%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU214+3 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 12:52:25 PM UTC 2026
% Result : Theorem 0.16s 0.52s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 12
% Syntax : Number of formulae : 113 ( 18 unt; 4 def)
% Number of atoms : 397 ( 45 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 512 ( 228 ~; 224 |; 27 &)
% ( 18 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 167 ( 0 sgn 157 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
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(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
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(f9,axiom,
! [X0,X1] :
( ( relation(X0)
& relation(X1) )
=> relation(relation_composition(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k5_relat_1) ).
fof(f13,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(f33,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(f34,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)],[f33]) ).
fof(f49,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(f50,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,[],[f49]) ).
fof(f51,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(f52,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(f53,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(flattening,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f58,plain,
! [X0,X1] :
( ( relation(relation_composition(X0,X1))
& function(relation_composition(X0,X1)) )
| ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1) ),
inference(flattening,[],[f57]) ).
fof(f66,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,[],[f34]) ).
fof(f67,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,[],[f66]) ).
fof(f80,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f81,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(ordered_pair(X1,X2),X0)
| apply(X0,X1) = X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f82,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(ordered_pair(X1,X2),X0)
| apply(X0,X1) != X2 ),
inference(cnf_transformation,[],[f50]) ).
fof(f85,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(ordered_pair(X2,X3),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(ordered_pair(X2,sK1(X0,X2)),X0)
| ~ in(X2,X1)
| relation_dom(X0) != X1 ),
inference(cnf_transformation,[],[f51]) ).
fof(f89,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(sK5(X0,X1,X3,X4),X4),X1)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f94,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(ordered_pair(X3,sK5(X0,X1,X3,X4)),X0)
| ~ in(ordered_pair(X3,X4),X2)
| relation_composition(X0,X1) != X2 ),
inference(cnf_transformation,[],[f52]) ).
fof(f96,plain,
! [X0,X1] :
( relation(relation_composition(X0,X1))
| ~ relation(X0)
| ~ relation(X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f102,plain,
! [X0,X1] :
( function(relation_composition(X0,X1))
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0)
| ~ function(X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f131,plain,
function(sK18),
inference(cnf_transformation,[],[f67]) ).
fof(f132,plain,
relation(sK18),
inference(cnf_transformation,[],[f67]) ).
fof(f133,plain,
in(sK16,relation_dom(relation_composition(sK18,sK17))),
inference(cnf_transformation,[],[f67]) ).
fof(f134,plain,
apply(relation_composition(sK18,sK17),sK16) != apply(sK17,apply(sK18,sK16)),
inference(cnf_transformation,[],[f67]) ).
fof(f135,plain,
function(sK17),
inference(cnf_transformation,[],[f67]) ).
fof(f136,plain,
relation(sK17),
inference(cnf_transformation,[],[f67]) ).
fof(f144,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) != X2 ),
inference(definition_unfolding,[],[f82,f89]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),X0)
| apply(X0,X1) = X2 ),
inference(definition_unfolding,[],[f81,f89]) ).
fof(f148,plain,
! [X2,X0,X1] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X2,sK1(X0,X2)),singleton(X2)),X0)
| ~ in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f86,f89]) ).
fof(f149,plain,
! [X2,X3,X0,X1] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,X1)
| relation_dom(X0) != X1 ),
inference(definition_unfolding,[],[f85,f89]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(X3,sK5(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f94,f89,f89]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(X2)
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),X2)
| relation_composition(X0,X1) != X2 ),
inference(definition_unfolding,[],[f93,f89,f89]) ).
fof(f159,plain,
! [X0,X1] :
( ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| in(unordered_pair(unordered_pair(X1,apply(X0,X1)),singleton(X1)),X0) ),
inference(equality_resolution,[],[f144]) ).
fof(f160,plain,
! [X2,X0] :
( ~ relation(X0)
| in(unordered_pair(unordered_pair(X2,sK1(X0,X2)),singleton(X2)),X0)
| ~ in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f148]) ).
fof(f161,plain,
! [X2,X3,X0] :
( ~ relation(X0)
| ~ in(unordered_pair(unordered_pair(X2,X3),singleton(X2)),X0)
| in(X2,relation_dom(X0)) ),
inference(equality_resolution,[],[f149]) ).
fof(f163,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(X3,sK5(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f151]) ).
fof(f164,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| ~ relation(relation_composition(X0,X1))
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(equality_resolution,[],[f152]) ).
