ~ function(function_inverse(sK13))
| spl78_1
| ~ spl78_2
| ~ spl78_8
| ~ spl78_9 ),
inference(forward_subsumption_resolution,[],[f5703,f1338]) ).
fof(f5705,plain,
( $false
| spl78_1
| ~ spl78_2
| ~ spl78_7
| ~ spl78_8
| ~ spl78_9 ),
inference(forward_subsumption_resolution,[],[f5704,f1334]) ).
fof(f5706,plain,
( spl78_1
| ~ spl78_2
| ~ spl78_7
| ~ spl78_8
| ~ spl78_9 ),
inference(avatar_contradiction_clause,[],[f5705]) ).
cnf(s1,plain,
( ~ spl78_1
| ~ spl78_2 ),
inference(sat_conversion,[],[f1279]) ).
cnf(s6,plain,
spl78_7,
inference(sat_conversion,[],[f1358]) ).
cnf(s7,plain,
spl78_8,
inference(sat_conversion,[],[f1370]) ).
cnf(s18,plain,
spl78_9,
inference(sat_conversion,[],[f3255]) ).
cnf(s21,plain,
spl78_2,
inference(sat_conversion,[],[f4848]) ).
cnf(s42,plain,
( spl78_1
| ~ spl78_2
| ~ spl78_7
| ~ spl78_8
| ~ spl78_9 ),
inference(sat_conversion,[],[f5706]) ).
cnf(s45,plain,
spl78_1,
inference(rat,[],[s42,s18,s7,s21,s6]) ).
cnf(s47,plain,
$false,
inference(rat,[],[s1,s21,s45]) ).
fof(f5707,plain,
$false,
inference(avatar_sat_refutation,[],[s47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU220+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 % Computer : n009.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Mon Sep 28 04:08:00 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.44 Running first-order theorem proving
% 0.10/0.44 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
% 4.72/1.68 % (2649348)Detected formulas, will run a generic FOF schedule.
% 4.72/1.68 % (2649357)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3288232149:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 4.72/1.68 % (2649358)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1224984312:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 4.72/1.68 % (2649359)dis-21_1_sil=8000:lcm=predicate:random_seed=1388039514: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)
% 4.72/1.68 % (2649356)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3238348339:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 4.72/1.68 % (2649354)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=3881301003:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 4.72/1.68 % (2649355)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=3158023879:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 4.72/1.68 % (2649353)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=2681067742:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 4.72/1.68 % (2649357)Instruction limit reached!
% 4.72/1.68 % (2649357)------------------------------
% 4.72/1.68 % (2649357)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649357)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649357)Termination reason: Instruction limit
% 4.72/1.68 % (2649357)Termination phase: Saturation
% 4.72/1.68 % (2649357)Time elapsed: 0.044 s
% 4.72/1.68 % (2649357)Peak memory usage: 89 MB
% 4.72/1.68 % (2649357)Instructions burned: 121 (million)
% 4.72/1.68 % (2649356)Instruction limit reached!
% 4.72/1.68 % (2649356)------------------------------
% 4.72/1.68 % (2649356)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649356)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649356)Termination reason: Instruction limit
% 4.72/1.68 % (2649356)Termination phase: Saturation
% 4.72/1.68 % (2649356)Time elapsed: 0.071 s
% 4.72/1.68 % (2649356)Peak memory usage: 90 MB
% 4.72/1.68 % (2649356)Instructions burned: 110 (million)
% 4.72/1.68 % (2649359)Instruction limit reached!
% 4.72/1.68 % (2649359)------------------------------
% 4.72/1.68 % (2649359)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649359)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649359)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649359)Termination reason: Instruction limit
% 4.72/1.68 % (2649359)Termination phase: Saturation
% 4.72/1.68 % (2649359)Time elapsed: 0.076 s
% 4.72/1.68 % (2649359)Peak memory usage: 90 MB
% 4.72/1.68 % (2649359)Instructions burned: 131 (million)
% 4.72/1.68 % (2649358)Instruction limit reached!
% 4.72/1.68 % (2649358)------------------------------
% 4.72/1.68 % (2649358)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649358)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649358)Termination reason: Instruction limit
% 4.72/1.68 % (2649358)Termination phase: Saturation
% 4.72/1.68 % (2649358)Time elapsed: 0.096 s
% 4.72/1.68 % (2649358)Peak memory usage: 90 MB
% 4.72/1.68 % (2649358)Instructions burned: 140 (million)
% 4.72/1.68 % (2649367)lrs+10_1_sil=8000:sp=occurrence:random_seed=2858895491:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 4.72/1.68 % (2649368)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3266256857:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 4.72/1.68 % (2649369)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1194743098:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 4.72/1.68 % (2649367)Instruction limit reached!
