%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:48:06 PM UTC 2026
% Result : Theorem 2.58s 1.30s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 14
% Syntax : Number of formulae : 110 ( 18 unt; 6 def)
% Number of atoms : 406 ( 35 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 498 ( 202 ~; 214 |; 53 &)
% ( 19 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 7 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 131 ( 0 sgn 120 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectedness_r1_ordinal1) ).
fof(f10,axiom,
! [X0] :
( relation(X0)
=> ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14_relat_2) ).
fof(f11,axiom,
! [X0,X1] :
( relation(X1)
=> ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(X2,X0)
& in(X3,X0) )
=> ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_wellord2) ).
fof(f14,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/sandbox/benchmark/theBenchmark.p',d6_relat_2) ).
fof(f17,axiom,
! [X0] : relation(inclusion_relation(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_wellord2) ).
fof(f42,axiom,
! [X0,X1] :
( ( ordinal(X0)
& ordinal(X1) )
=> ( ordinal_subset(X0,X1)
<=> subset(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_r1_ordinal1) ).
fof(f47,axiom,
! [X0,X1] :
( ordinal(X1)
=> ( in(X0,X1)
=> ordinal(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t23_ordinal1) ).
fof(f51,conjecture,
! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_wellord2) ).
fof(f52,negated_conjecture,
~ ! [X0] :
( ordinal(X0)
=> connected(inclusion_relation(X0)) ),
inference(negated_conjecture,[status(cth)],[f51]) ).
fof(f73,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f74,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f73]) ).
fof(f75,plain,
! [X0] :
( ( connected(X0)
<=> is_connected_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f76,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(ennf_transformation,[],[f11]) ).
fof(f77,plain,
! [X0,X1] :
( ( X1 = inclusion_relation(X0)
<=> ( relation_field(X1) = X0
& ! [X2,X3] :
( ( in(ordered_pair(X2,X3),X1)
<=> subset(X2,X3) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) ) )
| ~ relation(X1) ),
inference(flattening,[],[f76]) ).
fof(f79,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,[],[f14]) ).
fof(f82,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f83,plain,
! [X0,X1] :
( ( ordinal_subset(X0,X1)
<=> subset(X0,X1) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(flattening,[],[f82]) ).
fof(f87,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(ennf_transformation,[],[f47]) ).
fof(f88,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(flattening,[],[f87]) ).
fof(f93,plain,
? [X0] :
( ~ connected(inclusion_relation(X0))
& ordinal(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f98,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,[],[f75]) ).
fof(f99,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(nnf_transformation,[],[f77]) ).
fof(f100,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X2,X3] :
( ( ( in(ordered_pair(X2,X3),X1)
| ~ subset(X2,X3) )
& ( subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) ) )
| ~ in(X2,X0)
| ~ in(X3,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(flattening,[],[f99]) ).
fof(f101,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ? [X2,X3] :
( ( ~ subset(X2,X3)
| ~ in(ordered_pair(X2,X3),X1) )
& ( subset(X2,X3)
| in(ordered_pair(X2,X3),X1) )
& in(X2,X0)
& in(X3,X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(rectify,[],[f100]) ).
fof(f102,plain,
! [X0,X1] :
( ( ( X1 = inclusion_relation(X0)
| relation_field(X1) != X0
| ( ( ~ subset(sK0(X0,X1),sK1(X0,X1))
| ~ in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& ( subset(sK0(X0,X1),sK1(X0,X1))
| in(ordered_pair(sK0(X0,X1),sK1(X0,X1)),X1) )
& in(sK0(X0,X1),X0)
& in(sK1(X0,X1),X0) ) )
& ( ( relation_field(X1) = X0
& ! [X4,X5] :
( ( ( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5) )
& ( subset(X4,X5)
| ~ in(ordered_pair(X4,X5),X1) ) )
| ~ in(X4,X0)
| ~ in(X5,X0) ) )
| inclusion_relation(X0) != X1 ) )
| ~ relation(X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X2,sK0(X0,X1)),skolemize(X3,sK1(X0,X1))],[f101]) ).
fof(f103,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,[],[f79]) ).
fof(f104,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,[],[f103]) ).
fof(f105,plain,
! [X0] :
( ! [X1] :
( ( is_connected_in(X0,X1)
| ( in(sK2(X0,X1),X1)
& in(sK3(X0,X1),X1)
& sK2(X0,X1) != sK3(X0,X1)
& ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
& ~ in(ordered_pair(sK3(X0,X1),sK2(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,[sK2,sK3]),skolemize(X2,sK2(X0,X1)),skolemize(X3,sK3(X0,X1))],[f104]) ).
