TSTP Solution File: SEU386+2 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU386+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:48 EDT 2023
% Result : Theorem 25.04s 4.12s
% Output : CNFRefutation 25.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 14
% Syntax : Number of formulae : 84 ( 26 unt; 0 def)
% Number of atoms : 594 ( 21 equ)
% Maximal formula atoms : 24 ( 7 avg)
% Number of connectives : 821 ( 311 ~; 341 |; 131 &)
% ( 9 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 192 ( 0 sgn; 130 !; 32 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f116,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,powerset(the_carrier(X0)))
=> ( lim_points_of_net(X0,X1) = X2
<=> ! [X3] :
( element(X3,the_carrier(X0))
=> ( in(X3,X2)
<=> ! [X4] :
( point_neighbourhood(X4,X0,X3)
=> is_eventually_in(X0,X1,X4) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d18_yellow_6) ).
fof(f217,axiom,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( point_neighbourhood(X3,X0,X2)
=> is_often_in(X0,X1,X3) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_waybel_9) ).
fof(f225,axiom,
! [X0,X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1)
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> element(lim_points_of_net(X0,X1),powerset(the_carrier(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k11_yellow_6) ).
fof(f311,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f541,axiom,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k1_pcomps_1) ).
fof(f717,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( is_eventually_in(X0,X1,X2)
=> is_often_in(X0,X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t28_yellow_6) ).
fof(f720,conjecture,
! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
=> is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_waybel_9) ).
fof(f721,negated_conjecture,
~ ! [X0] :
( ( top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( ( net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( in(X2,lim_points_of_net(X0,X1))
=> is_a_cluster_point_of_netstr(X0,X1,X2) ) ) ) ),
inference(negated_conjecture,[],[f720]) ).
fof(f1108,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( lim_points_of_net(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) ) )
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f116]) ).
fof(f1109,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( lim_points_of_net(X0,X1) = X2
<=> ! [X3] :
( ( in(X3,X2)
<=> ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) ) )
| ~ element(X3,the_carrier(X0)) ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f1108]) ).
fof(f1229,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f217]) ).
fof(f1230,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( is_a_cluster_point_of_netstr(X0,X1,X2)
<=> ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f1229]) ).
fof(f1241,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f225]) ).
fof(f1242,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f1241]) ).
fof(f1329,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f311]) ).
fof(f1806,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f717]) ).
fof(f1807,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f1806]) ).
fof(f1811,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
& in(X2,lim_points_of_net(X0,X1))
& element(X2,the_carrier(X0)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f721]) ).
fof(f1812,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
& in(X2,lim_points_of_net(X0,X1))
& element(X2,the_carrier(X0)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f1811]) ).
fof(f2218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) ) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f1109]) ).
fof(f2219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X3] :
( ( ( in(X3,X2)
| ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) ) )
& ( ! [X4] :
( is_eventually_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) ) )
| ~ element(X3,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f2218]) ).
fof(f2220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ? [X7] :
( ~ is_eventually_in(X0,X1,X7)
& point_neighbourhood(X7,X0,X6) ) )
& ( ! [X8] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6) )
| ~ in(X6,X2) ) )
| ~ element(X6,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f2219]) ).
fof(f2221,plain,
! [X0,X1,X2] :
( ? [X3] :
( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,X3) )
| ~ in(X3,X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,X3) )
| in(X3,X2) )
& element(X3,the_carrier(X0)) )
=> ( ( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,sK111(X0,X1,X2)) )
| ~ in(sK111(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK111(X0,X1,X2)) )
| in(sK111(X0,X1,X2),X2) )
& element(sK111(X0,X1,X2),the_carrier(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f2222,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ is_eventually_in(X0,X1,X4)
& point_neighbourhood(X4,X0,sK111(X0,X1,X2)) )
=> ( ~ is_eventually_in(X0,X1,sK112(X0,X1,X2))
& point_neighbourhood(sK112(X0,X1,X2),X0,sK111(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f2223,plain,
! [X0,X1,X6] :
( ? [X7] :
( ~ is_eventually_in(X0,X1,X7)
& point_neighbourhood(X7,X0,X6) )
=> ( ~ is_eventually_in(X0,X1,sK113(X0,X1,X6))
& point_neighbourhood(sK113(X0,X1,X6),X0,X6) ) ),
introduced(choice_axiom,[]) ).
