%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU220+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 : 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 1.07s 1.13s
% Output : Refutation 2.56s
% 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(f8,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(f32,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(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] :
( ( 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(f36,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(f37,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)],[f36]) ).
fof(f41,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,[],[f37]) ).
fof(f42,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,[],[f41]) ).
fof(f44,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,[],[f35]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f47,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f46]) ).
fof(f64,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(f65,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,[],[f64]) ).
fof(f66,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,[],[f32]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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(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 )
& sP0(X0,X2,X3,X1) ) ) )
| ~ relation(X1)
| ~ function(X1) )
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(definition_folding,[],[f65,f68]) ).
fof(f70,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)],[f42]) ).
fof(f77,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,[],[f69]) ).
fof(f78,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,[],[f77]) ).
fof(f79,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,[],[f78]) ).
fof(f80,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK7(X0,X1),relation_dom(X0))
| sK6(X0,X1) != apply(X0,sK7(X0,X1)) )
& in(sK6(X0,X1),relation_rng(X0))
& sK7(X0,X1) = apply(X1,sK6(X0,X1)) )
| ~ sP0(X0,sK6(X0,X1),sK7(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,[sK6,sK7]),skolemize(X2,sK6(X0,X1)),skolemize(X3,sK7(X0,X1))],[f79]) ).
fof(f81,plain,
function(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f82,plain,
relation(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f83,plain,
in(sK1,relation_rng(sK2)),
inference(cnf_transformation,[],[f70]) ).
fof(f84,plain,
one_to_one(sK2),
inference(cnf_transformation,[],[f70]) ).
fof(f85,plain,
( sK1 != apply(sK2,apply(function_inverse(sK2),sK1))
| sK1 != apply(relation_composition(function_inverse(sK2),sK2),sK1) ),
inference(cnf_transformation,[],[f70]) ).
fof(f88,plain,
! [X0] :
( relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f89,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f90,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f47]) ).
fof(f121,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,[],[f80]) ).
fof(f127,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,[],[f67]) ).
fof(f128,definition,
~ sP8(sK1),
introduced(definition,[new_symbols(definition,[sP8])],[inequality_splitting_name_introduction]) ).
fof(f129,definition,
~ sP9(sK1),
introduced(definition,[new_symbols(definition,[sP9])],[inequality_splitting_name_introduction]) ).
fof(f130,plain,
( sP8(apply(sK2,apply(function_inverse(sK2),sK1)))
| sP9(apply(relation_composition(function_inverse(sK2),sK2),sK1)) ),
inference(inequality_splitting,[],[f85,f129,f128]) ).
fof(f137,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,[],[f121]) ).
fof(f138,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,[],[f137]) ).
fof(f141,definition,
( spl10_1
<=> sP9(apply(relation_composition(function_inverse(sK2),sK2),sK1)) ),
introduced(definition,[new_symbols(definition,[spl10_1])],[avatar_definition]) ).
fof(f143,plain,
( sP9(apply(relation_composition(function_inverse(sK2),sK2),sK1))
| ~ spl10_1 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f145,definition,
( spl10_2
<=> sP8(apply(sK2,apply(function_inverse(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
fof(f147,plain,
( sP8(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f145]) ).
fof(f148,plain,
( spl10_1
| spl10_2 ),
inference(avatar_split_clause,[],[f130,f145,f141]) ).
fof(f153,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2) ),
inference(superposition,[],[f83,f88]) ).
fof(f154,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ relation(sK2)
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f153,f84]) ).
fof(f156,plain,
( in(sK1,relation_dom(function_inverse(sK2)))
| ~ function(sK2) ),
inference(forward_subsumption_resolution,[],[f154,f82]) ).
fof(f158,plain,
in(sK1,relation_dom(function_inverse(sK2))),
inference(forward_subsumption_resolution,[],[f156,f81]) ).
fof(f169,plain,
( sP8(sK1)
| ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(superposition,[],[f147,f138]) ).
fof(f170,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f169,f128]) ).
fof(f171,plain,
( ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f170,f83]) ).
fof(f172,plain,
( ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f171,f90]) ).
fof(f173,plain,
( ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f172,f89]) ).
fof(f174,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f173,f84]) ).
fof(f175,plain,
( ~ function(sK2)
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f174,f82]) ).
fof(f176,plain,
( $false
| ~ spl10_2 ),
inference(forward_subsumption_resolution,[],[f175,f81]) ).
fof(f177,plain,
~ spl10_2,
inference(avatar_contradiction_clause,[],[f176]) ).
fof(f178,plain,
( sP9(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))
| ~ spl10_1 ),
inference(superposition,[],[f143,f127]) ).
fof(f179,plain,
( sP9(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ relation(sK2)
| ~ function(sK2)
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f178,f158]) ).
fof(f180,plain,
( sP9(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ function(sK2)
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f179,f82]) ).
fof(f181,plain,
( sP9(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ spl10_1 ),
inference(forward_subsumption_resolution,[],[f180,f81]) ).
fof(f183,definition,
( spl10_3
<=> function(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
fof(f185,plain,
( ~ function(function_inverse(sK2))
| spl10_3 ),
inference(avatar_component_clause,[],[f183]) ).
fof(f187,definition,
( spl10_4
<=> relation(function_inverse(sK2)) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
fof(f189,plain,
( ~ relation(function_inverse(sK2))
| spl10_4 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f191,definition,
( spl10_5
<=> sP9(apply(sK2,apply(function_inverse(sK2),sK1))) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
fof(f193,plain,
( sP9(apply(sK2,apply(function_inverse(sK2),sK1)))
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f191]) ).
