%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n013.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 12:52:34 PM UTC 2026
% Result : Theorem 0.15s 20.52s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 111 ( 13 unt; 7 def)
% Number of atoms : 466 ( 52 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 597 ( 242 ~; 284 |; 53 &)
% ( 13 <=>; 4 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 127 ( 0 sgn 113 !; 14 ?)
% 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(f6,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14_relat_2) ).
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(f9,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
~ ( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_wellord1) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( connected(X0)
<=> ! [X1,X2] :
~ ( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f45,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( is_connected_in(X0,X1)
<=> ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| X2 = X3
| in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X3,X2),X0) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f50,plain,
? [X0] :
( ( connected(X0)
<~> ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f57,plain,
! [X0] :
( ( ( connected(X0)
| ~ is_connected_in(X0,relation_field(X0)) )
& ( is_connected_in(X0,relation_field(X0))
| ~ connected(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f45]) ).
fof(f58,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) )
& ( ! [X2,X3] :
( ~ in(X2,X1)
| ~ in(X3,X1)
| X2 = X3
| in(ordered_pair(X2,X3),X0)
| in(ordered_pair(X3,X2),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f47]) ).
fof(f59,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ? [X2,X3] :
( in(X2,X1)
& in(X3,X1)
& X2 != X3
& ~ in(ordered_pair(X2,X3),X0)
& ~ in(ordered_pair(X3,X2),X0) ) )
& ( ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X5,X4),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ( in(sK0(X0,X1),X1)
& in(sK1(X0,X1),X1)
& sK0(X0,X1) != sK1(X0,X1)
& ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
& ~ in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0) ) )
& ( ! [X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X5,X4),X0) )
| ~ is_connected_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f59]) ).
fof(f62,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| connected(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f63,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X1,X2] :
( ~ in(X1,relation_field(X0))
| ~ in(X2,relation_field(X0))
| X1 = X2
| in(ordered_pair(X1,X2),X0)
| in(ordered_pair(X2,X1),X0) )
| connected(X0) )
& relation(X0) ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
? [X0] :
( ( ? [X1,X2] :
( in(X1,relation_field(X0))
& in(X2,relation_field(X0))
& X1 != X2
& ~ in(ordered_pair(X1,X2),X0)
& ~ in(ordered_pair(X2,X1),X0) )
| ~ connected(X0) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(X0))
| ~ in(X4,relation_field(X0))
| X3 = X4
| in(ordered_pair(X3,X4),X0)
| in(ordered_pair(X4,X3),X0) )
| connected(X0) )
& relation(X0) ),
inference(rectify,[],[f63]) ).
fof(f65,plain,
( ( ( in(sK4,relation_field(sK3))
& in(sK5,relation_field(sK3))
& sK4 != sK5
& ~ in(ordered_pair(sK4,sK5),sK3)
& ~ in(ordered_pair(sK5,sK4),sK3) )
| ~ connected(sK3) )
& ( ! [X3,X4] :
( ~ in(X3,relation_field(sK3))
| ~ in(X4,relation_field(sK3))
| X3 = X4
| in(ordered_pair(X3,X4),sK3)
| in(ordered_pair(X4,X3),sK3) )
| connected(sK3) )
& relation(sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f64]) ).
fof(f75,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f77,plain,
! [X0] :
( is_connected_in(X0,relation_field(X0))
| ~ connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f78,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f79,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f81,plain,
! [X0,X1,X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(ordered_pair(X4,X5),X0)
| in(ordered_pair(X5,X4),X0)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f82,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK1(X0,X1),sK0(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f83,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f84,plain,
! [X0,X1] :
( sK0(X0,X1) != sK1(X0,X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f85,plain,
! [X0,X1] :
( in(sK1(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f86,plain,
! [X0,X1] :
( in(sK0(X0,X1),X1)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f60]) ).
fof(f93,plain,
relation(sK3),
inference(cnf_transformation,[],[f65]) ).
