%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU388+2 : 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 : n004.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 12:48:40 PM UTC 2026
% Result : Theorem 6.63s 1.95s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 14
% Syntax : Number of formulae : 110 ( 20 unt; 11 def)
% Number of atoms : 434 ( 21 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 555 ( 231 ~; 263 |; 36 &)
% ( 16 <=>; 7 =>; 0 <=; 2 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 19 ( 17 usr; 12 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn 66 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f146,axiom,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_yellow19) ).
fof(f458,axiom,
! [X0,X1,X2] :
( ( ~ empty_carrier(X1)
& topological_space(X1)
& top_str(X1)
& element(X2,the_carrier(X1)) )
=> ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fraenkel_a_2_0_yellow19) ).
fof(f791,conjecture,
! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_yellow19) ).
fof(f792,negated_conjecture,
~ ! [X0] :
( ( ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( in(X2,neighborhood_system(X0,X1))
<=> point_neighbourhood(X2,X0,X1) ) ) ),
inference(negated_conjecture,[status(cth)],[f791]) ).
fof(f1184,plain,
! [X0] :
( ! [X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f146]) ).
fof(f1185,plain,
! [X0] :
( ! [X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0)) )
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(flattening,[],[f1184]) ).
fof(f1534,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(ennf_transformation,[],[f458]) ).
fof(f1535,plain,
! [X0,X1,X2] :
( ( in(X0,a_2_0_yellow19(X1,X2))
<=> ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(flattening,[],[f1534]) ).
fof(f1940,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,neighborhood_system(X0,X1))
<~> point_neighbourhood(X2,X0,X1) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(ennf_transformation,[],[f792]) ).
fof(f1941,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( in(X2,neighborhood_system(X0,X1))
<~> point_neighbourhood(X2,X0,X1) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(flattening,[],[f1940]) ).
fof(f2411,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ? [X3] :
( point_neighbourhood(X3,X1,X2)
& X0 = X3 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(nnf_transformation,[],[f1535]) ).
fof(f2412,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ? [X4] :
( point_neighbourhood(X4,X1,X2)
& X0 = X4 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(rectify,[],[f2411]) ).
fof(f2413,plain,
! [X0,X1,X2] :
( ( ( in(X0,a_2_0_yellow19(X1,X2))
| ! [X3] :
( ~ point_neighbourhood(X3,X1,X2)
| X0 != X3 ) )
& ( ( point_neighbourhood(sK186(X0,X1,X2),X1,X2)
& sK186(X0,X1,X2) = X0 )
| ~ in(X0,a_2_0_yellow19(X1,X2)) ) )
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(X4,sK186(X0,X1,X2))],[f2412]) ).
fof(f2786,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( ~ point_neighbourhood(X2,X0,X1)
| ~ in(X2,neighborhood_system(X0,X1)) )
& ( point_neighbourhood(X2,X0,X1)
| in(X2,neighborhood_system(X0,X1)) ) )
& element(X1,the_carrier(X0)) )
& ~ empty_carrier(X0)
& topological_space(X0)
& top_str(X0) ),
inference(nnf_transformation,[],[f1941]) ).
fof(f2787,plain,
( ( ~ point_neighbourhood(sK562,sK560,sK561)
| ~ in(sK562,neighborhood_system(sK560,sK561)) )
& ( point_neighbourhood(sK562,sK560,sK561)
| in(sK562,neighborhood_system(sK560,sK561)) )
& element(sK561,the_carrier(sK560))
& ~ empty_carrier(sK560)
& topological_space(sK560)
& top_str(sK560) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK560,sK561,sK562]),skolemize(X0,sK560),skolemize(X1,sK561),skolemize(X2,sK562)],[f2786]) ).
fof(f3365,plain,
! [X0,X1] :
( neighborhood_system(X0,X1) = a_2_0_yellow19(X0,X1)
| ~ element(X1,the_carrier(X0))
| empty_carrier(X0)
| ~ topological_space(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1185]) ).
fof(f4231,plain,
! [X2,X0,X1] :
( sK186(X0,X1,X2) = X0
| ~ in(X0,a_2_0_yellow19(X1,X2))
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f4232,plain,
! [X2,X0,X1] :
( point_neighbourhood(sK186(X0,X1,X2),X1,X2)
| ~ in(X0,a_2_0_yellow19(X1,X2))
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f4233,plain,
! [X2,X3,X0,X1] :
( in(X0,a_2_0_yellow19(X1,X2))
| ~ point_neighbourhood(X3,X1,X2)
| X0 != X3
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(cnf_transformation,[],[f2413]) ).
