%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU221+1 : 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 : n008.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 2.71s 1.27s
% Output : Refutation 3.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 10
% Syntax : Number of formulae : 97 ( 13 unt; 5 def)
% Number of atoms : 459 ( 105 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 623 ( 261 ~; 257 |; 79 &)
% ( 12 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 90 ( 0 sgn 78 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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(f9,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(f34,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(f35,axiom,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ( ( one_to_one(X1)
& in(X0,relation_rng(X1)) )
=> ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t57_funct_1) ).
fof(f36,conjecture,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t62_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f48,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,[],[f5]) ).
fof(f49,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,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f51,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f50]) ).
fof(f69,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,[],[f34]) ).
fof(f70,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,[],[f69]) ).
fof(f71,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f72,plain,
! [X0,X1] :
( ( X0 = apply(X1,apply(function_inverse(X1),X0))
& X0 = apply(relation_composition(function_inverse(X1),X1),X0) )
| ~ one_to_one(X1)
| ~ in(X0,relation_rng(X1))
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f74,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f73]) ).
fof(f78,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(f79,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,[],[f70,f78]) ).
fof(f80,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,[],[f49]) ).
fof(f81,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,[],[f80]) ).
fof(f82,plain,
! [X0] :
( ( ( one_to_one(X0)
| ( sK1(X0) != sK2(X0)
& in(sK1(X0),relation_dom(X0))
& in(sK2(X0),relation_dom(X0))
& apply(X0,sK1(X0)) = apply(X0,sK2(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,[sK1,sK2]),skolemize(X1,sK1(X0)),skolemize(X2,sK2(X0))],[f81]) ).
fof(f95,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,[],[f79]) ).
fof(f96,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,[],[f95]) ).
fof(f97,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,[],[f96]) ).
fof(f98,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK13(X0,X1),relation_dom(X0))
| sK12(X0,X1) != apply(X0,sK13(X0,X1)) )
& in(sK12(X0,X1),relation_rng(X0))
& sK13(X0,X1) = apply(X1,sK12(X0,X1)) )
| ~ sP0(X0,sK12(X0,X1),sK13(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,[sK12,sK13]),skolemize(X2,sK12(X0,X1)),skolemize(X3,sK13(X0,X1))],[f97]) ).
fof(f99,plain,
( ~ one_to_one(function_inverse(sK14))
& one_to_one(sK14)
& relation(sK14)
& function(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f74]) ).
fof(f107,plain,
! [X0] :
( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f108,plain,
! [X0] :
( one_to_one(X0)
| in(sK2(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f109,plain,
! [X0] :
( one_to_one(X0)
| in(sK1(X0),relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f110,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f111,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f112,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f157,plain,
! [X0,X1] :
( relation_rng(X0) = relation_dom(X1)
| function_inverse(X0) != X1
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f162,plain,
! [X0,X1] :
( ~ in(X0,relation_rng(X1))
| ~ one_to_one(X1)
| apply(X1,apply(function_inverse(X1),X0)) = X0
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f72]) ).
fof(f163,plain,
function(sK14),
inference(cnf_transformation,[],[f99]) ).
fof(f164,plain,
relation(sK14),
inference(cnf_transformation,[],[f99]) ).
fof(f165,plain,
one_to_one(sK14),
inference(cnf_transformation,[],[f99]) ).
fof(f166,plain,
~ one_to_one(function_inverse(sK14)),
inference(cnf_transformation,[],[f99]) ).
fof(f173,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(equality_resolution,[],[f157]) ).
fof(f204,plain,
( in(sK2(function_inverse(sK14)),relation_dom(function_inverse(sK14)))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14)) ),
inference(resolution,[],[f108,f166]) ).
fof(f206,definition,
( spl15_1
<=> function(function_inverse(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_1])],[avatar_definition]) ).
fof(f207,plain,
( function(function_inverse(sK14))
| ~ spl15_1 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f208,plain,
( ~ function(function_inverse(sK14))
| spl15_1 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f210,definition,
( spl15_2
<=> relation(function_inverse(sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_2])],[avatar_definition]) ).
fof(f211,plain,
( relation(function_inverse(sK14))
| ~ spl15_2 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f212,plain,
( ~ relation(function_inverse(sK14))
| spl15_2 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f214,definition,
( spl15_3
<=> in(sK2(function_inverse(sK14)),relation_dom(function_inverse(sK14))) ),
introduced(definition,[new_symbols(definition,[spl15_3])],[avatar_definition]) ).
fof(f216,plain,
( in(sK2(function_inverse(sK14)),relation_dom(function_inverse(sK14)))
| ~ spl15_3 ),
inference(avatar_component_clause,[],[f214]) ).
fof(f217,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(avatar_split_clause,[],[f204,f214,f210,f206]) ).
fof(f218,plain,
( ~ relation(sK14)
| ~ function(sK14)
| spl15_1 ),
inference(resolution,[],[f208,f111]) ).