fof(f94,plain,
! [X3,X4] :
( ~ in(X3,relation_field(sK3))
| ~ in(X4,relation_field(sK3))
| X3 = X4
| in(ordered_pair(X3,X4),sK3)
| in(ordered_pair(X4,X3),sK3)
| connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
( ~ in(ordered_pair(sK5,sK4),sK3)
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f96,plain,
( ~ in(ordered_pair(sK4,sK5),sK3)
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
( sK4 != sK5
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f98,plain,
( in(sK5,relation_field(sK3))
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
( in(sK4,relation_field(sK3))
| ~ connected(sK3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f115,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK0(X0,X1),sK1(X0,X1)),singleton(sK0(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f83,f79]) ).
fof(f116,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK1(X0,X1),sK0(X0,X1)),singleton(sK1(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f82,f79]) ).
fof(f117,plain,
! [X0,X1,X4,X5] :
( ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(unordered_pair(unordered_pair(X4,X5),singleton(X4)),X0)
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f81,f79,f79]) ).
fof(f119,plain,
( ~ in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3)
| ~ connected(sK3) ),
inference(definition_unfolding,[],[f96,f79]) ).
fof(f120,plain,
( ~ in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3)
| ~ connected(sK3) ),
inference(definition_unfolding,[],[f95,f79]) ).
fof(f121,plain,
! [X3,X4] :
( ~ in(X3,relation_field(sK3))
| ~ in(X4,relation_field(sK3))
| X3 = X4
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| connected(sK3) ),
inference(definition_unfolding,[],[f94,f79,f79]) ).
fof(f123,definition,
( spl11_1
<=> connected(sK3) ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f125,plain,
( connected(sK3)
| ~ spl11_1 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f127,definition,
( spl11_2
<=> ! [X4,X3] :
( ~ in(X3,relation_field(sK3))
| in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| X3 = X4
| ~ in(X4,relation_field(sK3)) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f128,plain,
( ! [X3,X4] :
( in(unordered_pair(unordered_pair(X4,X3),singleton(X4)),sK3)
| in(unordered_pair(unordered_pair(X3,X4),singleton(X3)),sK3)
| ~ in(X3,relation_field(sK3))
| X3 = X4
| ~ in(X4,relation_field(sK3)) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f127]) ).
fof(f129,plain,
( spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f121,f127,f123]) ).
fof(f131,definition,
( spl11_3
<=> in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_3])],[avatar_definition]) ).
fof(f133,plain,
( ~ in(unordered_pair(unordered_pair(sK5,sK4),singleton(sK5)),sK3)
| spl11_3 ),
inference(avatar_component_clause,[],[f131]) ).
fof(f134,plain,
( ~ spl11_1
| ~ spl11_3 ),
inference(avatar_split_clause,[],[f120,f131,f123]) ).
fof(f136,definition,
( spl11_4
<=> in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3) ),
introduced(definition,[new_symbols(definition,[spl11_4])],[avatar_definition]) ).
fof(f138,plain,
( ~ in(unordered_pair(unordered_pair(sK4,sK5),singleton(sK4)),sK3)
| spl11_4 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f139,plain,
( ~ spl11_1
| ~ spl11_4 ),
inference(avatar_split_clause,[],[f119,f136,f123]) ).
fof(f141,definition,
( spl11_5
<=> sK4 = sK5 ),
introduced(definition,[new_symbols(definition,[spl11_5])],[avatar_definition]) ).
fof(f143,plain,
( sK4 != sK5
| spl11_5 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f144,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(avatar_split_clause,[],[f97,f141,f123]) ).
fof(f146,definition,
( spl11_6
<=> in(sK5,relation_field(sK3)) ),
introduced(definition,[new_symbols(definition,[spl11_6])],[avatar_definition]) ).
fof(f148,plain,
( in(sK5,relation_field(sK3))
| ~ spl11_6 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f149,plain,
( ~ spl11_1
| spl11_6 ),
inference(avatar_split_clause,[],[f98,f146,f123]) ).
fof(f151,definition,
( spl11_7
<=> in(sK4,relation_field(sK3)) ),
introduced(definition,[new_symbols(definition,[spl11_7])],[avatar_definition]) ).
fof(f153,plain,
( in(sK4,relation_field(sK3))
| ~ spl11_7 ),
inference(avatar_component_clause,[],[f151]) ).
fof(f154,plain,
( ~ spl11_1
| spl11_7 ),
inference(avatar_split_clause,[],[f99,f151,f123]) ).