fof(f5681,plain,
top_str(sK560),
inference(cnf_transformation,[],[f2787]) ).
fof(f5682,plain,
topological_space(sK560),
inference(cnf_transformation,[],[f2787]) ).
fof(f5683,plain,
~ empty_carrier(sK560),
inference(cnf_transformation,[],[f2787]) ).
fof(f5684,plain,
element(sK561,the_carrier(sK560)),
inference(cnf_transformation,[],[f2787]) ).
fof(f5685,plain,
( point_neighbourhood(sK562,sK560,sK561)
| in(sK562,neighborhood_system(sK560,sK561)) ),
inference(cnf_transformation,[],[f2787]) ).
fof(f5686,plain,
( ~ point_neighbourhood(sK562,sK560,sK561)
| ~ in(sK562,neighborhood_system(sK560,sK561)) ),
inference(cnf_transformation,[],[f2787]) ).
fof(f7133,plain,
! [X2,X3,X1] :
( in(X3,a_2_0_yellow19(X1,X2))
| ~ point_neighbourhood(X3,X1,X2)
| empty_carrier(X1)
| ~ topological_space(X1)
| ~ top_str(X1)
| ~ element(X2,the_carrier(X1)) ),
inference(equality_resolution,[],[f4233]) ).
fof(f7980,definition,
( spl725_1
<=> in(sK562,neighborhood_system(sK560,sK561)) ),
introduced(definition,[new_symbols(definition,[spl725_1])],[avatar_definition]) ).
fof(f7981,plain,
( ~ in(sK562,neighborhood_system(sK560,sK561))
| spl725_1 ),
inference(avatar_component_clause,[],[f7980]) ).
fof(f7982,plain,
( in(sK562,neighborhood_system(sK560,sK561))
| ~ spl725_1 ),
inference(avatar_component_clause,[],[f7980]) ).
fof(f7984,definition,
( spl725_2
<=> point_neighbourhood(sK562,sK560,sK561) ),
introduced(definition,[new_symbols(definition,[spl725_2])],[avatar_definition]) ).
fof(f7985,plain,
( ~ point_neighbourhood(sK562,sK560,sK561)
| spl725_2 ),
inference(avatar_component_clause,[],[f7984]) ).
fof(f7986,plain,
( point_neighbourhood(sK562,sK560,sK561)
| ~ spl725_2 ),
inference(avatar_component_clause,[],[f7984]) ).
fof(f7987,plain,
( spl725_1
| spl725_2 ),
inference(avatar_split_clause,[],[f5685,f7984,f7980]) ).
fof(f7988,plain,
( ~ in(sK562,neighborhood_system(sK560,sK561))
| ~ spl725_2 ),
inference(backward_subsumption_resolution,[],[f5686,f7986]) ).
fof(f7990,definition,
( spl725_3
<=> empty_carrier(sK560) ),
introduced(definition,[new_symbols(definition,[spl725_3])],[avatar_definition]) ).
fof(f7992,plain,
( ~ empty_carrier(sK560)
| spl725_3 ),
inference(avatar_component_clause,[],[f7990]) ).
fof(f7993,plain,
~ spl725_3,
inference(avatar_split_clause,[],[f5683,f7990]) ).
fof(f7994,plain,
( ~ spl725_1
| ~ spl725_2 ),
inference(avatar_split_clause,[],[f7988,f7984,f7980]) ).
fof(f7995,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| empty_carrier(sK560)
| ~ topological_space(sK560)
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560))
| ~ spl725_2 ),
inference(resolution,[],[f7986,f7133]) ).
fof(f8004,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| ~ topological_space(sK560)
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560))
| ~ spl725_2
| spl725_3 ),
inference(forward_subsumption_resolution,[],[f7995,f7992]) ).
fof(f8009,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560))
| ~ spl725_2
| spl725_3 ),
inference(forward_subsumption_resolution,[],[f8004,f5682]) ).
fof(f8014,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| ~ element(sK561,the_carrier(sK560))
| ~ spl725_2
| spl725_3 ),
inference(forward_subsumption_resolution,[],[f8009,f5681]) ).
fof(f8019,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| ~ spl725_2
| spl725_3 ),
inference(forward_subsumption_resolution,[],[f8014,f5684]) ).
