%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : 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 3.18s 1.32s
% Output : Refutation 3.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 10
% Syntax : Number of formulae : 96 ( 13 unt; 5 def)
% Number of atoms : 461 ( 105 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 627 ( 262 ~; 260 |; 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(f6,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(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/sandbox/benchmark/theBenchmark.p',t54_funct_1) ).
fof(f36,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(f38,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(f39,negated_conjecture,
~ ! [X0] :
( ( relation(X0)
& function(X0) )
=> ( one_to_one(X0)
=> one_to_one(function_inverse(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f38]) ).
fof(f52,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(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f55,plain,
! [X0] :
( ( relation(function_inverse(X0))
& function(function_inverse(X0)) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f54]) ).
fof(f77,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(f78,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,[],[f77]) ).
fof(f79,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,[],[f36]) ).
fof(f80,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,[],[f79]) ).
fof(f82,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(ennf_transformation,[],[f39]) ).
fof(f83,plain,
? [X0] :
( ~ one_to_one(function_inverse(X0))
& one_to_one(X0)
& relation(X0)
& function(X0) ),
inference(flattening,[],[f82]) ).
fof(f87,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(f88,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,[],[f78,f87]) ).
fof(f89,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,[],[f53]) ).
fof(f90,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,[],[f89]) ).
fof(f91,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))],[f90]) ).
fof(f106,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,[],[f88]) ).
fof(f107,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,[],[f106]) ).
fof(f108,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,[],[f107]) ).
fof(f109,plain,
! [X0] :
( ! [X1] :
( ( ( X1 = function_inverse(X0)
| relation_rng(X0) != relation_dom(X1)
| ( ( ~ in(sK15(X0,X1),relation_dom(X0))
| sK14(X0,X1) != apply(X0,sK15(X0,X1)) )
& in(sK14(X0,X1),relation_rng(X0))
& sK15(X0,X1) = apply(X1,sK14(X0,X1)) )
| ~ sP0(X0,sK14(X0,X1),sK15(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,[sK14,sK15]),skolemize(X2,sK14(X0,X1)),skolemize(X3,sK15(X0,X1))],[f108]) ).
fof(f110,plain,
( ~ one_to_one(function_inverse(sK16))
& one_to_one(sK16)
& relation(sK16)
& function(sK16) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(X0,sK16)],[f83]) ).
fof(f118,plain,
! [X0] :
( apply(X0,sK1(X0)) = apply(X0,sK2(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f119,plain,
! [X0] :
( in(sK2(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f120,plain,
! [X0] :
( in(sK1(X0),relation_dom(X0))
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f121,plain,
! [X0] :
( sK1(X0) != sK2(X0)
| one_to_one(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f122,plain,
! [X0] :
( function(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f123,plain,
! [X0] :
( relation(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f176,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,[],[f109]) ).
fof(f181,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,[],[f80]) ).
fof(f183,plain,
function(sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f184,plain,
relation(sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f185,plain,
one_to_one(sK16),
inference(cnf_transformation,[],[f110]) ).
fof(f186,plain,
~ one_to_one(function_inverse(sK16)),
inference(cnf_transformation,[],[f110]) ).
fof(f193,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,[],[f176]) ).
fof(f260,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,[],[f193,f123]) ).
fof(f261,plain,
! [X0] :
( ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f260,f122]) ).
fof(f262,plain,
( relation_rng(sK16) = relation_dom(function_inverse(sK16))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f261,f185]) ).
fof(f267,plain,
( relation_rng(sK16) = relation_dom(function_inverse(sK16))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f262,f184]) ).
fof(f270,plain,
relation_rng(sK16) = relation_dom(function_inverse(sK16)),
inference(forward_subsumption_resolution,[],[f267,f183]) ).
fof(f273,plain,
( in(sK1(function_inverse(sK16)),relation_rng(sK16))
| one_to_one(function_inverse(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16)) ),
inference(superposition,[],[f120,f270]) ).
fof(f274,plain,
( in(sK2(function_inverse(sK16)),relation_rng(sK16))
| one_to_one(function_inverse(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16)) ),
inference(superposition,[],[f119,f270]) ).
fof(f279,plain,
( in(sK2(function_inverse(sK16)),relation_rng(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16)) ),
inference(forward_subsumption_resolution,[],[f274,f186]) ).
fof(f280,plain,
( in(sK1(function_inverse(sK16)),relation_rng(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16)) ),
inference(forward_subsumption_resolution,[],[f273,f186]) ).
fof(f282,definition,
( spl17_1
<=> relation(function_inverse(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_1])],[avatar_definition]) ).
