%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 2.96s 1.34s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 93 ( 18 unt; 8 def)
% Number of atoms : 426 ( 85 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 588 ( 255 ~; 236 |; 72 &)
% ( 10 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 12 usr; 6 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 0 sgn 70 !; 10 ?)
% 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(f31,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/sandbox2/benchmark/theBenchmark.p',t23_funct_1) ).
fof(f35,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/sandbox2/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,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/sandbox2/benchmark/theBenchmark.p',t55_funct_1) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f38,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)],[f37]) ).
fof(f43,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,[],[f38]) ).
fof(f44,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,[],[f43]) ).
fof(f46,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,[],[f36]) ).
fof(f47,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,[],[f46]) ).
fof(f48,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f49,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f48]) ).
fof(f67,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,[],[f35]) ).
fof(f68,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,[],[f67]) ).
fof(f69,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,[],[f31]) ).
fof(f70,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,[],[f69]) ).
fof(f71,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(f72,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,[],[f68,f71]) ).
fof(f73,plain,
( ( sK1 != apply(sK2,apply(function_inverse(sK2),sK1))
| sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1) )
& one_to_one(sK2)
& in(sK1,relation_rng(sK2))
& relation(sK2)
& function(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f44]) ).
fof(f82,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,[],[f72]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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,[],[f83]) ).
fof(f85,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))],[f84]) ).
fof(f86,plain,
function(sK2),
inference(cnf_transformation,[],[f73]) ).
fof(f87,plain,
relation(sK2),
inference(cnf_transformation,[],[f73]) ).
fof(f88,plain,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f73]) ).
fof(f89,plain,
one_to_one(sK2),
inference(cnf_transformation,[],[f73]) ).
fof(f90,plain,
( sK1 != apply(sK2,apply(function_inverse(sK2),sK1))
| sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1) ),
inference(cnf_transformation,[],[f73]) ).
fof(f93,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f94,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f95,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f131,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,[],[f85]) ).
fof(f137,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,[],[f70]) ).
fof(f138,definition,
~ sP10(sK1),
introduced(definition,[new_symbols(definition,[sP10])],[inequality_splitting_name_introduction]) ).
fof(f139,definition,
~ sP11(sK1),
introduced(definition,[new_symbols(definition,[sP11])],[inequality_splitting_name_introduction]) ).
fof(f140,plain,
( sP10(apply(sK2,apply(function_inverse(sK2),sK1)))
| sP11(apply(relation_composition(function_inverse(sK2),sK2),sK1)) ),
inference(inequality_splitting,[],[f90,f139,f138]) ).
fof(f147,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,[],[f131]) ).
fof(f148,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,[],[f147]) ).
fof(f151,definition,
( spl12_1
<=> sP11(apply(relation_composition(function_inverse(sK2),sK2),sK1)) ),
introduced(definition,[new_symbols(definition,[spl12_1])],[avatar_definition]) ).
fof(f153,plain,
( sP11(apply(relation_composition(function_inverse(sK2),sK2),sK1))
| ~ spl12_1 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f155,definition,
( spl12_2
<=> sP10(apply(sK2,apply(function_inverse(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl12_2])],[avatar_definition]) ).
fof(f157,plain,
( sP10(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ spl12_2 ),
inference(avatar_component_clause,[],[f155]) ).
fof(f158,plain,
( spl12_1
| spl12_2 ),
inference(avatar_split_clause,[],[f140,f155,f151]) ).
fof(f163,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f88,f93]) ).
fof(f164,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f163,f89]) ).
fof(f166,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f164,f87]) ).
fof(f168,plain,
in(sK1,relation_dom(function_inverse(sK2))),
inference(forward_subsumption_resolution,[],[f166,f86]) ).
fof(f179,plain,
( sP10(sK1)
| ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(superposition,[],[f157,f148]) ).
fof(f180,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f179,f138]) ).
fof(f181,plain,
( ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f180,f88]) ).
fof(f182,plain,
( ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f181,f95]) ).
fof(f183,plain,
( ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f182,f94]) ).
fof(f184,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f183,f89]) ).
fof(f185,plain,
( ~ function(sK2)
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f184,f87]) ).
fof(f186,plain,
( $false
| ~ spl12_2 ),
inference(forward_subsumption_resolution,[],[f185,f86]) ).
fof(f187,plain,
~ spl12_2,
inference(avatar_contradiction_clause,[],[f186]) ).
fof(f188,plain,
( sP11(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ in(sK1,relation_dom(function_inverse(sK2)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl12_1 ),
inference(superposition,[],[f153,f137]) ).
fof(f189,plain,
( sP11(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f188,f168]) ).
fof(f190,plain,
( sP11(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ function(sK2)
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f189,f87]) ).
fof(f191,plain,
( sP11(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl12_1 ),
inference(forward_subsumption_resolution,[],[f190,f86]) ).
fof(f193,definition,
( spl12_3
<=> function(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl12_3])],[avatar_definition]) ).
fof(f195,plain,
( ~ function(function_inverse(sK2))
| spl12_3 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f197,definition,
( spl12_4
<=> relation(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl12_4])],[avatar_definition]) ).
fof(f199,plain,
( ~ relation(function_inverse(sK2))
| spl12_4 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f201,definition,
( spl12_5
<=> sP11(apply(sK2,apply(function_inverse(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl12_5])],[avatar_definition]) ).
