TSTP Solution File: SEU341+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n003.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 : Fri May  3 03:05:52 EDT 2024

% Result   : Theorem 2.35s 1.13s
% Output   : CNFRefutation 2.35s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,the_carrier(X0))
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_connsp_2) ).

fof(f40,axiom,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0) )
     => ! [X1] :
          ( top_str(X1)
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ! [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                 => ( ( interior(X0,X2) = X2
                     => open_subset(X2,X0) )
                    & ( open_subset(X3,X1)
                     => interior(X1,X3) = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).

fof(f41,conjecture,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ! [X2] :
              ( element(X2,the_carrier(X0))
             => ( ( in(X2,X1)
                  & open_subset(X1,X0) )
               => point_neighbourhood(X1,X0,X2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_connsp_2) ).

fof(f42,negated_conjecture,
    ~ ! [X0] :
        ( ( top_str(X0)
          & topological_space(X0)
          & ~ empty_carrier(X0) )
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ! [X2] :
                ( element(X2,the_carrier(X0))
               => ( ( in(X2,X1)
                    & open_subset(X1,X0) )
                 => point_neighbourhood(X1,X0,X2) ) ) ) ),
    inference(negated_conjecture,[],[f41]) ).

fof(f77,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f78,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( point_neighbourhood(X2,X0,X1)
              <=> in(X1,interior(X0,X2)) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(flattening,[],[f77]) ).

fof(f92,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( open_subset(X2,X0)
                      | interior(X0,X2) != X2 )
                    & ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) ) )
                  | ~ element(X3,powerset(the_carrier(X1))) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f93,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ! [X3] :
                  ( ( ( open_subset(X2,X0)
                      | interior(X0,X2) != X2 )
                    & ( interior(X1,X3) = X3
                      | ~ open_subset(X3,X1) ) )
                  | ~ element(X3,powerset(the_carrier(X1))) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ top_str(X1) )
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(flattening,[],[f92]) ).

fof(f94,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,X0,X2)
              & in(X2,X1)
              & open_subset(X1,X0)
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0)
      & topological_space(X0)
      & ~ empty_carrier(X0) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f95,plain,
    ? [X0] :
      ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,X0,X2)
              & in(X2,X1)
              & open_subset(X1,X0)
              & element(X2,the_carrier(X0)) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0)
      & topological_space(X0)
      & ~ empty_carrier(X0) ),
    inference(flattening,[],[f94]) ).

fof(f100,plain,
    ! [X0] :
      ( ! [X1] :
          ( ! [X2] :
              ( ( ( point_neighbourhood(X2,X0,X1)
                  | ~ in(X1,interior(X0,X2)) )
                & ( in(X1,interior(X0,X2))
                  | ~ point_neighbourhood(X2,X0,X1) ) )
              | ~ element(X2,powerset(the_carrier(X0))) )
          | ~ element(X1,the_carrier(X0)) )
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(nnf_transformation,[],[f78]) ).

fof(f113,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ? [X2] :
                ( ~ point_neighbourhood(X1,X0,X2)
                & in(X2,X1)
                & open_subset(X1,X0)
                & element(X2,the_carrier(X0)) )
            & element(X1,powerset(the_carrier(X0))) )
        & top_str(X0)
        & topological_space(X0)
        & ~ empty_carrier(X0) )
   => ( ? [X1] :
          ( ? [X2] :
              ( ~ point_neighbourhood(X1,sK6,X2)
              & in(X2,X1)
              & open_subset(X1,sK6)
              & element(X2,the_carrier(sK6)) )
          & element(X1,powerset(the_carrier(sK6))) )
      & top_str(sK6)
      & topological_space(sK6)
      & ~ empty_carrier(sK6) ) ),
    introduced(choice_axiom,[]) ).