fof(f283,plain,
( relation(function_inverse(sK16))
| ~ spl17_1 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f284,plain,
( ~ relation(function_inverse(sK16))
| spl17_1 ),
inference(avatar_component_clause,[],[f282]) ).
fof(f291,definition,
( spl17_3
<=> function(function_inverse(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_3])],[avatar_definition]) ).
fof(f292,plain,
( function(function_inverse(sK16))
| ~ spl17_3 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f293,plain,
( ~ function(function_inverse(sK16))
| spl17_3 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f295,definition,
( spl17_4
<=> in(sK2(function_inverse(sK16)),relation_rng(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_4])],[avatar_definition]) ).
fof(f297,plain,
( in(sK2(function_inverse(sK16)),relation_rng(sK16))
| ~ spl17_4 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f298,plain,
( ~ spl17_3
| ~ spl17_1
| spl17_4 ),
inference(avatar_split_clause,[],[f279,f295,f282,f291]) ).
fof(f300,definition,
( spl17_5
<=> in(sK1(function_inverse(sK16)),relation_rng(sK16)) ),
introduced(definition,[new_symbols(definition,[spl17_5])],[avatar_definition]) ).
fof(f302,plain,
( in(sK1(function_inverse(sK16)),relation_rng(sK16))
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f300]) ).
fof(f303,plain,
( ~ spl17_3
| ~ spl17_1
| spl17_5 ),
inference(avatar_split_clause,[],[f280,f300,f282,f291]) ).
fof(f306,plain,
( ~ relation(sK16)
| ~ function(sK16)
| spl17_1 ),
inference(resolution,[],[f284,f123]) ).
fof(f308,plain,
( ~ function(sK16)
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f306,f184]) ).
fof(f309,plain,
( $false
| spl17_1 ),
inference(forward_subsumption_resolution,[],[f308,f183]) ).
fof(f310,plain,
spl17_1,
inference(avatar_contradiction_clause,[],[f309]) ).
fof(f326,plain,
( ~ relation(sK16)
| ~ function(sK16)
| spl17_3 ),
inference(resolution,[],[f293,f122]) ).
fof(f328,plain,
( ~ function(sK16)
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f326,f184]) ).
fof(f329,plain,
( $false
| spl17_3 ),
inference(forward_subsumption_resolution,[],[f328,f183]) ).
fof(f330,plain,
spl17_3,
inference(avatar_contradiction_clause,[],[f329]) ).
fof(f336,plain,
( ~ one_to_one(sK16)
| sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK2(function_inverse(sK16))))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_4 ),
inference(resolution,[],[f297,f181]) ).
fof(f342,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK2(function_inverse(sK16))))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f336,f185]) ).
fof(f345,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK2(function_inverse(sK16))))
| ~ function(sK16)
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f342,f184]) ).
fof(f348,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK2(function_inverse(sK16))))
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f345,f183]) ).
fof(f351,plain,
( ~ one_to_one(sK16)
| sK1(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_5 ),
inference(resolution,[],[f302,f181]) ).
fof(f357,plain,
( sK1(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ relation(sK16)
| ~ function(sK16)
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f351,f185]) ).
fof(f360,plain,
( sK1(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ function(sK16)
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f357,f184]) ).
fof(f363,plain,
( sK1(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f360,f183]) ).
fof(f686,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| one_to_one(function_inverse(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16))
| ~ spl17_4 ),
inference(superposition,[],[f348,f118]) ).
fof(f691,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16))
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f686,f186]) ).
fof(f694,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ function(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f691,f283]) ).
fof(f697,plain,
( sK2(function_inverse(sK16)) = apply(sK16,apply(function_inverse(sK16),sK1(function_inverse(sK16))))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4 ),
inference(forward_subsumption_resolution,[],[f694,f292]) ).
fof(f771,plain,
( sK1(function_inverse(sK16)) = sK2(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(forward_demodulation,[],[f697,f363]) ).
fof(f787,plain,
( sK1(function_inverse(sK16)) != sK1(function_inverse(sK16))
| one_to_one(function_inverse(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(superposition,[],[f121,f771]) ).
fof(f789,plain,
( one_to_one(function_inverse(sK16))
| ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(trivial_inequality_removal,[],[f787]) ).
fof(f790,plain,
( ~ relation(function_inverse(sK16))
| ~ function(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f789,f186]) ).
fof(f791,plain,
( ~ function(function_inverse(sK16))
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f790,f283]) ).
fof(f792,plain,
( $false
| ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(forward_subsumption_resolution,[],[f791,f292]) ).
fof(f793,plain,
( ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(avatar_contradiction_clause,[],[f792]) ).
cnf(s2,plain,
( ~ spl17_1
| ~ spl17_3
| spl17_4 ),
inference(sat_conversion,[],[f298]) ).