fof(f2224,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( lim_points_of_net(X0,X1) = X2
| ( ( ( ~ is_eventually_in(X0,X1,sK112(X0,X1,X2))
& point_neighbourhood(sK112(X0,X1,X2),X0,sK111(X0,X1,X2)) )
| ~ in(sK111(X0,X1,X2),X2) )
& ( ! [X5] :
( is_eventually_in(X0,X1,X5)
| ~ point_neighbourhood(X5,X0,sK111(X0,X1,X2)) )
| in(sK111(X0,X1,X2),X2) )
& element(sK111(X0,X1,X2),the_carrier(X0)) ) )
& ( ! [X6] :
( ( ( in(X6,X2)
| ( ~ is_eventually_in(X0,X1,sK113(X0,X1,X6))
& point_neighbourhood(sK113(X0,X1,X6),X0,X6) ) )
& ( ! [X8] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6) )
| ~ in(X6,X2) ) )
| ~ element(X6,the_carrier(X0)) )
| lim_points_of_net(X0,X1) != X2 ) )
| ~ element(X2,powerset(the_carrier(X0))) )
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK111,sK112,sK113])],[f2220,f2223,f2222,f2221]) ).
fof(f2545,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ? [X3] :
( ~ is_often_in(X0,X1,X3)
& point_neighbourhood(X3,X0,X2) ) )
& ( ! [X3] :
( is_often_in(X0,X1,X3)
| ~ point_neighbourhood(X3,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f1230]) ).
fof(f2546,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ? [X3] :
( ~ is_often_in(X0,X1,X3)
& point_neighbourhood(X3,X0,X2) ) )
& ( ! [X4] :
( is_often_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(rectify,[],[f2545]) ).
fof(f2547,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ is_often_in(X0,X1,X3)
& point_neighbourhood(X3,X0,X2) )
=> ( ~ is_often_in(X0,X1,sK227(X0,X1,X2))
& point_neighbourhood(sK227(X0,X1,X2),X0,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f2548,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( is_a_cluster_point_of_netstr(X0,X1,X2)
| ( ~ is_often_in(X0,X1,sK227(X0,X1,X2))
& point_neighbourhood(sK227(X0,X1,X2),X0,X2) ) )
& ( ! [X4] :
( is_often_in(X0,X1,X4)
| ~ point_neighbourhood(X4,X0,X2) )
| ~ is_a_cluster_point_of_netstr(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ net_str(X1,X0)
| empty_carrier(X1) )
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK227])],[f2546,f2547]) ).
fof(f3287,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(X0,X1,X2)
& in(X2,lim_points_of_net(X0,X1))
& element(X2,the_carrier(X0)) )
& net_str(X1,X0)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(X0)
& topological_space(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(sK602,X1,X2)
& in(X2,lim_points_of_net(sK602,X1))
& element(X2,the_carrier(sK602)) )
& net_str(X1,sK602)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
& top_str(sK602)
& topological_space(sK602)
& ~ empty_carrier(sK602) ) ),
introduced(choice_axiom,[]) ).
fof(f3288,plain,
( ? [X1] :
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(sK602,X1,X2)
& in(X2,lim_points_of_net(sK602,X1))
& element(X2,the_carrier(sK602)) )
& net_str(X1,sK602)
& directed_relstr(X1)
& transitive_relstr(X1)
& ~ empty_carrier(X1) )
=> ( ? [X2] :
( ~ is_a_cluster_point_of_netstr(sK602,sK603,X2)
& in(X2,lim_points_of_net(sK602,sK603))
& element(X2,the_carrier(sK602)) )
& net_str(sK603,sK602)
& directed_relstr(sK603)
& transitive_relstr(sK603)
& ~ empty_carrier(sK603) ) ),
introduced(choice_axiom,[]) ).
fof(f3289,plain,
( ? [X2] :
( ~ is_a_cluster_point_of_netstr(sK602,sK603,X2)
& in(X2,lim_points_of_net(sK602,sK603))
& element(X2,the_carrier(sK602)) )
=> ( ~ is_a_cluster_point_of_netstr(sK602,sK603,sK604)
& in(sK604,lim_points_of_net(sK602,sK603))
& element(sK604,the_carrier(sK602)) ) ),
introduced(choice_axiom,[]) ).
fof(f3290,plain,
( ~ is_a_cluster_point_of_netstr(sK602,sK603,sK604)
& in(sK604,lim_points_of_net(sK602,sK603))
& element(sK604,the_carrier(sK602))
& net_str(sK603,sK602)
& directed_relstr(sK603)
& transitive_relstr(sK603)
& ~ empty_carrier(sK603)
& top_str(sK602)
& topological_space(sK602)
& ~ empty_carrier(sK602) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK602,sK603,sK604])],[f1812,f3289,f3288,f3287]) ).