fof(f8023,definition,
( spl725_4
<=> topological_space(sK560) ),
introduced(definition,[new_symbols(definition,[spl725_4])],[avatar_definition]) ).
fof(f8025,plain,
( topological_space(sK560)
| ~ spl725_4 ),
inference(avatar_component_clause,[],[f8023]) ).
fof(f8026,plain,
spl725_4,
inference(avatar_split_clause,[],[f5682,f8023]) ).
fof(f8028,definition,
( spl725_5
<=> top_str(sK560) ),
introduced(definition,[new_symbols(definition,[spl725_5])],[avatar_definition]) ).
fof(f8030,plain,
( top_str(sK560)
| ~ spl725_5 ),
inference(avatar_component_clause,[],[f8028]) ).
fof(f8031,plain,
spl725_5,
inference(avatar_split_clause,[],[f5681,f8028]) ).
fof(f9023,definition,
( spl725_6
<=> element(sK561,the_carrier(sK560)) ),
introduced(definition,[new_symbols(definition,[spl725_6])],[avatar_definition]) ).
fof(f9025,plain,
( element(sK561,the_carrier(sK560))
| ~ spl725_6 ),
inference(avatar_component_clause,[],[f9023]) ).
fof(f9026,plain,
spl725_6,
inference(avatar_split_clause,[],[f5684,f9023]) ).
fof(f9065,plain,
( neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561)
| empty_carrier(sK560)
| ~ topological_space(sK560)
| ~ top_str(sK560)
| ~ spl725_6 ),
inference(resolution,[],[f9025,f3365]) ).
fof(f9163,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| empty_carrier(sK560)
| ~ topological_space(sK560)
| ~ top_str(sK560) )
| ~ spl725_6 ),
inference(resolution,[],[f9025,f4232]) ).
fof(f9330,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| ~ topological_space(sK560)
| ~ top_str(sK560) )
| spl725_3
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9163,f7992]) ).
fof(f9373,plain,
( neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561)
| ~ topological_space(sK560)
| ~ top_str(sK560)
| spl725_3
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9065,f7992]) ).
fof(f9427,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| ~ top_str(sK560) )
| spl725_3
| ~ spl725_4
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9330,f8025]) ).
fof(f9434,plain,
( neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561)
| ~ top_str(sK560)
| spl725_3
| ~ spl725_4
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9373,f8025]) ).
fof(f9448,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561)) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9427,f8030]) ).
fof(f9454,plain,
( neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561)
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6 ),
inference(forward_subsumption_resolution,[],[f9434,f8030]) ).
fof(f9789,definition,
( spl725_8
<=> in(sK562,a_2_0_yellow19(sK560,sK561)) ),
introduced(definition,[new_symbols(definition,[spl725_8])],[avatar_definition]) ).
fof(f9791,plain,
( in(sK562,a_2_0_yellow19(sK560,sK561))
| ~ spl725_8 ),
inference(avatar_component_clause,[],[f9789]) ).
fof(f9792,plain,
( spl725_8
| ~ spl725_2
| spl725_3 ),
inference(avatar_split_clause,[],[f8019,f7990,f7984,f9789]) ).
fof(f10053,definition,
( spl725_11
<=> ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561)) ) ),
introduced(definition,[new_symbols(definition,[spl725_11])],[avatar_definition]) ).
fof(f10054,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,a_2_0_yellow19(sK560,sK561)) )
| ~ spl725_11 ),
inference(avatar_component_clause,[],[f10053]) ).
fof(f10055,plain,
( spl725_11
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6 ),
inference(avatar_split_clause,[],[f9448,f9023,f8028,f8023,f7990,f10053]) ).
fof(f10056,plain,
( ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_11 ),
inference(forward_demodulation,[],[f10054,f9454]) ).
fof(f10058,definition,
( spl725_12
<=> neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561) ),
introduced(definition,[new_symbols(definition,[spl725_12])],[avatar_definition]) ).
fof(f10060,plain,
( neighborhood_system(sK560,sK561) = a_2_0_yellow19(sK560,sK561)
| ~ spl725_12 ),
inference(avatar_component_clause,[],[f10058]) ).
fof(f10061,plain,
( spl725_12
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6 ),
inference(avatar_split_clause,[],[f9454,f9023,f8028,f8023,f7990,f10058]) ).
fof(f10074,definition,
( spl725_13
<=> ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561) ) ),
introduced(definition,[new_symbols(definition,[spl725_13])],[avatar_definition]) ).