fof(f197,plain,
( ! [X0,X1] :
( in(unordered_pair(unordered_pair(X0,X1),singleton(X1)),sK3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| ~ in(X0,relation_field(sK3))
| X0 = X1
| ~ in(X1,relation_field(sK3)) )
| ~ spl11_2 ),
inference(superposition,[],[f128,f75]) ).
fof(f204,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK3)
| in(unordered_pair(unordered_pair(X0,X1),singleton(X0)),sK3)
| ~ in(X0,relation_field(sK3))
| X0 = X1
| ~ in(X1,relation_field(sK3)) )
| ~ spl11_2 ),
inference(forward_demodulation,[],[f197,f75]) ).
fof(f213,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),sK3)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),sK3)
| ~ in(X0,relation_field(sK3))
| X0 = X1
| ~ in(X1,relation_field(sK3)) )
| ~ spl11_2 ),
inference(forward_demodulation,[],[f204,f75]) ).
fof(f298,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK0(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f115,f75]) ).
fof(f307,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK1(X0,X1),sK0(X0,X1))),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f116,f75]) ).
fof(f308,plain,
! [X0,X1] :
( ~ in(unordered_pair(singleton(sK1(X0,X1)),unordered_pair(sK0(X0,X1),sK1(X0,X1))),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f307,f75]) ).
fof(f311,plain,
( ! [X0] :
( is_connected_in(sK3,X0)
| ~ relation(sK3)
| in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3)
| ~ in(sK0(sK3,X0),relation_field(sK3))
| sK0(sK3,X0) = sK1(sK3,X0)
| ~ in(sK1(sK3,X0),relation_field(sK3)) )
| ~ spl11_2 ),
inference(resolution,[],[f308,f213]) ).
fof(f312,plain,
( ! [X0] :
( in(unordered_pair(singleton(sK0(sK3,X0)),unordered_pair(sK0(sK3,X0),sK1(sK3,X0))),sK3)
| is_connected_in(sK3,X0)
| ~ in(sK0(sK3,X0),relation_field(sK3))
| sK0(sK3,X0) = sK1(sK3,X0)
| ~ in(sK1(sK3,X0),relation_field(sK3)) )
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f311,f93]) ).
fof(f313,plain,
! [X0,X1,X4,X5] :
( in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(unordered_pair(unordered_pair(X5,X4),singleton(X5)),X0)
| ~ is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f117,f75]) ).
fof(f314,plain,
! [X0,X1,X4,X5] :
( ~ is_connected_in(X0,X1)
| in(unordered_pair(singleton(X4),unordered_pair(X4,X5)),X0)
| ~ in(X4,X1)
| ~ in(X5,X1)
| X4 = X5
| in(unordered_pair(singleton(X5),unordered_pair(X5,X4)),X0)
| ~ relation(X0) ),
inference(forward_demodulation,[],[f313,f75]) ).
fof(f317,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(X0,relation_field(X2))
| ~ in(X1,relation_field(X2))
| X0 = X1
| in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| ~ relation(X2)
| ~ connected(X2)
| ~ relation(X2) ),
inference(resolution,[],[f314,f77]) ).
fof(f318,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X1,X0)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(X1,relation_field(X2))
| X0 = X1
| ~ in(X0,relation_field(X2))
| ~ relation(X2)
| ~ connected(X2) ),
inference(duplicate_literal_removal,[],[f317]) ).
fof(f423,plain,
! [X2,X0,X1] :
( in(unordered_pair(singleton(X1),unordered_pair(X0,X1)),X2)
| in(unordered_pair(singleton(X0),unordered_pair(X0,X1)),X2)
| ~ in(X1,relation_field(X2))
| X0 = X1
| ~ in(X0,relation_field(X2))
| ~ relation(X2)
| ~ connected(X2) ),
inference(superposition,[],[f318,f75]) ).
fof(f430,plain,
( ! [X0] :
( is_connected_in(sK3,X0)
| ~ in(sK0(sK3,X0),relation_field(sK3))
| sK0(sK3,X0) = sK1(sK3,X0)
| ~ in(sK1(sK3,X0),relation_field(sK3))
| is_connected_in(sK3,X0)
| ~ relation(sK3) )
| ~ spl11_2 ),
inference(resolution,[],[f312,f298]) ).