fof(f220,plain,
( ~ function(sK14)
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f218,f164]) ).
fof(f221,plain,
( $false
| spl15_1 ),
inference(forward_subsumption_resolution,[],[f220,f163]) ).
fof(f222,plain,
spl15_1,
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f223,plain,
( in(sK1(function_inverse(sK14)),relation_dom(function_inverse(sK14)))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14)) ),
inference(resolution,[],[f109,f166]) ).
fof(f225,definition,
( spl15_4
<=> in(sK1(function_inverse(sK14)),relation_dom(function_inverse(sK14))) ),
introduced(definition,[new_symbols(definition,[spl15_4])],[avatar_definition]) ).
fof(f227,plain,
( in(sK1(function_inverse(sK14)),relation_dom(function_inverse(sK14)))
| ~ spl15_4 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f228,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_4 ),
inference(avatar_split_clause,[],[f223,f225,f210,f206]) ).
fof(f229,plain,
( ~ relation(sK14)
| ~ function(sK14)
| spl15_2 ),
inference(resolution,[],[f212,f112]) ).
fof(f231,plain,
( ~ function(sK14)
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f229,f164]) ).
fof(f232,plain,
( $false
| spl15_2 ),
inference(forward_subsumption_resolution,[],[f231,f163]) ).
fof(f233,plain,
spl15_2,
inference(avatar_contradiction_clause,[],[f232]) ).
fof(f243,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ function(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f173,f112]) ).
fof(f244,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f243,f111]) ).
fof(f246,plain,
( relation_dom(function_inverse(sK14)) = relation_rng(sK14)
| ~ relation(sK14)
| ~ function(sK14) ),
inference(resolution,[],[f244,f165]) ).
fof(f255,plain,
( relation_dom(function_inverse(sK14)) = relation_rng(sK14)
| ~ function(sK14) ),
inference(forward_subsumption_resolution,[],[f246,f164]) ).
fof(f258,plain,
relation_dom(function_inverse(sK14)) = relation_rng(sK14),
inference(forward_subsumption_resolution,[],[f255,f163]) ).
fof(f262,plain,
( in(sK1(function_inverse(sK14)),relation_rng(sK14))
| ~ spl15_4 ),
inference(superposition,[],[f227,f258]) ).
fof(f264,plain,
( in(sK2(function_inverse(sK14)),relation_rng(sK14))
| ~ spl15_3 ),
inference(superposition,[],[f216,f258]) ).
fof(f277,plain,
( ~ one_to_one(sK14)
| sK1(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_4 ),
inference(resolution,[],[f262,f162]) ).
fof(f282,plain,
( sK1(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f277,f165]) ).
fof(f285,plain,
( sK1(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ function(sK14)
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f282,f164]) ).
fof(f288,plain,
( sK1(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f285,f163]) ).
fof(f297,plain,
( ~ one_to_one(sK14)
| sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14))))
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_3 ),
inference(resolution,[],[f264,f162]) ).
fof(f302,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14))))
| ~ relation(sK14)
| ~ function(sK14)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f297,f165]) ).
fof(f305,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14))))
| ~ function(sK14)
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f302,f164]) ).
fof(f308,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK2(function_inverse(sK14))))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f305,f163]) ).
fof(f623,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| one_to_one(function_inverse(sK14))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14))
| ~ spl15_3 ),
inference(superposition,[],[f308,f107]) ).
fof(f628,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14))
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f623,f166]) ).
fof(f631,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ function(function_inverse(sK14))
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f628,f211]) ).
fof(f634,plain,
( sK2(function_inverse(sK14)) = apply(sK14,apply(function_inverse(sK14),sK1(function_inverse(sK14))))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3 ),
inference(forward_subsumption_resolution,[],[f631,f207]) ).
fof(f637,plain,
( sK2(function_inverse(sK14)) = sK1(function_inverse(sK14))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_demodulation,[],[f634,f288]) ).
fof(f658,plain,
( sK1(function_inverse(sK14)) != sK1(function_inverse(sK14))
| one_to_one(function_inverse(sK14))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(superposition,[],[f110,f637]) ).
fof(f659,plain,
( one_to_one(function_inverse(sK14))
| ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(trivial_inequality_removal,[],[f658]) ).
fof(f660,plain,
( ~ relation(function_inverse(sK14))
| ~ function(function_inverse(sK14))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f659,f166]) ).
fof(f661,plain,
( ~ function(function_inverse(sK14))
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f660,f211]) ).
fof(f662,plain,
( $false
| ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(forward_subsumption_resolution,[],[f661,f207]) ).
fof(f663,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(avatar_contradiction_clause,[],[f662]) ).
cnf(s1,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_3 ),
inference(sat_conversion,[],[f217]) ).
cnf(s2,plain,
spl15_1,
inference(sat_conversion,[],[f222]) ).
