%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 12:47:46 PM UTC 2026
% Result : Theorem 2.67s 1.28s
% Output : Refutation 3.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 8
% Syntax : Number of formulae : 92 ( 18 unt; 2 def)
% Number of atoms : 380 ( 52 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 487 ( 199 ~; 198 |; 59 &)
% ( 16 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 3 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-4 aty)
% Number of variables : 170 ( 0 sgn 146 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0] :
( ( relation(X0)
& function(X0) )
=> ! [X1,X2] :
( ( in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) ) )
& ( ~ in(X1,relation_dom(X0))
=> ( X2 = apply(X0,X1)
<=> X2 = empty_set ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_funct_1) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_relat_1) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( relation(X1)
=> ! [X2] :
( relation(X2)
=> ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_relat_1) ).
fof(f15,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f20,axiom,
! [X0,X1] :
( ( relation(X0)
& function(X0)
& relation(X1)
& function(X1) )
=> ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_funct_1) ).
fof(f36,conjecture,
! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t22_funct_1) ).
fof(f37,negated_conjecture,
~ ! [X0,X1] :
( ( relation(X1)
& function(X1) )
=> ! [X2] :
( ( relation(X2)
& function(X2) )
=> ( in(X0,relation_dom(relation_composition(X2,X1)))
=> apply(relation_composition(X2,X1),X0) = apply(X1,apply(X2,X0)) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f47,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f48,plain,
! [X0] :
( ! [X1,X2] :
( ( ( X2 = apply(X0,X1)
<=> in(ordered_pair(X1,X2),X0) )
| ~ in(X1,relation_dom(X0)) )
& ( ( X2 = apply(X0,X1)
<=> X2 = empty_set )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(flattening,[],[f47]) ).
fof(f49,plain,
! [X0] :
( ! [X1] :
( X1 = relation_dom(X0)
<=> ! [X2] :
( in(X2,X1)
<=> ? [X3] : in(ordered_pair(X2,X3),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( X2 = relation_composition(X0,X1)
<=> ! [X3,X4] :
( in(ordered_pair(X3,X4),X2)
<=> ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) ) ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f51,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f52,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f51]) ).
fof(f55,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f56,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f55]) ).
fof(f63,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f64,plain,
? [X0,X1] :
( ? [X2] :
( apply(relation_composition(X2,X1),X0) != apply(X1,apply(X2,X0))
& in(X0,relation_dom(relation_composition(X2,X1)))
& relation(X2)
& function(X2) )
& relation(X1)
& function(X1) ),
inference(flattening,[],[f63]) ).
fof(f70,plain,
! [X0] :
( ! [X1,X2] :
( ( ( ( X2 = apply(X0,X1)
| ~ in(ordered_pair(X1,X2),X0) )
& ( in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ) )
| ~ in(X1,relation_dom(X0)) )
& ( ( ( X2 = apply(X0,X1)
| empty_set != X2 )
& ( X2 = empty_set
| apply(X0,X1) != X2 ) )
| in(X1,relation_dom(X0)) ) )
| ~ relation(X0)
| ~ function(X0) ),
inference(nnf_transformation,[],[f48]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| in(X2,X1) ) ) )
& ( ! [X2] :
( ( in(X2,X1)
| ! [X3] : ~ in(ordered_pair(X2,X3),X0) )
& ( ? [X3] : in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ? [X2] :
( ( ! [X3] : ~ in(ordered_pair(X2,X3),X0)
| ~ in(X2,X1) )
& ( ? [X4] : in(ordered_pair(X2,X4),X0)
| in(X2,X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( ? [X7] : in(ordered_pair(X5,X7),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(rectify,[],[f71]) ).
fof(f73,plain,
! [X0] :
( ! [X1] :
( ( X1 = relation_dom(X0)
| ( ( ! [X3] : ~ in(ordered_pair(sK0(X0,X1),X3),X0)
| ~ in(sK0(X0,X1),X1) )
& ( in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| in(sK0(X0,X1),X1) ) ) )
& ( ! [X5] :
( ( in(X5,X1)
| ! [X6] : ~ in(ordered_pair(X5,X6),X0) )
& ( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1) ) )
| relation_dom(X0) != X1 ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X2,sK0(X0,X1)),skolemize(X4,sK1(X0,X1)),skolemize(X7,sK2(X0,X5))],[f72]) ).