cnf(s3,plain,
( ~ spl17_1
| ~ spl17_3
| spl17_5 ),
inference(sat_conversion,[],[f303]) ).
cnf(s4,plain,
spl17_1,
inference(sat_conversion,[],[f310]) ).
cnf(s5,plain,
spl17_3,
inference(sat_conversion,[],[f330]) ).
cnf(s26,plain,
( ~ spl17_1
| ~ spl17_3
| ~ spl17_4
| ~ spl17_5 ),
inference(sat_conversion,[],[f793]) ).
cnf(s33,plain,
spl17_5,
inference(rat,[],[s3,s5,s4]) ).
cnf(s34,plain,
~ spl17_4,
inference(rat,[],[s26,s4,s5,s33]) ).
cnf(s35,plain,
$false,
inference(rat,[],[s2,s34,s5,s4]) ).
fof(f794,plain,
$false,
inference(avatar_sat_refutation,[],[s35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU221+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n008.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 04:09:10 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.18/1.32 % (1860491)Detected formulas, will run a generic FOF schedule.
% 3.18/1.32 % (1860500)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=230033182:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.18/1.32 % (1860500)Refutation not found, incomplete strategy
% 3.18/1.32 % (1860500)------------------------------
% 3.18/1.32 % (1860500)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.32 % (1860500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.32 % (1860500)CaDiCaL version: 2.1.3
% 3.18/1.32 % (1860500)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.32 % (1860500)Time elapsed: 0.001 s
% 3.18/1.32 % (1860500)Peak memory usage: 88 MB
% 3.18/1.32 % (1860502)dis-21_1_sil=8000:lcm=predicate:random_seed=2847187128:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.18/1.32 % (1860498)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=2953602372:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.18/1.32 % (1860497)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=3791161764:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.18/1.32 % (1860501)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2494145267:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.18/1.32 % (1860499)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1607676127:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.18/1.32 % (1860496)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=352162580:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.18/1.32 % (1860499)Refutation not found, incomplete strategy
% 3.18/1.32 % (1860499)------------------------------
% 3.18/1.32 % (1860499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.32 % (1860499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.32 % (1860499)CaDiCaL version: 2.1.3
% 3.18/1.32 % (1860499)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.32 % (1860499)Time elapsed: 0.002 s
% 3.18/1.32 % (1860499)Peak memory usage: 88 MB
% 3.18/1.32 % (1860501)First to succeed.
% 3.18/1.32 % (1860501)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1860491"
% 3.18/1.32 % (1860502)Instruction limit reached!
% 3.18/1.32 % (1860502)------------------------------
% 3.18/1.32 % (1860502)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.18/1.32 % (1860502)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.18/1.32 % (1860502)CaDiCaL version: 2.1.3
% 3.18/1.32 % (1860502)Termination reason: Instruction limit
% 3.18/1.32 % (1860502)Termination phase: Saturation
% 3.18/1.32 % (1860502)Time elapsed: 0.078 s
% 3.18/1.32 % (1860502)Peak memory usage: 90 MB
% 3.18/1.32 % (1860502)Instructions burned: 130 (million)
% 3.18/1.32 % (1860500)------------------------------
% 3.18/1.32 % (1860500)------------------------------
% 3.18/1.32 % (1860510)lrs+10_1_sil=8000:sp=occurrence:random_seed=658800442:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.18/1.32 % (1860499)------------------------------
% 3.18/1.32 % (1860499)------------------------------
% 3.18/1.32 % (1860510)Also succeeded, but the first one will report.
% 3.18/1.32 % (1860511)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1943504885:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.18/1.32 % (1860511)Also succeeded, but the first one will report.
% 3.18/1.32 % (1860501)Refutation found. Thanks to Tanya!
% 3.18/1.32 % SZS status Theorem for theBenchmark
% 3.18/1.32 % SZS output start Proof for theBenchmark
% See solution above
% 3.83/1.51 % (1860501)------------------------------
% 3.83/1.51 % (1860501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.83/1.51 % (1860501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.83/1.51 % (1860501)CaDiCaL version: 2.1.3
% 3.83/1.51 % (1860501)Termination reason: Refutation
% 3.83/1.51 % (1860501)Time elapsed: 0.018 s
% 3.83/1.51 % (1860501)Peak memory usage: 90 MB
% 3.83/1.51 % (1860501)Instructions burned: 23 (million)
% 3.83/1.51 % (1860501)------------------------------
% 3.83/1.51 % (1860501)------------------------------
% 3.83/1.51 % (1860491)Success in time 0.447 s
% 3.83/1.51 % Vampire exiting
%------------------------------------------------------------------------------