cnf(s3,plain,
( ~ spl15_1
| ~ spl15_2
| spl15_4 ),
inference(sat_conversion,[],[f228]) ).
cnf(s4,plain,
spl15_2,
inference(sat_conversion,[],[f233]) ).
cnf(s32,plain,
( ~ spl15_1
| ~ spl15_2
| ~ spl15_3
| ~ spl15_4 ),
inference(sat_conversion,[],[f663]) ).
cnf(s39,plain,
( ~ spl15_1
| spl15_4 ),
inference(rat,[],[s3,s4]) ).
cnf(s40,plain,
spl15_4,
inference(rat,[],[s39,s2]) ).
cnf(s41,plain,
~ spl15_3,
inference(rat,[],[s32,s2,s4,s40]) ).
cnf(s42,plain,
$false,
inference(rat,[],[s1,s41,s4,s2]) ).
fof(f664,plain,
$false,
inference(avatar_sat_refutation,[],[s42]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU221+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n008.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 04:08:55 UTC 2026
% 0.13/0.37 % CPUTime :
% 0.13/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 2.71/1.27 % (1860088)Detected formulas, will run a generic FOF schedule.
% 2.71/1.27 % (1860096)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1143152066:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.71/1.27 % (1860096)Refutation not found, incomplete strategy
% 2.71/1.27 % (1860096)------------------------------
% 2.71/1.27 % (1860096)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.27 % (1860096)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.27 % (1860096)CaDiCaL version: 2.1.3
% 2.71/1.27 % (1860096)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.27 % (1860096)Time elapsed: 0.001 s
% 2.71/1.27 % (1860096)Peak memory usage: 88 MB
% 2.71/1.27 % (1860094)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=2145822840:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.71/1.27 % (1860095)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=3742320718:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.71/1.27 % (1860093)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=635659965:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.71/1.27 % (1860098)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4040655794:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.71/1.27 % (1860097)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1683055741:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.71/1.27 % (1860099)dis-21_1_sil=8000:lcm=predicate:random_seed=3917734304: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)
% 2.71/1.27 % (1860097)Refutation not found, incomplete strategy
% 2.71/1.27 % (1860097)------------------------------
% 2.71/1.27 % (1860097)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.27 % (1860097)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.27 % (1860097)CaDiCaL version: 2.1.3
% 2.71/1.27 % (1860097)Termination reason: Refutation not found, incomplete strategy
% 2.71/1.27 % (1860097)Time elapsed: 0.001 s
% 2.71/1.27 % (1860097)Peak memory usage: 88 MB
% 2.71/1.27 % (1860098)First to succeed.
% 2.71/1.27 % (1860098)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1860088"
% 2.71/1.27 % (1860099)Instruction limit reached!
% 2.71/1.27 % (1860099)------------------------------
% 2.71/1.27 % (1860099)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.27 % (1860099)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.27 % (1860099)CaDiCaL version: 2.1.3
% 2.71/1.27 % (1860099)Termination reason: Instruction limit
% 2.71/1.27 % (1860099)Termination phase: Saturation
% 2.71/1.27 % (1860099)Time elapsed: 0.071 s
% 2.71/1.27 % (1860099)Peak memory usage: 89 MB
% 2.71/1.27 % (1860099)Instructions burned: 130 (million)
% 2.71/1.27 % (1860096)------------------------------
% 2.71/1.27 % (1860096)------------------------------
% 2.71/1.27 % (1860107)lrs+10_1_sil=8000:sp=occurrence:random_seed=3182046048:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.71/1.27 % (1860108)lrs+10_1_sil=32000:urr=on:br=off:random_seed=935111309:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.71/1.27 % (1860108)Also succeeded, but the first one will report.
% 2.71/1.27 % (1860107)Also succeeded, but the first one will report.
% 2.71/1.27 % (1860097)------------------------------
% 2.71/1.27 % (1860097)------------------------------
% 2.71/1.27 % (1860098)Refutation found. Thanks to Tanya!
% 2.71/1.27 % SZS status Theorem for theBenchmark
% 2.71/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 3.60/1.44 % (1860098)------------------------------
% 3.60/1.44 % (1860098)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.60/1.44 % (1860098)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.60/1.44 % (1860098)CaDiCaL version: 2.1.3
% 3.60/1.44 % (1860098)Termination reason: Refutation
% 3.60/1.44 % (1860098)Time elapsed: 0.017 s
% 3.60/1.44 % (1860098)Peak memory usage: 89 MB
% 3.60/1.44 % (1860098)Instructions burned: 19 (million)
% 3.60/1.44 % (1860098)------------------------------
% 3.60/1.44 % (1860098)------------------------------
% 3.60/1.44 % (1860088)Success in time 0.424 s
% 3.60/1.44 % Vampire exiting
%------------------------------------------------------------------------------