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  
%------------------------------------------------------------------------------