fof(f74,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X3,X4] :
( ( in(ordered_pair(X3,X4),X2)
| ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) ) )
& ( ? [X5] :
( in(ordered_pair(X3,X5),X0)
& in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ? [X3,X4] :
( ( ! [X5] :
( ~ in(ordered_pair(X3,X5),X0)
| ~ in(ordered_pair(X5,X4),X1) )
| ~ in(ordered_pair(X3,X4),X2) )
& ( ? [X6] :
( in(ordered_pair(X3,X6),X0)
& in(ordered_pair(X6,X4),X1) )
| in(ordered_pair(X3,X4),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ? [X10] :
( in(ordered_pair(X7,X10),X0)
& in(ordered_pair(X10,X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(rectify,[],[f74]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( X2 = relation_composition(X0,X1)
| ( ( ! [X5] :
( ~ in(ordered_pair(sK3(X0,X1,X2),X5),X0)
| ~ in(ordered_pair(X5,sK4(X0,X1,X2)),X1) )
| ~ in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) )
& ( ( in(ordered_pair(sK3(X0,X1,X2),sK5(X0,X1,X2)),X0)
& in(ordered_pair(sK5(X0,X1,X2),sK4(X0,X1,X2)),X1) )
| in(ordered_pair(sK3(X0,X1,X2),sK4(X0,X1,X2)),X2) ) ) )
& ( ! [X7,X8] :
( ( in(ordered_pair(X7,X8),X2)
| ! [X9] :
( ~ in(ordered_pair(X7,X9),X0)
| ~ in(ordered_pair(X9,X8),X1) ) )
& ( ( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
& in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1) )
| ~ in(ordered_pair(X7,X8),X2) ) )
| relation_composition(X0,X1) != X2 ) )
| ~ relation(X2) )
| ~ relation(X1) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6]),skolemize(X3,sK3(X0,X1,X2)),skolemize(X4,sK4(X0,X1,X2)),skolemize(X6,sK5(X0,X1,X2)),skolemize(X10,sK6(X0,X1,X7,X8))],[f75]) ).
fof(f84,plain,
( apply(relation_composition(sK16,sK15),sK14) != apply(sK15,apply(sK16,sK14))
& in(sK14,relation_dom(relation_composition(sK16,sK15)))
& relation(sK16)
& function(sK16)
& relation(sK15)
& function(sK15) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14,sK15,sK16]),skolemize(X0,sK14),skolemize(X1,sK15),skolemize(X2,sK16)],[f64]) ).
fof(f92,plain,
! [X2,X0,X1] :
( apply(X0,X1) = X2
| ~ in(ordered_pair(X1,X2),X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0)
| ~ function(X0) ),
inference(cnf_transformation,[],[f70]) ).
fof(f93,plain,
! [X0,X1,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,X1)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f94,plain,
! [X0,X1,X6,X5] :
( in(X5,X1)
| ~ in(ordered_pair(X5,X6),X0)
| relation_dom(X0) != X1
| ~ relation(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f98,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f99,plain,
! [X2,X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),X2)
| relation_composition(X0,X1) != X2
| ~ relation(X2)
| ~ relation(X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f76]) ).
fof(f104,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f110,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f133,plain,
function(sK15),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
relation(sK15),
inference(cnf_transformation,[],[f84]) ).
fof(f135,plain,
function(sK16),
inference(cnf_transformation,[],[f84]) ).
fof(f136,plain,
relation(sK16),
inference(cnf_transformation,[],[f84]) ).
fof(f137,plain,
in(sK14,relation_dom(relation_composition(sK16,sK15))),
inference(cnf_transformation,[],[f84]) ).
fof(f138,plain,
apply(relation_composition(sK16,sK15),sK14) != apply(sK15,apply(sK16,sK14)),
inference(cnf_transformation,[],[f84]) ).
fof(f146,plain,
! [X0,X6,X5] :
( ~ in(ordered_pair(X5,X6),X0)
| in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f94]) ).
fof(f147,plain,
! [X0,X5] :
( in(ordered_pair(X5,sK2(X0,X5)),X0)
| ~ in(X5,relation_dom(X0))
| ~ relation(X0) ),
inference(equality_resolution,[],[f93]) ).
fof(f149,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f150,plain,
! [X0,X1,X8,X7] :
( in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| ~ relation(relation_composition(X0,X1))
| ~ relation(X1)
| ~ relation(X0) ),
inference(equality_resolution,[],[f98]) ).