fof(f434,plain,
( ! [X0] :
( is_connected_in(sK3,X0)
| ~ in(sK0(sK3,X0),relation_field(sK3))
| sK0(sK3,X0) = sK1(sK3,X0)
| ~ in(sK1(sK3,X0),relation_field(sK3))
| ~ relation(sK3) )
| ~ spl11_2 ),
inference(duplicate_literal_removal,[],[f430]) ).
fof(f435,plain,
( ! [X0] :
( ~ in(sK1(sK3,X0),relation_field(sK3))
| ~ in(sK0(sK3,X0),relation_field(sK3))
| sK0(sK3,X0) = sK1(sK3,X0)
| is_connected_in(sK3,X0) )
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f434,f93]) ).
fof(f436,plain,
( ~ in(sK0(sK3,relation_field(sK3)),relation_field(sK3))
| sK0(sK3,relation_field(sK3)) = sK1(sK3,relation_field(sK3))
| is_connected_in(sK3,relation_field(sK3))
| is_connected_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_2 ),
inference(resolution,[],[f435,f85]) ).
fof(f437,plain,
( ~ in(sK0(sK3,relation_field(sK3)),relation_field(sK3))
| sK0(sK3,relation_field(sK3)) = sK1(sK3,relation_field(sK3))
| is_connected_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_2 ),
inference(duplicate_literal_removal,[],[f436]) ).
fof(f438,plain,
( sK0(sK3,relation_field(sK3)) = sK1(sK3,relation_field(sK3))
| is_connected_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f437,f86]) ).
fof(f439,plain,
( is_connected_in(sK3,relation_field(sK3))
| ~ relation(sK3)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f438,f84]) ).
fof(f440,plain,
( is_connected_in(sK3,relation_field(sK3))
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f439,f93]) ).
fof(f445,plain,
( connected(sK3)
| ~ relation(sK3)
| ~ spl11_2 ),
inference(resolution,[],[f440,f78]) ).
fof(f450,plain,
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK5,sK4)),sK3)
| spl11_3 ),
inference(forward_demodulation,[],[f133,f75]) ).
fof(f451,plain,
( ~ in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK3)
| spl11_4 ),
inference(forward_demodulation,[],[f138,f75]) ).
fof(f452,plain,
( connected(sK3)
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f445,f93]) ).
fof(f453,plain,
( ~ in(unordered_pair(singleton(sK5),unordered_pair(sK4,sK5)),sK3)
| spl11_3 ),
inference(forward_demodulation,[],[f450,f75]) ).
fof(f454,plain,
( spl11_1
| ~ spl11_2 ),
inference(avatar_split_clause,[],[f452,f127,f123]) ).
fof(f543,plain,
( in(unordered_pair(singleton(sK4),unordered_pair(sK4,sK5)),sK3)
| ~ in(sK5,relation_field(sK3))
| sK4 = sK5
| ~ in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ connected(sK3)
| spl11_3 ),
inference(resolution,[],[f423,f453]) ).
fof(f575,plain,
( ~ in(sK5,relation_field(sK3))
| sK4 = sK5
| ~ in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ connected(sK3)
| spl11_3
| spl11_4 ),
inference(forward_subsumption_resolution,[],[f543,f451]) ).
fof(f577,plain,
( sK4 = sK5
| ~ in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ connected(sK3)
| spl11_3
| spl11_4
| ~ spl11_6 ),
inference(forward_subsumption_resolution,[],[f575,f148]) ).
fof(f579,plain,
( ~ in(sK4,relation_field(sK3))
| ~ relation(sK3)
| ~ connected(sK3)
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6 ),
inference(forward_subsumption_resolution,[],[f577,f143]) ).
fof(f580,plain,
( ~ relation(sK3)
| ~ connected(sK3)
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| ~ spl11_7 ),
inference(forward_subsumption_resolution,[],[f579,f153]) ).
fof(f581,plain,
( ~ connected(sK3)
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| ~ spl11_7 ),
inference(forward_subsumption_resolution,[],[f580,f93]) ).
fof(f582,plain,
( $false
| ~ spl11_1
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| ~ spl11_7 ),
inference(forward_subsumption_resolution,[],[f581,f125]) ).