fof(f3803,plain,
! [X2,X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,X2)
| ~ element(X6,the_carrier(X0))
| lim_points_of_net(X0,X1) != X2
| ~ element(X2,powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f2224]) ).
fof(f4233,plain,
! [X2,X0,X1] :
( is_a_cluster_point_of_netstr(X0,X1,X2)
| point_neighbourhood(sK227(X0,X1,X2),X0,X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f4234,plain,
! [X2,X0,X1] :
( is_a_cluster_point_of_netstr(X0,X1,X2)
| ~ is_often_in(X0,X1,sK227(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f2548]) ).
fof(f4250,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),powerset(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1242]) ).
fof(f4338,plain,
! [X0] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f1329]) ).
fof(f5198,plain,
! [X0] : powerset(X0) = k1_pcomps_1(X0),
inference(cnf_transformation,[],[f541]) ).
fof(f5918,plain,
! [X2,X0,X1] :
( is_often_in(X0,X1,X2)
| ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f1807]) ).
fof(f5923,plain,
~ empty_carrier(sK602),
inference(cnf_transformation,[],[f3290]) ).
fof(f5924,plain,
topological_space(sK602),
inference(cnf_transformation,[],[f3290]) ).
fof(f5925,plain,
top_str(sK602),
inference(cnf_transformation,[],[f3290]) ).
fof(f5926,plain,
~ empty_carrier(sK603),
inference(cnf_transformation,[],[f3290]) ).
fof(f5927,plain,
transitive_relstr(sK603),
inference(cnf_transformation,[],[f3290]) ).
fof(f5928,plain,
directed_relstr(sK603),
inference(cnf_transformation,[],[f3290]) ).
fof(f5929,plain,
net_str(sK603,sK602),
inference(cnf_transformation,[],[f3290]) ).
fof(f5930,plain,
element(sK604,the_carrier(sK602)),
inference(cnf_transformation,[],[f3290]) ).
fof(f5931,plain,
in(sK604,lim_points_of_net(sK602,sK603)),
inference(cnf_transformation,[],[f3290]) ).
fof(f5932,plain,
~ is_a_cluster_point_of_netstr(sK602,sK603,sK604),
inference(cnf_transformation,[],[f3290]) ).
fof(f6250,plain,
! [X2,X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,X2)
| ~ element(X6,the_carrier(X0))
| lim_points_of_net(X0,X1) != X2
| ~ element(X2,k1_pcomps_1(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(definition_unfolding,[],[f3803,f5198]) ).
fof(f6391,plain,
! [X0,X1] :
( element(lim_points_of_net(X0,X1),k1_pcomps_1(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(definition_unfolding,[],[f4250,f5198]) ).
fof(f7087,plain,
! [X0,X1,X8,X6] :
( is_eventually_in(X0,X1,X8)
| ~ point_neighbourhood(X8,X0,X6)
| ~ in(X6,lim_points_of_net(X0,X1))
| ~ element(X6,the_carrier(X0))
| ~ element(lim_points_of_net(X0,X1),k1_pcomps_1(the_carrier(X0)))
| ~ net_str(X1,X0)
| ~ directed_relstr(X1)
| ~ transitive_relstr(X1)
| empty_carrier(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0) ),
inference(equality_resolution,[],[f6250]) ).
cnf(c_413,plain,
( ~ element(lim_points_of_net(X0,X1),k1_pcomps_1(the_carrier(X0)))
| ~ in(X2,lim_points_of_net(X0,X1))
| ~ point_neighbourhood(X3,X0,X2)
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| ~ top_str(X0)
| ~ topological_space(X0)
| is_eventually_in(X0,X1,X3)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f7087]) ).
cnf(c_832,plain,
( ~ is_often_in(X0,X1,sK227(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| is_a_cluster_point_of_netstr(X0,X1,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f4234]) ).
cnf(c_833,plain,
( ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(sK227(X1,X2,X0),X1,X0)
| is_a_cluster_point_of_netstr(X1,X2,X0)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(cnf_transformation,[],[f4233]) ).
cnf(c_850,plain,
( ~ net_str(X0,X1)
| ~ transitive_relstr(X0)
| ~ directed_relstr(X0)
| ~ top_str(X1)
| ~ topological_space(X1)
| element(lim_points_of_net(X1,X0),k1_pcomps_1(the_carrier(X1)))
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f6391]) ).
cnf(c_938,plain,
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f4338]) ).