fof(f194,plain,
( ~ spl10_3
| ~ spl10_4
| spl10_5
| ~ spl10_1 ),
inference(avatar_split_clause,[],[f181,f141,f191,f187,f183]) ).
fof(f195,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl10_3 ),
inference(resolution,[],[f185,f89]) ).
fof(f196,plain,
( ~ function(sK2)
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f195,f82]) ).
fof(f197,plain,
( $false
| spl10_3 ),
inference(forward_subsumption_resolution,[],[f196,f81]) ).
fof(f198,plain,
spl10_3,
inference(avatar_contradiction_clause,[],[f197]) ).
fof(f200,plain,
( ~ relation(sK2)
| ~ function(sK2)
| spl10_4 ),
inference(resolution,[],[f189,f90]) ).
fof(f201,plain,
( ~ function(sK2)
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f200,f82]) ).
fof(f202,plain,
( $false
| spl10_4 ),
inference(forward_subsumption_resolution,[],[f201,f81]) ).
fof(f203,plain,
spl10_4,
inference(avatar_contradiction_clause,[],[f202]) ).
fof(f225,plain,
( sP9(sK1)
| ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(superposition,[],[f193,f138]) ).
fof(f226,plain,
( ~ in(sK1,relation_rng(sK2))
| ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f225,f129]) ).
fof(f227,plain,
( ~ relation(function_inverse(sK2))
| ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f226,f83]) ).
fof(f228,plain,
( ~ function(function_inverse(sK2))
| ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f227,f90]) ).
fof(f229,plain,
( ~ one_to_one(sK2)
| ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f228,f89]) ).
fof(f230,plain,
( ~ relation(sK2)
| ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f229,f84]) ).
fof(f231,plain,
( ~ function(sK2)
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f230,f82]) ).
fof(f232,plain,
( $false
| ~ spl10_5 ),
inference(forward_subsumption_resolution,[],[f231,f81]) ).
fof(f233,plain,
~ spl10_5,
inference(avatar_contradiction_clause,[],[f232]) ).
cnf(s1,plain,
( spl10_1
| spl10_2 ),
inference(sat_conversion,[],[f148]) ).
cnf(s2,plain,
~ spl10_2,
inference(sat_conversion,[],[f177]) ).
cnf(s3,plain,
( ~ spl10_1
| ~ spl10_3
| ~ spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f194]) ).
cnf(s4,plain,
spl10_3,
inference(sat_conversion,[],[f198]) ).
cnf(s5,plain,
spl10_4,
inference(sat_conversion,[],[f203]) ).
cnf(s7,plain,
~ spl10_5,
inference(sat_conversion,[],[f233]) ).
cnf(s8,plain,
~ spl10_1,
inference(rat,[],[s3,s7,s5,s4]) ).
cnf(s9,plain,
$false,
inference(rat,[],[s1,s2,s8]) ).
fof(f234,plain,
$false,
inference(avatar_sat_refutation,[],[s9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU220+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n009.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 28 04:08:15 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 1.07/1.13 % (2649762)Detected formulas, will run a generic FOF schedule.
% 1.07/1.13 % (2649770)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=99112654:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 1.07/1.13 % (2649770)First to succeed.
% 1.07/1.13 % (2649770)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2649762"
% 1.07/1.13 % (2649771)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=846844093:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 1.07/1.13 % (2649772)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2515797275:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 1.07/1.13 % (2649769)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=2613615264:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 1.07/1.13 % (2649773)dis-21_1_sil=8000:lcm=predicate:random_seed=1116645135: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)
% 1.07/1.13 % (2649768)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=1536416643:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 1.07/1.13 % (2649767)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=1321914682:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 1.07/1.13 % (2649771)Also succeeded, but the first one will report.
% 1.07/1.13 % (2649772)Also succeeded, but the first one will report.
% 1.07/1.13 % (2649773)Instruction limit reached!
% 1.07/1.13 % (2649773)------------------------------
% 1.07/1.13 % (2649773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.07/1.13 % (2649773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/1.13 % (2649773)CaDiCaL version: 2.1.3
% 1.07/1.13 % (2649773)Termination reason: Instruction limit
% 1.07/1.13 % (2649773)Termination phase: Saturation
% 1.07/1.13 % (2649773)Time elapsed: 0.077 s
% 1.07/1.13 % (2649773)Peak memory usage: 91 MB
% 1.07/1.13 % (2649773)Instructions burned: 130 (million)
% 1.07/1.13 % (2649770)Refutation found. Thanks to Tanya!
% 1.07/1.13 % SZS status Theorem for theBenchmark
% 1.07/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.56/1.26 % (2649770)------------------------------
% 2.56/1.26 % (2649770)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.56/1.26 % (2649770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.56/1.26 % (2649770)CaDiCaL version: 2.1.3
% 2.56/1.26 % (2649770)Termination reason: Refutation
% 2.56/1.26 % (2649770)Time elapsed: 0.004 s
% 2.56/1.26 % (2649770)Peak memory usage: 89 MB
% 2.56/1.26 % (2649770)Instructions burned: 8 (million)
% 2.56/1.26 % (2649770)------------------------------
% 2.56/1.26 % (2649770)------------------------------
% 2.56/1.26 % (2649762)Success in time 0.293 s
% 2.56/1.26 % Vampire exiting
%------------------------------------------------------------------------------