fof(f270,plain,
! [X2,X0,X1] :
( ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2
| ~ relation(X0)
| ~ function(X0) ),
inference(forward_subsumption_resolution,[],[f92,f146]) ).
fof(f274,plain,
! [X0,X1] :
( apply(X0,X1) = sK2(X0,X1)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| ~ relation(X0) ),
inference(resolution,[],[f270,f147]) ).
fof(f275,plain,
! [X0,X1] :
( apply(X0,X1) = sK2(X0,X1)
| ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0)) ),
inference(duplicate_literal_removal,[],[f274]) ).
fof(f292,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(X7,sK6(X0,X1,X7,X8)),X0)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f149,f104]) ).
fof(f313,plain,
! [X2,X0,X1] :
( in(ordered_pair(X0,sK6(X1,X2,X0,sK2(relation_composition(X1,X2),X0))),X1)
| ~ relation(X2)
| ~ relation(X1)
| ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ relation(relation_composition(X1,X2)) ),
inference(resolution,[],[f292,f147]) ).
fof(f314,plain,
! [X2,X0,X1] :
( ~ in(X0,relation_dom(relation_composition(X1,X2)))
| ~ relation(X2)
| ~ relation(X1)
| in(ordered_pair(X0,sK6(X1,X2,X0,sK2(relation_composition(X1,X2),X0))),X1) ),
inference(forward_subsumption_resolution,[],[f313,f104]) ).
fof(f318,plain,
! [X0,X1,X8,X7] :
( ~ in(ordered_pair(X7,X8),relation_composition(X0,X1))
| in(ordered_pair(sK6(X0,X1,X7,X8),X8),X1)
| ~ relation(X1)
| ~ relation(X0) ),
inference(forward_subsumption_resolution,[],[f150,f104]) ).
fof(f320,plain,
! [X2,X0,X1] :
( in(ordered_pair(sK6(X0,X1,X2,sK2(relation_composition(X0,X1),X2)),sK2(relation_composition(X0,X1),X2)),X1)
| ~ relation(X1)
| ~ relation(X0)
| ~ in(X2,relation_dom(relation_composition(X0,X1)))
| ~ relation(relation_composition(X0,X1)) ),
inference(resolution,[],[f318,f147]) ).
fof(f321,plain,
! [X2,X0,X1] :
( ~ in(X2,relation_dom(relation_composition(X0,X1)))
| ~ relation(X1)
| ~ relation(X0)
| in(ordered_pair(sK6(X0,X1,X2,sK2(relation_composition(X0,X1),X2)),sK2(relation_composition(X0,X1),X2)),X1) ),
inference(forward_subsumption_resolution,[],[f320,f104]) ).
fof(f646,plain,
( ~ relation(sK15)
| ~ relation(sK16)
| in(ordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),sK16) ),
inference(resolution,[],[f314,f137]) ).
fof(f647,plain,
( ~ relation(sK16)
| in(ordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),sK16) ),
inference(forward_subsumption_resolution,[],[f646,f134]) ).
fof(f648,plain,
in(ordered_pair(sK14,sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))),sK16),
inference(forward_subsumption_resolution,[],[f647,f136]) ).
fof(f650,plain,
( apply(sK16,sK14) = sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))
| ~ relation(sK16)
| ~ function(sK16) ),
inference(resolution,[],[f648,f270]) ).
fof(f657,plain,
( apply(sK16,sK14) = sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14))
| ~ function(sK16) ),
inference(forward_subsumption_resolution,[],[f650,f136]) ).
fof(f660,definition,
( spl17_31
<=> function(relation_composition(sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl17_31])],[avatar_definition]) ).
fof(f661,plain,
( function(relation_composition(sK16,sK15))
| ~ spl17_31 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f662,plain,
( ~ function(relation_composition(sK16,sK15))
| spl17_31 ),
inference(avatar_component_clause,[],[f660]) ).
fof(f664,definition,
( spl17_32
<=> relation(relation_composition(sK16,sK15)) ),
introduced(definition,[new_symbols(definition,[spl17_32])],[avatar_definition]) ).
fof(f665,plain,
( relation(relation_composition(sK16,sK15))
| ~ spl17_32 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f666,plain,
( ~ relation(relation_composition(sK16,sK15))
| spl17_32 ),
inference(avatar_component_clause,[],[f664]) ).
fof(f672,plain,
apply(sK16,sK14) = sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),
inference(forward_subsumption_resolution,[],[f657,f135]) ).