cnf(c_2514,plain,
( ~ is_eventually_in(X0,X1,X2)
| ~ net_str(X1,X0)
| ~ one_sorted_str(X0)
| ~ transitive_relstr(X1)
| ~ directed_relstr(X1)
| is_often_in(X0,X1,X2)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(cnf_transformation,[],[f5918]) ).
cnf(c_2519,negated_conjecture,
~ is_a_cluster_point_of_netstr(sK602,sK603,sK604),
inference(cnf_transformation,[],[f5932]) ).
cnf(c_2520,negated_conjecture,
in(sK604,lim_points_of_net(sK602,sK603)),
inference(cnf_transformation,[],[f5931]) ).
cnf(c_2521,negated_conjecture,
element(sK604,the_carrier(sK602)),
inference(cnf_transformation,[],[f5930]) ).
cnf(c_2522,negated_conjecture,
net_str(sK603,sK602),
inference(cnf_transformation,[],[f5929]) ).
cnf(c_2523,negated_conjecture,
directed_relstr(sK603),
inference(cnf_transformation,[],[f5928]) ).
cnf(c_2524,negated_conjecture,
transitive_relstr(sK603),
inference(cnf_transformation,[],[f5927]) ).
cnf(c_2525,negated_conjecture,
~ empty_carrier(sK603),
inference(cnf_transformation,[],[f5926]) ).
cnf(c_2526,negated_conjecture,
top_str(sK602),
inference(cnf_transformation,[],[f5925]) ).
cnf(c_2527,negated_conjecture,
topological_space(sK602),
inference(cnf_transformation,[],[f5924]) ).
cnf(c_2528,negated_conjecture,
~ empty_carrier(sK602),
inference(cnf_transformation,[],[f5923]) ).
cnf(c_24894,plain,
( ~ in(X0,lim_points_of_net(X1,X2))
| ~ point_neighbourhood(X3,X1,X0)
| ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ transitive_relstr(X2)
| ~ directed_relstr(X2)
| ~ top_str(X1)
| ~ topological_space(X1)
| is_eventually_in(X1,X2,X3)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_413,c_850]) ).
cnf(c_44333,plain,
( X0 != sK602
| X1 != sK603
| X2 != sK604
| ~ is_often_in(X0,X1,sK227(X0,X1,X2))
| ~ element(X2,the_carrier(X0))
| ~ net_str(X1,X0)
| ~ top_str(X0)
| ~ topological_space(X0)
| empty_carrier(X0)
| empty_carrier(X1) ),
inference(resolution_lifted,[status(thm)],[c_832,c_2519]) ).
cnf(c_44334,plain,
( ~ is_often_in(sK602,sK603,sK227(sK602,sK603,sK604))
| ~ element(sK604,the_carrier(sK602))
| ~ net_str(sK603,sK602)
| ~ top_str(sK602)
| ~ topological_space(sK602)
| empty_carrier(sK602)
| empty_carrier(sK603) ),
inference(unflattening,[status(thm)],[c_44333]) ).
cnf(c_44370,plain,
( X0 != sK604
| X1 != sK602
| X2 != sK603
| ~ element(X0,the_carrier(X1))
| ~ net_str(X2,X1)
| ~ top_str(X1)
| ~ topological_space(X1)
| point_neighbourhood(sK227(X1,X2,X0),X1,X0)
| empty_carrier(X1)
| empty_carrier(X2) ),
inference(resolution_lifted,[status(thm)],[c_833,c_2519]) ).
cnf(c_44371,plain,
( ~ element(sK604,the_carrier(sK602))
| ~ net_str(sK603,sK602)
| ~ top_str(sK602)
| ~ topological_space(sK602)
| point_neighbourhood(sK227(sK602,sK603,sK604),sK602,sK604)
| empty_carrier(sK602)
| empty_carrier(sK603) ),
inference(unflattening,[status(thm)],[c_44370]) ).
cnf(c_44372,plain,
point_neighbourhood(sK227(sK602,sK603,sK604),sK602,sK604),
inference(global_subsumption_just,[status(thm)],[c_44371,c_2527,c_2526,c_2528,c_2525,c_2522,c_2521,c_44371]) ).
cnf(c_71600,plain,
one_sorted_str(sK602),
inference(superposition,[status(thm)],[c_2526,c_938]) ).
cnf(c_71688,plain,
( ~ point_neighbourhood(X0,sK602,sK604)
| ~ element(sK604,the_carrier(sK602))
| ~ net_str(sK603,sK602)
| ~ transitive_relstr(sK603)
| ~ directed_relstr(sK603)
| ~ top_str(sK602)
| ~ topological_space(sK602)
| is_eventually_in(sK602,sK603,X0)
| empty_carrier(sK602)
| empty_carrier(sK603) ),
inference(superposition,[status(thm)],[c_2520,c_24894]) ).