fof(f114,plain,
    ( ? [X1] :
        ( ? [X2] :
            ( ~ point_neighbourhood(X1,sK6,X2)
            & in(X2,X1)
            & open_subset(X1,sK6)
            & element(X2,the_carrier(sK6)) )
        & element(X1,powerset(the_carrier(sK6))) )
   => ( ? [X2] :
          ( ~ point_neighbourhood(sK7,sK6,X2)
          & in(X2,sK7)
          & open_subset(sK7,sK6)
          & element(X2,the_carrier(sK6)) )
      & element(sK7,powerset(the_carrier(sK6))) ) ),
    introduced(choice_axiom,[]) ).

fof(f115,plain,
    ( ? [X2] :
        ( ~ point_neighbourhood(sK7,sK6,X2)
        & in(X2,sK7)
        & open_subset(sK7,sK6)
        & element(X2,the_carrier(sK6)) )
   => ( ~ point_neighbourhood(sK7,sK6,sK8)
      & in(sK8,sK7)
      & open_subset(sK7,sK6)
      & element(sK8,the_carrier(sK6)) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ( ~ point_neighbourhood(sK7,sK6,sK8)
    & in(sK8,sK7)
    & open_subset(sK7,sK6)
    & element(sK8,the_carrier(sK6))
    & element(sK7,powerset(the_carrier(sK6)))
    & top_str(sK6)
    & topological_space(sK6)
    & ~ empty_carrier(sK6) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8])],[f95,f115,f114,f113]) ).

fof(f143,plain,
    ! [X2,X0,X1] :
      ( point_neighbourhood(X2,X0,X1)
      | ~ in(X1,interior(X0,X2))
      | ~ element(X2,powerset(the_carrier(X0)))
      | ~ element(X1,the_carrier(X0))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | empty_carrier(X0) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f171,plain,
    ! [X2,X3,X0,X1] :
      ( interior(X1,X3) = X3
      | ~ open_subset(X3,X1)
      | ~ element(X3,powerset(the_carrier(X1)))
      | ~ element(X2,powerset(the_carrier(X0)))
      | ~ top_str(X1)
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f173,plain,
    ~ empty_carrier(sK6),
    inference(cnf_transformation,[],[f116]) ).

fof(f174,plain,
    topological_space(sK6),
    inference(cnf_transformation,[],[f116]) ).

fof(f175,plain,
    top_str(sK6),
    inference(cnf_transformation,[],[f116]) ).

fof(f176,plain,
    element(sK7,powerset(the_carrier(sK6))),
    inference(cnf_transformation,[],[f116]) ).

fof(f177,plain,
    element(sK8,the_carrier(sK6)),
    inference(cnf_transformation,[],[f116]) ).

fof(f178,plain,
    open_subset(sK7,sK6),
    inference(cnf_transformation,[],[f116]) ).

fof(f179,plain,
    in(sK8,sK7),
    inference(cnf_transformation,[],[f116]) ).

fof(f180,plain,
    ~ point_neighbourhood(sK7,sK6,sK8),
    inference(cnf_transformation,[],[f116]) ).

cnf(c_74,plain,
    ( ~ in(X0,interior(X1,X2))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ element(X0,the_carrier(X1))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | point_neighbourhood(X2,X1,X0)
    | empty_carrier(X1) ),
    inference(cnf_transformation,[],[f143]) ).

cnf(c_104,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ element(X2,powerset(the_carrier(X3)))
    | ~ open_subset(X2,X3)
    | ~ top_str(X1)
    | ~ top_str(X3)
    | ~ topological_space(X1)
    | interior(X3,X2) = X2 ),
    inference(cnf_transformation,[],[f171]) ).

cnf(c_105,negated_conjecture,
    ~ point_neighbourhood(sK7,sK6,sK8),
    inference(cnf_transformation,[],[f180]) ).

cnf(c_106,negated_conjecture,
    in(sK8,sK7),
    inference(cnf_transformation,[],[f179]) ).

cnf(c_107,negated_conjecture,
    open_subset(sK7,sK6),
    inference(cnf_transformation,[],[f178]) ).