fof(f116,plain,
! [X0,X1] :
( ( ( ordinal_subset(X0,X1)
| ~ subset(X0,X1) )
& ( subset(X0,X1)
| ~ ordinal_subset(X0,X1) ) )
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(nnf_transformation,[],[f83]) ).
fof(f118,plain,
( ~ connected(inclusion_relation(sK14))
& ordinal(sK14) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(X0,sK14)],[f93]) ).
fof(f131,plain,
! [X0,X1] :
( ordinal_subset(X0,X1)
| ordinal_subset(X1,X0)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f74]) ).
fof(f133,plain,
! [X0] :
( ~ is_connected_in(X0,relation_field(X0))
| connected(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f135,plain,
! [X0,X1,X4,X5] :
( in(ordered_pair(X4,X5),X1)
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f136,plain,
! [X0,X1] :
( relation_field(X1) = X0
| inclusion_relation(X0) != X1
| ~ relation(X1) ),
inference(cnf_transformation,[],[f102]) ).
fof(f144,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK3(X0,X1),sK2(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f145,plain,
! [X0,X1] :
( ~ in(ordered_pair(sK2(X0,X1),sK3(X0,X1)),X0)
| is_connected_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f147,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| in(sK3(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f148,plain,
! [X0,X1] :
( is_connected_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f149,plain,
! [X0] : relation(inclusion_relation(X0)),
inference(cnf_transformation,[],[f17]) ).
fof(f186,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ ordinal_subset(X0,X1)
| ~ ordinal(X0)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f116]) ).
fof(f192,plain,
! [X0,X1] :
( ordinal(X0)
| ~ in(X0,X1)
| ~ ordinal(X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f197,plain,
ordinal(sK14),
inference(cnf_transformation,[],[f118]) ).
fof(f198,plain,
~ connected(inclusion_relation(sK14)),
inference(cnf_transformation,[],[f118]) ).
fof(f207,plain,
! [X0] :
( relation_field(inclusion_relation(X0)) = X0
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f136]) ).
fof(f208,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0)
| ~ relation(inclusion_relation(X0)) ),
inference(equality_resolution,[],[f135]) ).
fof(f219,plain,
! [X0] : relation_field(inclusion_relation(X0)) = X0,
inference(forward_subsumption_resolution,[],[f207,f149]) ).
fof(f220,plain,
! [X0] :
( ~ is_connected_in(inclusion_relation(X0),X0)
| connected(inclusion_relation(X0))
| ~ relation(inclusion_relation(X0)) ),
inference(superposition,[],[f133,f219]) ).
fof(f223,plain,
! [X0] :
( ~ is_connected_in(inclusion_relation(X0),X0)
| connected(inclusion_relation(X0)) ),
inference(forward_subsumption_resolution,[],[f220,f149]) ).
fof(f224,plain,
! [X0,X4,X5] :
( in(ordered_pair(X4,X5),inclusion_relation(X0))
| ~ subset(X4,X5)
| ~ in(X4,X0)
| ~ in(X5,X0) ),
inference(forward_subsumption_resolution,[],[f208,f149]) ).
fof(f290,plain,
! [X0] :
( in(sK3(inclusion_relation(X0),X0),X0)
| ~ relation(inclusion_relation(X0))
| connected(inclusion_relation(X0)) ),
inference(resolution,[],[f147,f223]) ).
fof(f292,plain,
! [X0] :
( connected(inclusion_relation(X0))
| in(sK3(inclusion_relation(X0),X0),X0) ),
inference(forward_subsumption_resolution,[],[f290,f149]) ).
fof(f296,plain,
! [X0] :
( in(sK2(inclusion_relation(X0),X0),X0)
| ~ relation(inclusion_relation(X0))
| connected(inclusion_relation(X0)) ),
inference(resolution,[],[f148,f223]) ).
fof(f298,plain,
! [X0] :
( connected(inclusion_relation(X0))
| in(sK2(inclusion_relation(X0),X0),X0) ),
inference(forward_subsumption_resolution,[],[f296,f149]) ).
fof(f337,plain,
! [X0,X1] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0))
| ~ subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
| ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(resolution,[],[f144,f224]) ).
fof(f338,plain,
! [X0,X1] :
( ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ subset(sK3(inclusion_relation(X0),X1),sK2(inclusion_relation(X0),X1))
| is_connected_in(inclusion_relation(X0),X1)
| ~ in(sK2(inclusion_relation(X0),X1),X0) ),
inference(forward_subsumption_resolution,[],[f337,f149]) ).