cnf(c_71700,plain,
( ~ point_neighbourhood(X0,sK602,sK604)
| is_eventually_in(sK602,sK603,X0) ),
inference(global_subsumption_just,[status(thm)],[c_71688,c_2527,c_2526,c_2524,c_2523,c_2528,c_2525,c_2522,c_2521,c_71688]) ).
cnf(c_72119,plain,
( ~ point_neighbourhood(X0,sK602,sK604)
| ~ element(sK604,the_carrier(sK602))
| ~ net_str(sK603,sK602)
| ~ transitive_relstr(sK603)
| ~ directed_relstr(sK603)
| ~ top_str(sK602)
| ~ topological_space(sK602)
| is_eventually_in(sK602,sK603,X0)
| empty_carrier(sK602)
| empty_carrier(sK603) ),
inference(superposition,[status(thm)],[c_2520,c_24894]) ).
cnf(c_72465,plain,
( ~ point_neighbourhood(X0,sK602,sK604)
| is_eventually_in(sK602,sK603,X0) ),
inference(global_subsumption_just,[status(thm)],[c_72119,c_71700]) ).
cnf(c_72473,plain,
is_eventually_in(sK602,sK603,sK227(sK602,sK603,sK604)),
inference(superposition,[status(thm)],[c_44372,c_72465]) ).
cnf(c_73142,plain,
( ~ net_str(sK603,sK602)
| ~ one_sorted_str(sK602)
| ~ transitive_relstr(sK603)
| ~ directed_relstr(sK603)
| is_often_in(sK602,sK603,sK227(sK602,sK603,sK604))
| empty_carrier(sK602)
| empty_carrier(sK603) ),
inference(superposition,[status(thm)],[c_72473,c_2514]) ).
cnf(c_73145,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_73142,c_71600,c_44334,c_2521,c_2522,c_2525,c_2528,c_2523,c_2524,c_2526,c_2527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU386+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n020.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Wed Aug 23 23:59:45 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.46 Running first-order theorem proving
% 0.19/0.46 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 25.04/4.12 % SZS status Started for theBenchmark.p
% 25.04/4.12 % SZS status Theorem for theBenchmark.p
% 25.04/4.12
% 25.04/4.12 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 25.04/4.12
% 25.04/4.12 ------ iProver source info
% 25.04/4.12
% 25.04/4.12 git: date: 2023-05-31 18:12:56 +0000
% 25.04/4.12 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 25.04/4.12 git: non_committed_changes: false
% 25.04/4.12 git: last_make_outside_of_git: false
% 25.04/4.12
% 25.04/4.12 ------ Parsing...
% 25.04/4.12 ------ Clausification by vclausify_rel & Parsing by iProver...
% 25.04/4.12
% 25.04/4.12 ------ Preprocessing... sup_sim: 143 sf_s rm: 97 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe:32:0s pe_e
% 25.04/4.12
% 25.04/4.12 ------ Preprocessing... gs_s sp: 18 0s gs_e snvd_s sp: 0 0s snvd_e
% 25.04/4.12
% 25.04/4.12 ------ Preprocessing... sf_s rm: 5 0s sf_e
% 25.04/4.12 ------ Proving...
% 25.04/4.12 ------ Problem Properties
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12 clauses 2187
% 25.04/4.12 conjectures 9
% 25.04/4.12 EPR 466
% 25.04/4.12 Horn 1492
% 25.04/4.12 unary 406
% 25.04/4.12 binary 474
% 25.04/4.12 lits 7370
% 25.04/4.12 lits eq 740
% 25.04/4.12 fd_pure 0
% 25.04/4.12 fd_pseudo 0
% 25.04/4.12 fd_cond 51
% 25.04/4.12 fd_pseudo_cond 163
% 25.04/4.12 AC symbols 0
% 25.04/4.12
% 25.04/4.12 ------ Input Options Time Limit: Unbounded
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12 ------
% 25.04/4.12 Current options:
% 25.04/4.12 ------
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12 ------ Proving...
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12 ------ Proving...
% 25.04/4.12
% 25.04/4.12
% 25.04/4.12 % SZS status Theorem for theBenchmark.p
% 25.04/4.12
% 25.04/4.12 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 25.04/4.12
% 25.04/4.12
%------------------------------------------------------------------------------