fof(f226,plain,
! [X2,X3,X0] :
( ~ in(unordered_pair(singleton(X2),unordered_pair(X2,X3)),X0)
| ~ relation(X0)
| in(X2,relation_dom(X0)) ),
inference(forward_demodulation,[],[f161,f80]) ).
fof(f230,plain,
! [X2,X0] :
( ~ in(X2,relation_dom(X0))
| ~ relation(X0)
| in(unordered_pair(singleton(X2),unordered_pair(X2,sK1(X0,X2))),X0) ),
inference(forward_demodulation,[],[f160,f80]) ).
fof(f231,plain,
( ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK1(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(resolution,[],[f230,f133]) ).
fof(f235,definition,
( spl19_1
<=> in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK1(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_1])],[avatar_definition]) ).
fof(f237,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK1(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ spl19_1 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f239,definition,
( spl19_2
<=> relation(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_2])],[avatar_definition]) ).
fof(f240,plain,
( relation(relation_composition(sK18,sK17))
| ~ spl19_2 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f241,plain,
( ~ relation(relation_composition(sK18,sK17))
| spl19_2 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f242,plain,
( spl19_1
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f231,f239,f235]) ).
fof(f245,plain,
( ~ relation(sK18)
| ~ relation(sK17)
| spl19_2 ),
inference(resolution,[],[f241,f96]) ).
fof(f246,plain,
( ~ relation(sK17)
| spl19_2 ),
inference(forward_subsumption_resolution,[],[f245,f132]) ).
fof(f247,plain,
( $false
| spl19_2 ),
inference(forward_subsumption_resolution,[],[f246,f136]) ).
fof(f248,plain,
spl19_2,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f249,plain,
! [X0,X1] :
( ~ in(X1,relation_dom(X0))
| ~ function(X0)
| ~ relation(X0)
| in(unordered_pair(singleton(X1),unordered_pair(X1,apply(X0,X1))),X0) ),
inference(forward_demodulation,[],[f159,f80]) ).
fof(f250,plain,
( ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
inference(resolution,[],[f249,f133]) ).
fof(f253,plain,
( ~ function(relation_composition(sK18,sK17))
| in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ spl19_2 ),
inference(forward_subsumption_resolution,[],[f250,f240]) ).
fof(f255,definition,
( spl19_3
<=> in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_3])],[avatar_definition]) ).
fof(f257,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,apply(relation_composition(sK18,sK17),sK16))),relation_composition(sK18,sK17))
| ~ spl19_3 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f259,definition,
( spl19_4
<=> function(relation_composition(sK18,sK17)) ),
introduced(definition,[new_symbols(definition,[spl19_4])],[avatar_definition]) ).
fof(f260,plain,
( function(relation_composition(sK18,sK17))
| ~ spl19_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f261,plain,
( ~ function(relation_composition(sK18,sK17))
| spl19_4 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f262,plain,
( spl19_3
| ~ spl19_4
| ~ spl19_2 ),
inference(avatar_split_clause,[],[f253,f239,f259,f255]) ).
fof(f263,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ function(X0)
| ~ relation(X0)
| ~ in(X1,relation_dom(X0))
| apply(X0,X1) = X2 ),
inference(forward_demodulation,[],[f145,f80]) ).
fof(f264,plain,
! [X2,X0,X1] :
( ~ in(unordered_pair(singleton(X1),unordered_pair(X1,X2)),X0)
| ~ function(X0)
| ~ relation(X0)
| apply(X0,X1) = X2 ),
inference(forward_subsumption_resolution,[],[f263,f226]) ).
fof(f281,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(X3,sK5(X0,X1,X3,X4)),singleton(X3)),X0)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f163,f96]) ).
fof(f282,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1,X3,X4))),X0)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f281,f80]) ).
fof(f283,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| in(unordered_pair(singleton(X3),unordered_pair(X3,sK5(X0,X1,X3,X4))),X0)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f282,f80]) ).
fof(f297,plain,
( ~ relation(sK17)
| ~ function(sK18)
| ~ relation(sK18)
| ~ function(sK17)
| spl19_4 ),
inference(resolution,[],[f261,f102]) ).
fof(f298,plain,
( ~ function(sK18)
| ~ relation(sK18)
| ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f297,f136]) ).
fof(f299,plain,
( ~ relation(sK18)
| ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f298,f131]) ).