cnf(c_108,negated_conjecture,
    element(sK8,the_carrier(sK6)),
    inference(cnf_transformation,[],[f177]) ).

cnf(c_109,negated_conjecture,
    element(sK7,powerset(the_carrier(sK6))),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_110,negated_conjecture,
    top_str(sK6),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_111,negated_conjecture,
    topological_space(sK6),
    inference(cnf_transformation,[],[f174]) ).

cnf(c_112,negated_conjecture,
    ~ empty_carrier(sK6),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_734,plain,
    ( X0 != sK7
    | X1 != sK6
    | ~ element(X0,powerset(the_carrier(X1)))
    | ~ element(X2,powerset(the_carrier(X3)))
    | ~ top_str(X1)
    | ~ top_str(X3)
    | ~ topological_space(X3)
    | interior(X1,X0) = X0 ),
    inference(resolution_lifted,[status(thm)],[c_104,c_107]) ).

cnf(c_735,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ element(sK7,powerset(the_carrier(sK6)))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | ~ top_str(sK6)
    | interior(sK6,sK7) = sK7 ),
    inference(unflattening,[status(thm)],[c_734]) ).

cnf(c_737,plain,
    ( ~ topological_space(X1)
    | ~ top_str(X1)
    | ~ element(X0,powerset(the_carrier(X1)))
    | interior(sK6,sK7) = sK7 ),
    inference(global_subsumption_just,[status(thm)],[c_735,c_110,c_109,c_735]) ).

cnf(c_738,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | interior(sK6,sK7) = sK7 ),
    inference(renaming,[status(thm)],[c_737]) ).

cnf(c_798,plain,
    ( X0 != sK6
    | ~ in(X1,interior(X0,X2))
    | ~ element(X2,powerset(the_carrier(X0)))
    | ~ element(X1,the_carrier(X0))
    | ~ top_str(X0)
    | ~ topological_space(X0)
    | point_neighbourhood(X2,X0,X1) ),
    inference(resolution_lifted,[status(thm)],[c_74,c_112]) ).

cnf(c_799,plain,
    ( ~ in(X0,interior(sK6,X1))
    | ~ element(X1,powerset(the_carrier(sK6)))
    | ~ element(X0,the_carrier(sK6))
    | ~ top_str(sK6)
    | ~ topological_space(sK6)
    | point_neighbourhood(X1,sK6,X0) ),
    inference(unflattening,[status(thm)],[c_798]) ).

cnf(c_801,plain,
    ( ~ in(X0,interior(sK6,X1))
    | ~ element(X1,powerset(the_carrier(sK6)))
    | ~ element(X0,the_carrier(sK6))
    | point_neighbourhood(X1,sK6,X0) ),
    inference(global_subsumption_just,[status(thm)],[c_799,c_111,c_110,c_799]) ).

cnf(c_828,plain,
    ( X0 != sK6
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ top_str(X0)
    | interior(sK6,sK7) = sK7 ),
    inference(resolution_lifted,[status(thm)],[c_738,c_111]) ).

cnf(c_829,plain,
    ( ~ element(X0,powerset(the_carrier(sK6)))
    | ~ top_str(sK6)
    | interior(sK6,sK7) = sK7 ),
    inference(unflattening,[status(thm)],[c_828]) ).

cnf(c_831,plain,
    ( ~ element(X0,powerset(the_carrier(sK6)))
    | interior(sK6,sK7) = sK7 ),
    inference(global_subsumption_just,[status(thm)],[c_829,c_110,c_829]) ).

cnf(c_871,plain,
    ( X0 != sK7
    | X1 != sK8
    | sK6 != sK6
    | ~ in(X1,interior(sK6,X0))
    | ~ element(X0,powerset(the_carrier(sK6)))
    | ~ element(X1,the_carrier(sK6)) ),
    inference(resolution_lifted,[status(thm)],[c_105,c_801]) ).