fof(f10075,plain,
( ! [X0] :
( point_neighbourhood(sK186(X0,sK560,sK561),sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561)) )
| ~ spl725_13 ),
inference(avatar_component_clause,[],[f10074]) ).
fof(f10076,plain,
( spl725_13
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_11 ),
inference(avatar_split_clause,[],[f10056,f10053,f9023,f8028,f8023,f7990,f10074]) ).
fof(f10082,plain,
( ! [X0] :
( point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561))
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| empty_carrier(sK560)
| ~ topological_space(sK560)
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560)) )
| ~ spl725_13 ),
inference(superposition,[],[f10075,f4231]) ).
fof(f10083,plain,
( ! [X0] :
( point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561))
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| ~ topological_space(sK560)
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560)) )
| spl725_3
| ~ spl725_13 ),
inference(forward_subsumption_resolution,[],[f10082,f7992]) ).
fof(f10089,plain,
( ! [X0] :
( point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561))
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| ~ top_str(sK560)
| ~ element(sK561,the_carrier(sK560)) )
| spl725_3
| ~ spl725_4
| ~ spl725_13 ),
inference(forward_subsumption_resolution,[],[f10083,f8025]) ).
fof(f10095,plain,
( ! [X0] :
( point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561))
| ~ in(X0,a_2_0_yellow19(sK560,sK561))
| ~ element(sK561,the_carrier(sK560)) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_13 ),
inference(forward_subsumption_resolution,[],[f10089,f8030]) ).
fof(f10101,plain,
( ! [X0] :
( point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561))
| ~ in(X0,a_2_0_yellow19(sK560,sK561)) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_13 ),
inference(forward_subsumption_resolution,[],[f10095,f9025]) ).
fof(f10107,plain,
( ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(X0,sK560,sK561)
| ~ in(X0,neighborhood_system(sK560,sK561)) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_12
| ~ spl725_13 ),
inference(forward_demodulation,[],[f10101,f10060]) ).
fof(f10108,plain,
( ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(X0,sK560,sK561) )
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_12
| ~ spl725_13 ),
inference(duplicate_literal_removal,[],[f10107]) ).
fof(f10152,definition,
( spl725_15
<=> ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(X0,sK560,sK561) ) ),
introduced(definition,[new_symbols(definition,[spl725_15])],[avatar_definition]) ).
fof(f10153,plain,
( ! [X0] :
( ~ in(X0,neighborhood_system(sK560,sK561))
| point_neighbourhood(X0,sK560,sK561) )
| ~ spl725_15 ),
inference(avatar_component_clause,[],[f10152]) ).
fof(f10154,plain,
( spl725_15
| spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_12
| ~ spl725_13 ),
inference(avatar_split_clause,[],[f10108,f10074,f10058,f9023,f8028,f8023,f7990,f10152]) ).
fof(f10337,plain,
( point_neighbourhood(sK562,sK560,sK561)
| ~ spl725_1
| ~ spl725_15 ),
inference(resolution,[],[f10153,f7982]) ).
fof(f10339,plain,
( $false
| ~ spl725_1
| spl725_2
| ~ spl725_15 ),
inference(forward_subsumption_resolution,[],[f10337,f7985]) ).
fof(f10340,plain,
( ~ spl725_1
| spl725_2
| ~ spl725_15 ),
inference(avatar_contradiction_clause,[],[f10339]) ).
fof(f10352,plain,
( in(sK562,neighborhood_system(sK560,sK561))
| ~ spl725_8
| ~ spl725_12 ),
inference(forward_demodulation,[],[f9791,f10060]) ).
fof(f10355,plain,
( $false
| spl725_1
| ~ spl725_8
| ~ spl725_12 ),
inference(forward_subsumption_resolution,[],[f10352,f7981]) ).
fof(f10356,plain,
( spl725_1
| ~ spl725_8
| ~ spl725_12 ),
inference(avatar_contradiction_clause,[],[f10355]) ).
cnf(s1,plain,
( spl725_1
| spl725_2 ),
inference(sat_conversion,[],[f7987]) ).
cnf(s2,plain,
~ spl725_3,
inference(sat_conversion,[],[f7993]) ).
cnf(s3,plain,
( ~ spl725_1
| ~ spl725_2 ),
inference(sat_conversion,[],[f7994]) ).