fof(f203,plain,
( sP11(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ spl12_5 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f204,plain,
( ~ spl12_3
| ~ spl12_4
| spl12_5
| ~ spl12_1 ),
inference(avatar_split_clause,[],[f191,f151,f201,f197,f193]) ).
fof(f205,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl12_3 ),
inference(resolution,[],[f195,f94]) ).
fof(f206,plain,
( ~ function(sK2)
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f205,f87]) ).
fof(f207,plain,
( $false
| spl12_3 ),
inference(forward_subsumption_resolution,[],[f206,f86]) ).
fof(f208,plain,
spl12_3,
inference(avatar_contradiction_clause,[],[f207]) ).
fof(f210,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl12_4 ),
inference(resolution,[],[f199,f95]) ).
fof(f211,plain,
( ~ function(sK2)
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f210,f87]) ).
fof(f212,plain,
( $false
| spl12_4 ),
inference(forward_subsumption_resolution,[],[f211,f86]) ).
fof(f213,plain,
spl12_4,
inference(avatar_contradiction_clause,[],[f212]) ).
fof(f235,plain,
( sP11(sK1)
| ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(superposition,[],[f203,f148]) ).
fof(f236,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f235,f139]) ).
fof(f237,plain,
( ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f236,f88]) ).
fof(f238,plain,
( ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f237,f95]) ).
fof(f239,plain,
( ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f238,f94]) ).
fof(f240,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f239,f89]) ).
fof(f241,plain,
( ~ function(sK2)
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f240,f87]) ).
fof(f242,plain,
( $false
| ~ spl12_5 ),
inference(forward_subsumption_resolution,[],[f241,f86]) ).
fof(f243,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[],[f242]) ).
cnf(s1,plain,
( spl12_1
| spl12_2 ),
inference(sat_conversion,[],[f158]) ).
cnf(s2,plain,
~ spl12_2,
inference(sat_conversion,[],[f187]) ).
cnf(s3,plain,
( ~ spl12_1
| ~ spl12_3
| ~ spl12_4
| spl12_5 ),
inference(sat_conversion,[],[f204]) ).
cnf(s4,plain,
spl12_3,
inference(sat_conversion,[],[f208]) ).
cnf(s5,plain,
spl12_4,
inference(sat_conversion,[],[f213]) ).
cnf(s7,plain,
~ spl12_5,
inference(sat_conversion,[],[f243]) ).
cnf(s8,plain,
~ spl12_1,
inference(rat,[],[s3,s7,s5,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
fof(f244,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU220+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.45 % Computer : n016.cluster.edu
% 0.14/0.45 % Model : x86_64 x86_64
% 0.14/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.45 % Memory : 8046.5625MB
% 0.14/0.45 % OS : Linux 6.8.0-71-generic
% 0.14/0.45 % CPULimit : 300
% 0.14/0.45 % WCLimit : 300
% 0.14/0.45 % DateTime : Mon Sep 28 04:13:19 UTC 2026
% 0.14/0.45 % CPUTime :
% 0.14/0.45 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.48 Running first-order theorem proving
% 0.18/0.48 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.96/1.34 % (3248730)Detected formulas, will run a generic FOF schedule.
% 2.96/1.34 % (3248736)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=908679324:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.96/1.34 % (3248735)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=793995159:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.96/1.34 % (3248739)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1748789517:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.96/1.34 % (3248740)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3922527485:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.96/1.34 % (3248737)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=1574567584:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.96/1.34 % (3248741)dis-21_1_sil=8000:lcm=predicate:random_seed=2078259607:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.96/1.34 % (3248738)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2181669176:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.96/1.34 % (3248738)First to succeed.
% 2.96/1.34 % (3248739)Also succeeded, but the first one will report.
% 2.96/1.34 % (3248738)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3248730"
% 2.96/1.34 % (3248740)Also succeeded, but the first one will report.
% 2.96/1.34 % (3248741)Instruction limit reached!
% 2.96/1.34 % (3248741)------------------------------
% 2.96/1.34 % (3248741)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.96/1.34 % (3248741)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.96/1.34 % (3248741)CaDiCaL version: 2.1.3
% 2.96/1.34 % (3248741)Termination reason: Instruction limit
% 2.96/1.34 % (3248741)Termination phase: Saturation
% 2.96/1.34 % (3248741)Time elapsed: 0.074 s
% 2.96/1.34 % (3248741)Peak memory usage: 89 MB
% 2.96/1.34 % (3248741)Instructions burned: 130 (million)
% 2.96/1.34 % (3248749)lrs+10_1_sil=8000:sp=occurrence:random_seed=1136556251:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.96/1.34 % (3248738)Refutation found. Thanks to Tanya!
% 2.96/1.34 % SZS status Theorem for theBenchmark
% 2.96/1.34 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.52 % (3248738)------------------------------
% 3.57/1.52 % (3248738)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.52 % (3248738)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.52 % (3248738)CaDiCaL version: 2.1.3
% 3.57/1.52 % (3248738)Termination reason: Refutation
% 3.57/1.52 % (3248738)Time elapsed: 0.006 s
% 3.57/1.52 % (3248738)Peak memory usage: 89 MB
% 3.57/1.52 % (3248738)Instructions burned: 8 (million)
% 3.57/1.52 % (3248738)------------------------------
% 3.57/1.52 % (3248738)------------------------------
% 3.57/1.52 % (3248730)Success in time 0.414 s
% 3.57/1.52 % Vampire exiting
%------------------------------------------------------------------------------