fof(f694,plain,
( ~ relation(sK15)
| ~ relation(sK16)
| in(ordered_pair(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),sK2(relation_composition(sK16,sK15),sK14)),sK15) ),
inference(resolution,[],[f321,f137]) ).
fof(f695,plain,
( ~ relation(sK16)
| in(ordered_pair(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),sK2(relation_composition(sK16,sK15),sK14)),sK15) ),
inference(forward_subsumption_resolution,[],[f694,f134]) ).
fof(f696,plain,
in(ordered_pair(sK6(sK16,sK15,sK14,sK2(relation_composition(sK16,sK15),sK14)),sK2(relation_composition(sK16,sK15),sK14)),sK15),
inference(forward_subsumption_resolution,[],[f695,f136]) ).
fof(f697,plain,
( ~ relation(sK16)
| ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15)
| spl17_31 ),
inference(resolution,[],[f662,f110]) ).
fof(f699,plain,
( ~ function(sK16)
| ~ relation(sK15)
| ~ function(sK15)
| spl17_31 ),
inference(forward_subsumption_resolution,[],[f697,f136]) ).
fof(f700,plain,
( ~ relation(sK15)
| ~ function(sK15)
| spl17_31 ),
inference(forward_subsumption_resolution,[],[f699,f135]) ).
fof(f701,plain,
( ~ function(sK15)
| spl17_31 ),
inference(forward_subsumption_resolution,[],[f700,f134]) ).
fof(f702,plain,
( $false
| spl17_31 ),
inference(forward_subsumption_resolution,[],[f701,f133]) ).
fof(f703,plain,
spl17_31,
inference(avatar_contradiction_clause,[],[f702]) ).
fof(f754,plain,
( ~ relation(sK16)
| ~ relation(sK15)
| spl17_32 ),
inference(resolution,[],[f666,f104]) ).
fof(f756,plain,
( ~ relation(sK15)
| spl17_32 ),
inference(forward_subsumption_resolution,[],[f754,f136]) ).
fof(f757,plain,
( $false
| spl17_32 ),
inference(forward_subsumption_resolution,[],[f756,f134]) ).
fof(f758,plain,
spl17_32,
inference(avatar_contradiction_clause,[],[f757]) ).
fof(f903,plain,
in(ordered_pair(apply(sK16,sK14),sK2(relation_composition(sK16,sK15),sK14)),sK15),
inference(forward_demodulation,[],[f696,f672]) ).
fof(f906,plain,
( apply(sK15,apply(sK16,sK14)) = sK2(relation_composition(sK16,sK15),sK14)
| ~ relation(sK15)
| ~ function(sK15) ),
inference(resolution,[],[f903,f270]) ).
fof(f914,plain,
( apply(sK15,apply(sK16,sK14)) = sK2(relation_composition(sK16,sK15),sK14)
| ~ function(sK15) ),
inference(forward_subsumption_resolution,[],[f906,f134]) ).
fof(f918,plain,
apply(sK15,apply(sK16,sK14)) = sK2(relation_composition(sK16,sK15),sK14),
inference(forward_subsumption_resolution,[],[f914,f133]) ).
fof(f974,plain,
( apply(relation_composition(sK16,sK15),sK14) = apply(sK15,apply(sK16,sK14))
| ~ relation(relation_composition(sK16,sK15))
| ~ function(relation_composition(sK16,sK15))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(superposition,[],[f918,f275]) ).
fof(f988,plain,
( ~ relation(relation_composition(sK16,sK15))
| ~ function(relation_composition(sK16,sK15))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15))) ),
inference(forward_subsumption_resolution,[],[f974,f138]) ).
fof(f993,plain,
( ~ function(relation_composition(sK16,sK15))
| ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ spl17_32 ),
inference(forward_subsumption_resolution,[],[f988,f665]) ).
fof(f995,plain,
( ~ in(sK14,relation_dom(relation_composition(sK16,sK15)))
| ~ spl17_31
| ~ spl17_32 ),
inference(forward_subsumption_resolution,[],[f993,f661]) ).
fof(f998,plain,
( $false
| ~ spl17_31
| ~ spl17_32 ),
inference(forward_subsumption_resolution,[],[f995,f137]) ).
fof(f999,plain,
( ~ spl17_31
| ~ spl17_32 ),
inference(avatar_contradiction_clause,[],[f998]) ).