cnf(s4,plain,
spl725_4,
inference(sat_conversion,[],[f8026]) ).
cnf(s5,plain,
spl725_5,
inference(sat_conversion,[],[f8031]) ).
cnf(s6,plain,
spl725_6,
inference(sat_conversion,[],[f9026]) ).
cnf(s8,plain,
( ~ spl725_2
| spl725_3
| spl725_8 ),
inference(sat_conversion,[],[f9792]) ).
cnf(s11,plain,
( spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| spl725_11 ),
inference(sat_conversion,[],[f10055]) ).
cnf(s12,plain,
( spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| spl725_12 ),
inference(sat_conversion,[],[f10061]) ).
cnf(s13,plain,
( spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_11
| spl725_13 ),
inference(sat_conversion,[],[f10076]) ).
cnf(s15,plain,
( spl725_3
| ~ spl725_4
| ~ spl725_5
| ~ spl725_6
| ~ spl725_12
| ~ spl725_13
| spl725_15 ),
inference(sat_conversion,[],[f10154]) ).
cnf(s16,plain,
( ~ spl725_1
| spl725_2
| ~ spl725_15 ),
inference(sat_conversion,[],[f10340]) ).
cnf(s17,plain,
( spl725_1
| ~ spl725_8
| ~ spl725_12 ),
inference(sat_conversion,[],[f10356]) ).
cnf(s20,plain,
spl725_12,
inference(rat,[],[s12,s4,s6,s5,s2]) ).
cnf(s21,plain,
spl725_11,
inference(rat,[],[s11,s4,s6,s5,s2]) ).
cnf(s23,plain,
spl725_13,
inference(rat,[],[s13,s2,s4,s6,s5,s21]) ).
cnf(s24,plain,
spl725_15,
inference(rat,[],[s15,s20,s2,s4,s6,s5,s23]) ).
cnf(s25,plain,
spl725_1,
inference(rat,[],[s8,s1,s17,s2,s20]) ).
cnf(s26,plain,
spl725_2,
inference(rat,[],[s16,s24,s25]) ).
cnf(s27,plain,
$false,
inference(rat,[],[s3,s26,s25]) ).
fof(f10363,plain,
$false,
inference(avatar_sat_refutation,[],[s27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU388+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.37 % Computer : n004.cluster.edu
% 0.13/0.37 % Model : x86_64 x86_64
% 0.13/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.37 % Memory : 8046.5625MB
% 0.13/0.37 % OS : Linux 6.8.0-71-generic
% 0.13/0.37 % CPULimit : 300
% 0.13/0.37 % WCLimit : 300
% 0.13/0.37 % DateTime : Mon Sep 28 05:03:37 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.41 Running first-order theorem proving
% 0.13/0.41 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
% 6.63/1.95 % (4165211)Detected formulas, will run a generic FOF schedule.
% 6.63/1.95 % (4165218)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=3610311190:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 6.63/1.95 % (4165220)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=925085596:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 6.63/1.95 % (4165219)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=534892223:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 6.63/1.95 % (4165217)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=2401100295:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 6.63/1.95 % (4165216)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=4175381372:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 6.63/1.95 % (4165222)dis-21_1_sil=8000:lcm=predicate:random_seed=1027741151: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)
% 6.63/1.95 % (4165221)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3995802081:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 6.63/1.95 % (4165219)Instruction limit reached!
% 6.63/1.95 % (4165219)------------------------------
% 6.63/1.95 % (4165219)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165219)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165219)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165219)Termination reason: Instruction limit
% 6.63/1.95 % (4165219)Termination phase: Blocked clause elimination
% 6.63/1.95 % (4165219)Time elapsed: 0.060 s
% 6.63/1.95 % (4165219)Peak memory usage: 90 MB
% 6.63/1.95 % (4165219)Instructions burned: 110 (million)
% 6.63/1.95 % (4165222)Instruction limit reached!
% 6.63/1.95 % (4165222)------------------------------
% 6.63/1.95 % (4165222)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165222)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165222)Termination reason: Instruction limit
% 6.63/1.95 % (4165222)Termination phase: Saturation
% 6.63/1.95 % (4165222)Time elapsed: 0.065 s
% 6.63/1.95 % (4165222)Peak memory usage: 92 MB
% 6.63/1.95 % (4165222)Instructions burned: 130 (million)
% 6.63/1.95 % (4165220)Instruction limit reached!