fof(f300,plain,
( ~ function(sK17)
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f299,f132]) ).
fof(f301,plain,
( $false
| spl19_4 ),
inference(forward_subsumption_resolution,[],[f300,f135]) ).
fof(f302,plain,
spl19_4,
inference(avatar_contradiction_clause,[],[f301]) ).
fof(f303,plain,
! [X3,X0,X1,X4] :
( ~ relation(X0)
| ~ relation(X1)
| in(unordered_pair(unordered_pair(sK5(X0,X1,X3,X4),X4),singleton(sK5(X0,X1,X3,X4))),X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_subsumption_resolution,[],[f164,f96]) ).
fof(f304,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(sK5(X0,X1,X3,X4),X4)),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f303,f80]) ).
fof(f305,plain,
! [X3,X0,X1,X4] :
( in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(X4,sK5(X0,X1,X3,X4))),X1)
| ~ relation(X0)
| ~ relation(X1)
| ~ in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),relation_composition(X0,X1)) ),
inference(forward_demodulation,[],[f304,f80]) ).
fof(f306,plain,
! [X3,X0,X1,X4] :
( ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X4)),relation_composition(X0,X1))
| in(unordered_pair(singleton(sK5(X0,X1,X3,X4)),unordered_pair(X4,sK5(X0,X1,X3,X4))),X1)
| ~ relation(X0)
| ~ relation(X1) ),
inference(forward_demodulation,[],[f305,f80]) ).
fof(f351,plain,
( in(unordered_pair(singleton(sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16))),unordered_pair(sK1(relation_composition(sK18,sK17),sK16),sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16)))),sK17)
| ~ relation(sK18)
| ~ relation(sK17)
| ~ spl19_1 ),
inference(resolution,[],[f237,f306]) ).
fof(f354,plain,
( ~ function(relation_composition(sK18,sK17))
| ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = sK1(relation_composition(sK18,sK17),sK16)
| ~ spl19_1 ),
inference(resolution,[],[f237,f264]) ).
fof(f359,plain,
( ~ relation(relation_composition(sK18,sK17))
| apply(relation_composition(sK18,sK17),sK16) = sK1(relation_composition(sK18,sK17),sK16)
| ~ spl19_1
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f354,f260]) ).
fof(f362,plain,
( in(unordered_pair(singleton(sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16))),unordered_pair(sK1(relation_composition(sK18,sK17),sK16),sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16)))),sK17)
| ~ relation(sK17)
| ~ spl19_1 ),
inference(forward_subsumption_resolution,[],[f351,f132]) ).
fof(f363,plain,
( apply(relation_composition(sK18,sK17),sK16) = sK1(relation_composition(sK18,sK17),sK16)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f359,f240]) ).
fof(f365,plain,
( in(unordered_pair(singleton(sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16))),unordered_pair(sK1(relation_composition(sK18,sK17),sK16),sK5(sK18,sK17,sK16,sK1(relation_composition(sK18,sK17),sK16)))),sK17)
| ~ spl19_1 ),
inference(forward_subsumption_resolution,[],[f362,f136]) ).
fof(f370,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)))),sK18)
| ~ relation(sK18)
| ~ relation(sK17)
| ~ spl19_3 ),
inference(resolution,[],[f257,f283]) ).
fof(f378,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)))),sK18)
| ~ relation(sK17)
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f370,f132]) ).
fof(f380,plain,
( in(unordered_pair(singleton(sK16),unordered_pair(sK16,sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)))),sK18)
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f378,f136]) ).
fof(f446,plain,
( ~ function(sK18)
| ~ relation(sK18)
| apply(sK18,sK16) = sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ spl19_3 ),
inference(resolution,[],[f380,f264]) ).
fof(f452,plain,
( ~ relation(sK18)
| apply(sK18,sK16) = sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f446,f131]) ).
fof(f454,plain,
( apply(sK18,sK16) = sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))
| ~ spl19_3 ),
inference(forward_subsumption_resolution,[],[f452,f132]) ).
fof(f1509,plain,
( in(unordered_pair(singleton(sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16))),unordered_pair(apply(relation_composition(sK18,sK17),sK16),sK5(sK18,sK17,sK16,apply(relation_composition(sK18,sK17),sK16)))),sK17)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_4 ),
inference(forward_demodulation,[],[f365,f363]) ).