fof(f349,plain,
! [X0,X1] :
( is_connected_in(inclusion_relation(X0),X1)
| ~ relation(inclusion_relation(X0))
| ~ subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| ~ in(sK3(inclusion_relation(X0),X1),X0) ),
inference(resolution,[],[f145,f224]) ).
fof(f350,plain,
! [X0,X1] :
( ~ in(sK3(inclusion_relation(X0),X1),X0)
| ~ subset(sK2(inclusion_relation(X0),X1),sK3(inclusion_relation(X0),X1))
| ~ in(sK2(inclusion_relation(X0),X1),X0)
| is_connected_in(inclusion_relation(X0),X1) ),
inference(forward_subsumption_resolution,[],[f349,f149]) ).
fof(f378,plain,
in(sK3(inclusion_relation(sK14),sK14),sK14),
inference(resolution,[],[f292,f198]) ).
fof(f383,plain,
in(sK2(inclusion_relation(sK14),sK14),sK14),
inference(resolution,[],[f298,f198]) ).
fof(f469,plain,
( ~ subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| is_connected_in(inclusion_relation(sK14),sK14)
| ~ in(sK2(inclusion_relation(sK14),sK14),sK14) ),
inference(resolution,[],[f338,f378]) ).
fof(f470,plain,
( ~ subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| is_connected_in(inclusion_relation(sK14),sK14) ),
inference(forward_subsumption_resolution,[],[f469,f383]) ).
fof(f472,definition,
( spl15_6
<=> is_connected_in(inclusion_relation(sK14),sK14) ),
introduced(definition,[new_symbols(definition,[spl15_6])],[avatar_definition]) ).
fof(f474,plain,
( is_connected_in(inclusion_relation(sK14),sK14)
| ~ spl15_6 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f476,definition,
( spl15_7
<=> subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_7])],[avatar_definition]) ).
fof(f478,plain,
( ~ subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| spl15_7 ),
inference(avatar_component_clause,[],[f476]) ).
fof(f479,plain,
( spl15_6
| ~ spl15_7 ),
inference(avatar_split_clause,[],[f470,f476,f472]) ).
fof(f482,plain,
( ~ ordinal_subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| ~ ordinal(sK2(inclusion_relation(sK14),sK14))
| spl15_7 ),
inference(resolution,[],[f478,f186]) ).
fof(f484,definition,
( spl15_8
<=> ordinal(sK2(inclusion_relation(sK14),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_8])],[avatar_definition]) ).
fof(f485,plain,
( ordinal(sK2(inclusion_relation(sK14),sK14))
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f486,plain,
( ~ ordinal(sK2(inclusion_relation(sK14),sK14))
| spl15_8 ),
inference(avatar_component_clause,[],[f484]) ).
fof(f488,definition,
( spl15_9
<=> ordinal(sK3(inclusion_relation(sK14),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_9])],[avatar_definition]) ).
fof(f489,plain,
( ordinal(sK3(inclusion_relation(sK14),sK14))
| ~ spl15_9 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f490,plain,
( ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| spl15_9 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f492,definition,
( spl15_10
<=> ordinal_subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_10])],[avatar_definition]) ).
fof(f495,plain,
( ~ spl15_8
| ~ spl15_9
| ~ spl15_10
| spl15_7 ),
inference(avatar_split_clause,[],[f482,f476,f492,f488,f484]) ).
fof(f496,plain,
( ~ subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| ~ in(sK2(inclusion_relation(sK14),sK14),sK14)
| is_connected_in(inclusion_relation(sK14),sK14) ),
inference(resolution,[],[f350,f378]) ).
fof(f497,plain,
( ~ subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| is_connected_in(inclusion_relation(sK14),sK14) ),
inference(forward_subsumption_resolution,[],[f496,f383]) ).
fof(f499,definition,
( spl15_11
<=> subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14)) ),
introduced(definition,[new_symbols(definition,[spl15_11])],[avatar_definition]) ).
fof(f501,plain,
( ~ subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| spl15_11 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f502,plain,
( spl15_6
| ~ spl15_11 ),
inference(avatar_split_clause,[],[f497,f499,f472]) ).
fof(f503,plain,
( ! [X0] :
( ~ in(sK2(inclusion_relation(sK14),sK14),X0)
| ~ ordinal(X0) )
| spl15_8 ),
inference(resolution,[],[f486,f192]) ).
fof(f547,plain,
( ~ ordinal(sK14)
| spl15_8 ),
inference(resolution,[],[f503,f383]) ).