% 6.63/1.95 % (4165220)------------------------------
% 6.63/1.95 % (4165220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165220)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165220)Termination reason: Instruction limit
% 6.63/1.95 % (4165220)Termination phase: Saturation
% 6.63/1.95 % (4165220)Time elapsed: 0.069 s
% 6.63/1.95 % (4165220)Peak memory usage: 92 MB
% 6.63/1.95 % (4165220)Instructions burned: 119 (million)
% 6.63/1.95 % (4165221)Instruction limit reached!
% 6.63/1.95 % (4165221)------------------------------
% 6.63/1.95 % (4165221)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165221)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165221)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165221)Termination reason: Instruction limit
% 6.63/1.95 % (4165221)Termination phase: Saturation
% 6.63/1.95 % (4165221)Time elapsed: 0.079 s
% 6.63/1.95 % (4165221)Peak memory usage: 92 MB
% 6.63/1.95 % (4165221)Instructions burned: 140 (million)
% 6.63/1.95 % (4165231)lrs+10_1_sil=32000:urr=on:br=off:random_seed=51094989:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 6.63/1.95 % (4165230)lrs+10_1_sil=8000:sp=occurrence:random_seed=1026654923:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 6.63/1.95 % (4165231)Refutation not found, incomplete strategy
% 6.63/1.95 % (4165231)------------------------------
% 6.63/1.95 % (4165231)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165231)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165231)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165231)Termination reason: Refutation not found, incomplete strategy
% 6.63/1.95 % (4165231)Time elapsed: 0.011 s
% 6.63/1.95 % (4165231)Peak memory usage: 90 MB
% 6.63/1.95 % (4165231)Instructions burned: 15 (million)
% 6.63/1.95 % (4165232)lrs+1011_1_sil=32000:sp=occurrence:random_seed=2811597892:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 6.63/1.95 % (4165233)dis+10_5:1_slsqr=1,4:sil=8000:fde=unused:erd=off:urr=full:fd=off:s2agt=8:br=off:slsq=on:random_seed=2400452802:s2a=on:i=248:s2at=1.23:gtg=position_2997 on theBenchmark for (2997ds/248Mi)
% 6.63/1.95 % (4165230)Instruction limit reached!
% 6.63/1.95 % (4165230)------------------------------
% 6.63/1.95 % (4165230)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165230)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165230)Termination reason: Instruction limit
% 6.63/1.95 % (4165230)Termination phase: Saturation
% 6.63/1.95 % (4165230)Time elapsed: 0.172 s
% 6.63/1.95 % (4165230)Peak memory usage: 95 MB
% 6.63/1.95 % (4165230)Instructions burned: 285 (million)
% 6.63/1.95 % (4165233)Instruction limit reached!
% 6.63/1.95 % (4165233)------------------------------
% 6.63/1.95 % (4165233)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165233)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165233)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165233)Termination reason: Instruction limit
% 6.63/1.95 % (4165233)Termination phase: Saturation
% 6.63/1.95 % (4165233)Time elapsed: 0.150 s
% 6.63/1.95 % (4165233)Peak memory usage: 94 MB
% 6.63/1.95 % (4165233)Instructions burned: 248 (million)
% 6.63/1.95 % (4165232)Instruction limit reached!
% 6.63/1.95 % (4165232)------------------------------
% 6.63/1.95 % (4165232)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165232)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165232)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165232)Termination reason: Instruction limit
% 6.63/1.95 % (4165232)Termination phase: Saturation
% 6.63/1.95 % (4165232)Time elapsed: 0.206 s
% 6.63/1.95 % (4165232)Peak memory usage: 95 MB
% 6.63/1.95 % (4165232)Instructions burned: 325 (million)
% 6.63/1.95 % (4165231)------------------------------
% 6.63/1.95 % (4165231)------------------------------
% 6.63/1.95 % (4165238)lrs+1002_1_to=lpo:sil=8000:sos=on:random_seed=1258460574:st=4:cts=off:i=294:sd=2:ins=7:amm=off:ss=axioms_2994 on theBenchmark for (2994ds/294Mi)
% 6.63/1.95 % (4165239)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=32000:tgt=ground:npcc=on:random_seed=1714425481:i=2350_2994 on theBenchmark for (2994ds/2350Mi)
% 6.63/1.95 % (4165240)dis-1011_32:1_sfv=off:sil=16000:sos=all:erd=off:acc=on:fd=off:flr=on:random_seed=3784562109:cts=off:i=113:fsr=off:ss=included:sgt=4_2994 on theBenchmark for (2994ds/113Mi)
% 6.63/1.95 % (4165241)lrs-1004_1_sil=8000:sp=occurrence:sos=all:erd=off:fs=off:bce=on:random_seed=1386026413:i=127:av=off:fsr=off:sup=off_2993 on theBenchmark for (2993ds/127Mi)
% 6.63/1.95 % (4165240)Instruction limit reached!