fof(f1510,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(relation_composition(sK18,sK17),sK16),apply(sK18,sK16))),sK17)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_demodulation,[],[f1509,f454]) ).
fof(f1511,plain,
( in(unordered_pair(singleton(apply(sK18,sK16)),unordered_pair(apply(sK18,sK16),apply(relation_composition(sK18,sK17),sK16))),sK17)
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_demodulation,[],[f1510,f80]) ).
fof(f1513,plain,
( ~ function(sK17)
| ~ relation(sK17)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(resolution,[],[f1511,f264]) ).
fof(f1520,plain,
( ~ relation(sK17)
| apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f1513,f135]) ).
fof(f1522,plain,
( apply(relation_composition(sK18,sK17),sK16) = apply(sK17,apply(sK18,sK16))
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f1520,f136]) ).
fof(f1523,plain,
( $false
| ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(forward_subsumption_resolution,[],[f1522,f134]) ).
fof(f1524,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(avatar_contradiction_clause,[],[f1523]) ).
cnf(s1,plain,
( spl19_1
| ~ spl19_2 ),
inference(sat_conversion,[],[f242]) ).
cnf(s2,plain,
spl19_2,
inference(sat_conversion,[],[f248]) ).
cnf(s3,plain,
( ~ spl19_2
| spl19_3
| ~ spl19_4 ),
inference(sat_conversion,[],[f262]) ).
cnf(s4,plain,
spl19_4,
inference(sat_conversion,[],[f302]) ).
cnf(s12,plain,
( ~ spl19_1
| ~ spl19_2
| ~ spl19_3
| ~ spl19_4 ),
inference(sat_conversion,[],[f1524]) ).
cnf(s15,plain,
( ~ spl19_2
| spl19_3 ),
inference(rat,[],[s3,s4]) ).
cnf(s16,plain,
spl19_3,
inference(rat,[],[s15,s2]) ).
cnf(s17,plain,
~ spl19_1,
inference(rat,[],[s12,s4,s2,s16]) ).
cnf(s18,plain,
$false,
inference(rat,[],[s1,s2,s17]) ).
fof(f1525,plain,
$false,
inference(avatar_sat_refutation,[],[s18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU214+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.37 % Computer : n006.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
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 04:04:56 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.52 % (3566569)Will run a generic schedule for satisfiability detection.
% 0.16/0.52 % (3566577)dis+10_1_sil=32000:sp=arity:random_seed=1229721445:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.52 % (3566575)% WARNING: option uhcvi not known.
% 0.16/0.52 % (3566576)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=389090995:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.52 % (3566574)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1736681283_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.52 % (3566575)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2036566351:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.52 % (3566579)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=668913747:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.52 % (3566578)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1831145660:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.52 % (3566580)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=324351555:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % (3566577)Instruction limit reached!
% 0.16/0.52 % (3566577)------------------------------
% 0.16/0.52 % (3566577)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3566577)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3566577)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3566577)Termination reason: Instruction limit
% 0.16/0.52 % (3566577)Termination phase: Saturation
% 0.16/0.52 % (3566577)Time elapsed: 0.035 s
% 0.16/0.52 % (3566577)Peak memory usage: 12 MB
% 0.16/0.52 % (3566577)Instructions burned: 104 (million)
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % (3566588)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3592473113:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.16/0.52 % TRYING [1]
% 0.16/0.52 % TRYING [2]
% 0.16/0.52 % TRYING [3]
% 0.16/0.52 % TRYING [4]
% 0.16/0.52 % (3566575) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3566569-3566575"...
% 0.16/0.52 % (3566575)...printing done.
% 0.16/0.52 % (3566575)Refutation found. Thanks to Tanya!
% 0.16/0.52 % SZS status Theorem for theBenchmark
% 0.16/0.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.52 % (3566575)------------------------------
% 0.16/0.52 % (3566575)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.52 % (3566575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.52 % (3566575)CaDiCaL version: 2.1.3
% 0.16/0.52 % (3566575)Termination reason: Refutation
% 0.16/0.52 % (3566575)Time elapsed: 0.060 s
% 0.16/0.52 % (3566575)Peak memory usage: 13 MB
% 0.16/0.52 % (3566575)Instructions burned: 97 (million)
% 0.16/0.52 % (3566569)Success in time 0.096 s
% 0.16/0.52 % Vampire exiting
%------------------------------------------------------------------------------