cnf(c_872,plain,
    ( ~ in(sK8,interior(sK6,sK7))
    | ~ element(sK7,powerset(the_carrier(sK6)))
    | ~ element(sK8,the_carrier(sK6)) ),
    inference(unflattening,[status(thm)],[c_871]) ).

cnf(c_873,plain,
    ~ in(sK8,interior(sK6,sK7)),
    inference(global_subsumption_just,[status(thm)],[c_872,c_108,c_109,c_872]) ).

cnf(c_1074,plain,
    the_carrier(sK6) = sP0_iProver_def,
    definition ).

cnf(c_1075,plain,
    powerset(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_1076,negated_conjecture,
    element(sK7,sP1_iProver_def),
    inference(demodulation,[status(thm)],[c_109,c_1074,c_1075]) ).

cnf(c_1078,negated_conjecture,
    in(sK8,sK7),
    inference(demodulation,[status(thm)],[c_106]) ).

cnf(c_1389,plain,
    ( ~ element(X0,sP1_iProver_def)
    | interior(sK6,sK7) = sK7 ),
    inference(light_normalisation,[status(thm)],[c_831,c_1074,c_1075]) ).

cnf(c_1392,plain,
    interior(sK6,sK7) = sK7,
    inference(superposition,[status(thm)],[c_1076,c_1389]) ).

cnf(c_1393,plain,
    ~ in(sK8,sK7),
    inference(demodulation,[status(thm)],[c_873,c_1392]) ).

cnf(c_1394,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_1393,c_1078]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : SEU341+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.11  % Command  : run_iprover %s %d THM
% 0.11/0.32  % Computer : n003.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Thu May  2 17:44:05 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.18/0.44  Running first-order theorem proving
% 0.18/0.44  Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.35/1.13  % SZS status Started for theBenchmark.p
% 2.35/1.13  % SZS status Theorem for theBenchmark.p
% 2.35/1.13  
% 2.35/1.13  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 2.35/1.13  
% 2.35/1.13  ------  iProver source info
% 2.35/1.13  
% 2.35/1.13  git: date: 2024-05-02 19:28:25 +0000
% 2.35/1.13  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 2.35/1.13  git: non_committed_changes: false
% 2.35/1.13  
% 2.35/1.13  ------ Parsing...
% 2.35/1.13  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 2.35/1.13  
% 2.35/1.13  ------ Preprocessing... sup_sim: 0  sf_s  rm: 40 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe_e  sup_sim: 0  sf_s  rm: 11 0s  sf_e  pe_s  pe_e 
% 2.35/1.13  
% 2.35/1.13  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 2.35/1.13  
% 2.35/1.13  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 2.35/1.13  ------ Proving...
% 2.35/1.13  ------ Problem Properties 
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  clauses                                 29
% 2.35/1.13  conjectures                             3
% 2.35/1.13  EPR                                     11
% 2.35/1.13  Horn                                    27
% 2.35/1.13  unary                                   14
% 2.35/1.13  binary                                  11
% 2.35/1.13  lits                                    48
% 2.35/1.13  lits eq                                 6
% 2.35/1.13  fd_pure                                 0
% 2.35/1.13  fd_pseudo                               0
% 2.35/1.13  fd_cond                                 1
% 2.35/1.13  fd_pseudo_cond                          1
% 2.35/1.13  AC symbols                              0
% 2.35/1.13  
% 2.35/1.13  ------ Schedule dynamic 5 is on 
% 2.35/1.13  
% 2.35/1.13  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  ------ 
% 2.35/1.13  Current options:
% 2.35/1.13  ------ 
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  ------ Proving...
% 2.35/1.13  
% 2.35/1.13  
% 2.35/1.13  % SZS status Theorem for theBenchmark.p
% 2.35/1.13  
% 2.35/1.13  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.35/1.13  
% 2.35/1.13  
%------------------------------------------------------------------------------