fof(f548,plain,
( $false
| spl15_8 ),
inference(forward_subsumption_resolution,[],[f547,f197]) ).
fof(f549,plain,
spl15_8,
inference(avatar_contradiction_clause,[],[f548]) ).
fof(f557,plain,
( ! [X0] :
( ~ in(sK3(inclusion_relation(sK14),sK14),X0)
| ~ ordinal(X0) )
| spl15_9 ),
inference(resolution,[],[f490,f192]) ).
fof(f575,plain,
( ~ ordinal(sK14)
| spl15_9 ),
inference(resolution,[],[f557,f378]) ).
fof(f576,plain,
( $false
| spl15_9 ),
inference(forward_subsumption_resolution,[],[f575,f197]) ).
fof(f577,plain,
spl15_9,
inference(avatar_contradiction_clause,[],[f576]) ).
fof(f594,plain,
( ~ ordinal_subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| ~ ordinal(sK2(inclusion_relation(sK14),sK14))
| ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| spl15_11 ),
inference(resolution,[],[f501,f186]) ).
fof(f595,plain,
( ~ ordinal_subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| ~ spl15_8
| spl15_11 ),
inference(forward_subsumption_resolution,[],[f594,f485]) ).
fof(f596,plain,
( ~ ordinal_subset(sK2(inclusion_relation(sK14),sK14),sK3(inclusion_relation(sK14),sK14))
| ~ spl15_8
| ~ spl15_9
| spl15_11 ),
inference(forward_subsumption_resolution,[],[f595,f489]) ).
fof(f607,plain,
( ordinal_subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| ~ ordinal(sK2(inclusion_relation(sK14),sK14))
| ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| ~ spl15_8
| ~ spl15_9
| spl15_11 ),
inference(resolution,[],[f596,f131]) ).
fof(f612,plain,
( ordinal_subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| ~ ordinal(sK3(inclusion_relation(sK14),sK14))
| ~ spl15_8
| ~ spl15_9
| spl15_11 ),
inference(forward_subsumption_resolution,[],[f607,f485]) ).
fof(f613,plain,
( ordinal_subset(sK3(inclusion_relation(sK14),sK14),sK2(inclusion_relation(sK14),sK14))
| ~ spl15_8
| ~ spl15_9
| spl15_11 ),
inference(forward_subsumption_resolution,[],[f612,f489]) ).
fof(f614,plain,
( spl15_10
| ~ spl15_8
| ~ spl15_9
| spl15_11 ),
inference(avatar_split_clause,[],[f613,f499,f488,f484,f492]) ).
fof(f620,plain,
( connected(inclusion_relation(sK14))
| ~ spl15_6 ),
inference(resolution,[],[f474,f223]) ).
fof(f623,plain,
( $false
| ~ spl15_6 ),
inference(forward_subsumption_resolution,[],[f620,f198]) ).
fof(f624,plain,
~ spl15_6,
inference(avatar_contradiction_clause,[],[f623]) ).
cnf(s4,plain,
( spl15_6
| ~ spl15_7 ),
inference(sat_conversion,[],[f479]) ).
cnf(s5,plain,
( spl15_7
| ~ spl15_8
| ~ spl15_9
| ~ spl15_10 ),
inference(sat_conversion,[],[f495]) ).
cnf(s6,plain,
( spl15_6
| ~ spl15_11 ),
inference(sat_conversion,[],[f502]) ).
cnf(s8,plain,
spl15_8,
inference(sat_conversion,[],[f549]) ).
cnf(s11,plain,
spl15_9,
inference(sat_conversion,[],[f577]) ).
cnf(s14,plain,
( ~ spl15_8
| ~ spl15_9
| spl15_10
| spl15_11 ),
inference(sat_conversion,[],[f614]) ).
cnf(s15,plain,
~ spl15_6,
inference(sat_conversion,[],[f624]) ).
cnf(s18,plain,
~ spl15_11,
inference(rat,[],[s6,s15]) ).
cnf(s19,plain,
spl15_10,
inference(rat,[],[s14,s8,s11,s18]) ).
cnf(s20,plain,
spl15_7,
inference(rat,[],[s5,s19,s11,s8]) ).
cnf(s21,plain,
$false,
inference(rat,[],[s4,s20,s15]) ).
fof(f625,plain,
$false,
inference(avatar_sat_refutation,[],[s21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU270+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n007.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Mon Sep 28 04:23:40 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 2.58/1.30 % (2021717)Detected formulas, will run a generic FOF schedule.