fof(f583,plain,
( ~ spl11_1
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| ~ spl11_7 ),
inference(avatar_contradiction_clause,[],[f582]) ).
cnf(s1,plain,
( spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f129]) ).
cnf(s2,plain,
( ~ spl11_1
| ~ spl11_3 ),
inference(sat_conversion,[],[f134]) ).
cnf(s3,plain,
( ~ spl11_1
| ~ spl11_4 ),
inference(sat_conversion,[],[f139]) ).
cnf(s4,plain,
( ~ spl11_1
| ~ spl11_5 ),
inference(sat_conversion,[],[f144]) ).
cnf(s5,plain,
( ~ spl11_1
| spl11_6 ),
inference(sat_conversion,[],[f149]) ).
cnf(s6,plain,
( ~ spl11_1
| spl11_7 ),
inference(sat_conversion,[],[f154]) ).
cnf(s18,plain,
( spl11_1
| ~ spl11_2 ),
inference(sat_conversion,[],[f454]) ).
cnf(s20,plain,
( ~ spl11_1
| spl11_3
| spl11_4
| spl11_5
| ~ spl11_6
| ~ spl11_7 ),
inference(sat_conversion,[],[f583]) ).
cnf(s21,plain,
spl11_1,
inference(rat,[],[s1,s18]) ).
cnf(s22,plain,
spl11_7,
inference(rat,[],[s6,s21]) ).
cnf(s23,plain,
spl11_6,
inference(rat,[],[s5,s21]) ).
cnf(s24,plain,
~ spl11_5,
inference(rat,[],[s4,s21]) ).
cnf(s25,plain,
~ spl11_4,
inference(rat,[],[s3,s21]) ).
cnf(s26,plain,
~ spl11_3,
inference(rat,[],[s2,s21]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s20,s22,s23,s24,s21,s25,s26]) ).
fof(f584,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU242+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/20.41 % Computer : n013.cluster.edu
% 0.10/20.41 % Model : x86_64 x86_64
% 0.10/20.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/20.41 % Memory : 8046.5625MB
% 0.10/20.41 % OS : Linux 6.8.0-71-generic
% 0.10/20.41 % CPULimit : 300
% 0.10/20.41 % WCLimit : 300
% 0.10/20.41 % DateTime : Mon Sep 28 04:16:31 UTC 2026
% 0.10/20.41 % CPUTime :
% 0.10/20.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/20.45 Running first-order model finding
% 0.10/20.45 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
% 0.15/20.52 % (796443)Will run a generic schedule for satisfiability detection.
% 0.15/20.52 % (796449)% WARNING: option uhcvi not known.
% 0.15/20.52 % (796449)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2802593392:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/20.52 % (796450)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2510730452:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/20.52 % (796448)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2856569809_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/20.52 % (796454)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1051379995:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/20.52 % (796451)dis+10_1_sil=32000:sp=arity:random_seed=4173631043:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/20.52 % (796452)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2636794285:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/20.52 % (796453)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3493048938:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/20.52 % TRYING [1]
% 0.15/20.52 % TRYING [2]
% 0.15/20.52 % TRYING [3]
% 0.15/20.52 % (796451) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-796443-796451"...
% 0.15/20.52 % (796454) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-796443-796454"...
% 0.15/20.52 % (796452) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-796443-796452"...
% 0.15/20.52 % (796451)...printing done.
% 0.15/20.52 % (796454)...printing done.
% 0.15/20.52 % (796451)Refutation found. Thanks to Tanya!
% 0.15/20.52 % SZS status Theorem for theBenchmark
% 0.15/20.52 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/20.52 % (796451)------------------------------
% 0.15/20.52 % (796451)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/20.52 % (796451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/20.52 % (796451)CaDiCaL version: 2.1.3
% 0.15/20.52 % (796451)Termination reason: Refutation
% 0.15/20.52 % (796451)Time elapsed: 0.021 s
% 0.15/20.52 % (796451)Peak memory usage: 12 MB
% 0.15/20.52 % (796451)Instructions burned: 32 (million)
% 0.15/20.52 % (796443)Success in time 0.061 s
% 0.15/20.52 % Vampire exiting
%------------------------------------------------------------------------------