% 4.72/1.68 % (2649367)------------------------------
% 4.72/1.68 % (2649367)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649367)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649367)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649367)Termination reason: Instruction limit
% 4.72/1.68 % (2649367)Termination phase: Saturation
% 4.72/1.68 % (2649367)Time elapsed: 0.103 s
% 4.72/1.68 % (2649367)Peak memory usage: 93 MB
% 4.72/1.68 % (2649367)Instructions burned: 287 (million)
% 4.72/1.68 % (2649370)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=698470605:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 4.72/1.68 % (2649368)Instruction limit reached!
% 4.72/1.68 % (2649368)------------------------------
% 4.72/1.68 % (2649368)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649368)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649368)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649368)Termination reason: Instruction limit
% 4.72/1.68 % (2649368)Termination phase: Saturation
% 4.72/1.68 % (2649368)Time elapsed: 0.080 s
% 4.72/1.68 % (2649368)Peak memory usage: 91 MB
% 4.72/1.68 % (2649368)Instructions burned: 157 (million)
% 4.72/1.68 % (2649375)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=2840251870:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2995 on theBenchmark for (2995ds/294Mi)
% 4.72/1.68 % (2649370)Instruction limit reached!
% 4.72/1.68 % (2649370)------------------------------
% 4.72/1.68 % (2649370)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649370)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649370)Termination reason: Instruction limit
% 4.72/1.68 % (2649370)Termination phase: Saturation
% 4.72/1.68 % (2649370)Time elapsed: 0.139 s
% 4.72/1.68 % (2649370)Peak memory usage: 94 MB
% 4.72/1.68 % (2649370)Instructions burned: 249 (million)
% 4.72/1.68 % (2649369)Instruction limit reached!
% 4.72/1.68 % (2649369)------------------------------
% 4.72/1.68 % (2649369)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649369)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649369)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649369)Termination reason: Instruction limit
% 4.72/1.68 % (2649369)Termination phase: Saturation
% 4.72/1.68 % (2649369)Time elapsed: 0.224 s
% 4.72/1.68 % (2649369)Peak memory usage: 92 MB
% 4.72/1.68 % (2649369)Instructions burned: 326 (million)
% 4.72/1.68 % (2649376)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=3268520642:i=2350_2995 on theBenchmark for (2995ds/2350Mi)
% 4.72/1.68 % (2649375)First to succeed.
% 4.72/1.68 % (2649375)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2649348"
% 4.72/1.68 % (2649378)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3738664598:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 4.72/1.68 % (2649378)Instruction limit reached!
% 4.72/1.68 % (2649378)------------------------------
% 4.72/1.68 % (2649378)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 4.72/1.68 % (2649378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 4.72/1.68 % (2649378)CaDiCaL version: 2.1.3
% 4.72/1.68 % (2649378)Termination reason: Instruction limit
% 4.72/1.68 % (2649378)Termination phase: Saturation
% 4.72/1.68 % (2649378)Time elapsed: 0.070 s
% 4.72/1.68 % (2649378)Peak memory usage: 90 MB
% 4.72/1.68 % (2649378)Instructions burned: 113 (million)
% 4.72/1.68 % (2649375)Refutation found. Thanks to Tanya!
% 4.72/1.68 % SZS status Theorem for theBenchmark
% 4.72/1.68 % SZS output start Proof for theBenchmark
% See solution above
% 6.19/1.88 % (2649375)------------------------------
% 6.19/1.88 % (2649375)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.19/1.88 % (2649375)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.19/1.88 % (2649375)CaDiCaL version: 2.1.3
% 6.19/1.88 % (2649375)Termination reason: Refutation
% 6.19/1.88 % (2649375)Time elapsed: 0.100 s
% 6.19/1.88 % (2649375)Peak memory usage: 92 MB
% 6.19/1.88 % (2649375)Instructions burned: 288 (million)
% 6.19/1.88 % (2649375)------------------------------
% 6.19/1.88 % (2649375)------------------------------
% 6.19/1.88 % (2649348)Success in time 0.8 s
% 6.19/1.88 % Vampire exiting
%------------------------------------------------------------------------------