% 2.58/1.30 % (2021827)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2487437345:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.30 % (2021827)Instruction limit reached!
% 2.58/1.30 % (2021827)------------------------------
% 2.58/1.30 % (2021827)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.30 % (2021827)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.30 % (2021827)CaDiCaL version: 2.1.3
% 2.58/1.30 % (2021827)Termination reason: Instruction limit
% 2.58/1.30 % (2021827)Termination phase: Saturation
% 2.58/1.30 % (2021827)Time elapsed: 0.036 s
% 2.58/1.30 % (2021827)Peak memory usage: 88 MB
% 2.58/1.30 % (2021827)Instructions burned: 121 (million)
% 2.58/1.30 % (2021829)dis-21_1_sil=8000:lcm=predicate:random_seed=3392084186: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)
% 2.58/1.30 % (2021828)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1320823564:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.30 % (2021825)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=1241782920:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.30 % (2021823)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=3003899624:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.30 % (2021824)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=634366143:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.30 % (2021826)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1287545222:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.30 % (2021826)Refutation not found, incomplete strategy
% 2.58/1.30 % (2021826)------------------------------
% 2.58/1.30 % (2021826)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.30 % (2021826)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.30 % (2021826)CaDiCaL version: 2.1.3
% 2.58/1.30 % (2021826)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.30 % (2021826)Time elapsed: 0.001 s
% 2.58/1.30 % (2021826)Peak memory usage: 88 MB
% 2.58/1.30 % (2021826)Instructions burned: 1 (million)
% 2.58/1.30 % (2021828)First to succeed.
% 2.58/1.30 % (2021828)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2021717"
% 2.58/1.30 % (2021829)Instruction limit reached!
% 2.58/1.30 % (2021829)------------------------------
% 2.58/1.30 % (2021829)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.30 % (2021829)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.30 % (2021829)CaDiCaL version: 2.1.3
% 2.58/1.30 % (2021829)Termination reason: Instruction limit
% 2.58/1.30 % (2021829)Termination phase: Saturation
% 2.58/1.30 % (2021829)Time elapsed: 0.083 s
% 2.58/1.30 % (2021829)Peak memory usage: 89 MB
% 2.58/1.30 % (2021829)Instructions burned: 130 (million)
% 2.58/1.30 % (2021831)lrs+10_1_sil=8000:sp=occurrence:random_seed=1425284551:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.58/1.30 % (2021831)Instruction limit reached!
% 2.58/1.30 % (2021831)------------------------------
% 2.58/1.30 % (2021831)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.30 % (2021831)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.30 % (2021831)CaDiCaL version: 2.1.3
% 2.58/1.30 % (2021831)Termination reason: Instruction limit
% 2.58/1.30 % (2021831)Termination phase: Saturation
% 2.58/1.30 % (2021831)Time elapsed: 0.086 s
% 2.58/1.30 % (2021831)Peak memory usage: 91 MB
% 2.58/1.30 % (2021831)Instructions burned: 287 (million)
% 2.58/1.30 % (2021826)------------------------------
% 2.58/1.30 % (2021826)------------------------------
% 2.58/1.30 % (2021851)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2570815744:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.58/1.30 % (2021851)Refutation not found, incomplete strategy
% 2.58/1.30 % (2021851)------------------------------
% 2.58/1.30 % (2021851)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.30 % (2021851)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.30 % (2021851)CaDiCaL version: 2.1.3
% 2.58/1.30 % (2021851)Termination reason: Refutation not found, incomplete strategy
% 2.58/1.30 % (2021851)Time elapsed: 0.003 s
% 2.58/1.30 % (2021851)Peak memory usage: 89 MB
% 2.58/1.30 % (2021851)Instructions burned: 2 (million)
% 2.58/1.30 % (2021828)Refutation found. Thanks to Tanya!
% 2.58/1.30 % SZS status Theorem for theBenchmark
% 2.58/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.49 % (2021828)------------------------------
% 3.68/1.49 % (2021828)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.49 % (2021828)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.49 % (2021828)CaDiCaL version: 2.1.3
% 3.68/1.49 % (2021828)Termination reason: Refutation
% 3.68/1.49 % (2021828)Time elapsed: 0.021 s
% 3.68/1.49 % (2021828)Peak memory usage: 90 MB
% 3.68/1.49 % (2021828)Instructions burned: 23 (million)
% 3.68/1.49 % (2021828)------------------------------
% 3.68/1.49 % (2021828)------------------------------
% 3.68/1.49 % (2021717)Success in time 0.437 s
% 3.68/1.49 % Vampire exiting
%------------------------------------------------------------------------------