% 6.63/1.95 % (4165240)------------------------------
% 6.63/1.95 % (4165240)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165240)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165240)Termination reason: Instruction limit
% 6.63/1.95 % (4165240)Termination phase: Saturation
% 6.63/1.95 % (4165240)Time elapsed: 0.061 s
% 6.63/1.95 % (4165240)Peak memory usage: 92 MB
% 6.63/1.95 % (4165240)Instructions burned: 113 (million)
% 6.63/1.95 % (4165241)Instruction limit reached!
% 6.63/1.95 % (4165241)------------------------------
% 6.63/1.95 % (4165241)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165241)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165241)Termination reason: Instruction limit
% 6.63/1.95 % (4165241)Termination phase: Blocked clause elimination
% 6.63/1.95 % (4165241)Time elapsed: 0.069 s
% 6.63/1.95 % (4165241)Peak memory usage: 91 MB
% 6.63/1.95 % (4165241)Instructions burned: 127 (million)
% 6.63/1.95 % (4165238)Instruction limit reached!
% 6.63/1.95 % (4165238)------------------------------
% 6.63/1.95 % (4165238)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165238)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165238)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165238)Termination reason: Instruction limit
% 6.63/1.95 % (4165238)Termination phase: Saturation
% 6.63/1.95 % (4165238)Time elapsed: 0.173 s
% 6.63/1.95 % (4165238)Peak memory usage: 94 MB
% 6.63/1.95 % (4165238)Instructions burned: 294 (million)
% 6.63/1.95 % (4165246)dis-1003_1024_sil=8000:sos=all:sac=on:random_seed=4108886494:cond=fast:i=114:sd=1:nm=0:fsr=off:gtg=exists_sym:ss=axioms_2992 on theBenchmark for (2992ds/114Mi)
% 6.63/1.95 % (4165218)First to succeed.
% 6.63/1.95 % (4165218)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-4165211"
% 6.63/1.95 % (4165247)lrs+10_1_sil=8000:sp=occurrence:random_seed=3138671464:st=1.2:i=907:sd=14:ss=axioms:sgt=12_2991 on theBenchmark for (2991ds/907Mi)
% 6.63/1.95 % (4165248)dis-1010_1_sil=16000:fde=unused:sp=occurrence:sos=on:random_seed=4056274861:i=437:sd=1:aac=none:ss=included_2991 on theBenchmark for (2991ds/437Mi)
% 6.63/1.95 % (4165246)Instruction limit reached!
% 6.63/1.95 % (4165246)------------------------------
% 6.63/1.95 % (4165246)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 6.63/1.95 % (4165246)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 6.63/1.95 % (4165246)CaDiCaL version: 2.1.3
% 6.63/1.95 % (4165246)Termination reason: Instruction limit
% 6.63/1.95 % (4165246)Termination phase: Saturation
% 6.63/1.95 % (4165246)Time elapsed: 0.068 s
% 6.63/1.95 % (4165246)Peak memory usage: 90 MB
% 6.63/1.95 % (4165246)Instructions burned: 115 (million)
% 6.63/1.95 % (4165218)Refutation found. Thanks to Tanya!
% 6.63/1.95 % SZS status Theorem for theBenchmark
% 6.63/1.95 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/2.14 % (4165218)------------------------------
% 0.16/2.14 % (4165218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.16/2.14 % (4165218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/2.14 % (4165218)CaDiCaL version: 2.1.3
% 0.16/2.14 % (4165218)Termination reason: Refutation
% 0.16/2.14 % (4165218)Time elapsed: 0.795 s
% 0.16/2.14 % (4165218)Peak memory usage: 151 MB
% 0.16/2.14 % (4165218)Instructions burned: 2327 (million)
% 0.16/2.14 % (4165218)------------------------------
% 0.16/2.14 % (4165218)------------------------------
% 0.16/2.14 % (4165211)Success in time 1.097 s
% 0.16/2.14 % Vampire exiting
%------------------------------------------------------------------------------