cnf(s25,plain,
spl17_31,
inference(sat_conversion,[],[f703]) ).
cnf(s28,plain,
spl17_32,
inference(sat_conversion,[],[f758]) ).
cnf(s31,plain,
( ~ spl17_31
| ~ spl17_32 ),
inference(sat_conversion,[],[f999]) ).
cnf(s32,plain,
~ spl17_31,
inference(rat,[],[s31,s28]) ).
cnf(s33,plain,
$false,
inference(rat,[],[s25,s32]) ).
fof(f1000,plain,
$false,
inference(avatar_sat_refutation,[],[s33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU214+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n006.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 28 04:04:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 2.67/1.28 % (3566150)Detected formulas, will run a generic FOF schedule.
% 2.67/1.28 % (3566156)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=700991953:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.67/1.28 % (3566161)dis-21_1_sil=8000:lcm=predicate:random_seed=1150227276: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)
% 2.67/1.28 % (3566159)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2273379272:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.67/1.28 % (3566155)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=281609561:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.67/1.28 % (3566160)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=634326800:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.67/1.28 % (3566158)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=697034149:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.67/1.28 % (3566157)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=2627292886:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.67/1.28 % (3566158)Refutation not found, incomplete strategy
% 2.67/1.28 % (3566158)------------------------------
% 2.67/1.28 % (3566158)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.28 % (3566158)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.28 % (3566158)CaDiCaL version: 2.1.3
% 2.67/1.28 % (3566158)Termination reason: Refutation not found, incomplete strategy
% 2.67/1.28 % (3566158)Time elapsed: 0.003 s
% 2.67/1.28 % (3566158)Peak memory usage: 88 MB
% 2.67/1.28 % (3566158)Instructions burned: 3 (million)
% 2.67/1.28 % (3566160)First to succeed.
% 2.67/1.28 % (3566160)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3566150"
% 2.67/1.28 % (3566159)Instruction limit reached!
% 2.67/1.28 % (3566159)------------------------------
% 2.67/1.28 % (3566159)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.28 % (3566159)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.28 % (3566159)CaDiCaL version: 2.1.3
% 2.67/1.28 % (3566159)Termination reason: Instruction limit
% 2.67/1.28 % (3566159)Termination phase: Saturation
% 2.67/1.28 % (3566159)Time elapsed: 0.065 s
% 2.67/1.28 % (3566159)Peak memory usage: 88 MB
% 2.67/1.28 % (3566159)Instructions burned: 120 (million)
% 2.67/1.28 % (3566161)Instruction limit reached!
% 2.67/1.28 % (3566161)------------------------------
% 2.67/1.28 % (3566161)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.67/1.28 % (3566161)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.67/1.28 % (3566161)CaDiCaL version: 2.1.3
% 2.67/1.28 % (3566161)Termination reason: Instruction limit
% 2.67/1.28 % (3566161)Termination phase: Saturation
% 2.67/1.28 % (3566161)Time elapsed: 0.086 s
% 2.67/1.28 % (3566161)Peak memory usage: 90 MB
% 2.67/1.28 % (3566161)Instructions burned: 129 (million)
% 2.67/1.28 % (3566169)lrs+10_1_sil=8000:sp=occurrence:random_seed=3814768706:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 2.67/1.28 % (3566170)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3634798595:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.67/1.28 % (3566158)------------------------------
% 2.67/1.28 % (3566158)------------------------------
% 2.67/1.28 % (3566160)Refutation found. Thanks to Tanya!
% 2.67/1.28 % SZS status Theorem for theBenchmark
% 2.67/1.28 % SZS output start Proof for theBenchmark
% See solution above
% 3.57/1.37 % (3566160)------------------------------
% 3.57/1.37 % (3566160)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.57/1.37 % (3566160)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.57/1.37 % (3566160)CaDiCaL version: 2.1.3
% 3.57/1.37 % (3566160)Termination reason: Refutation
% 3.57/1.37 % (3566160)Time elapsed: 0.038 s
% 3.57/1.37 % (3566160)Peak memory usage: 90 MB
% 3.57/1.37 % (3566160)Instructions burned: 45 (million)
% 3.57/1.37 % (3566160)------------------------------
% 3.57/1.37 % (3566160)------------------------------
% 3.57/1.37 % (3566150)Success in time 0.441 s
% 3.57/1.37 % Vampire exiting
%------------------------------------------------------------------------------