TSTP Solution File: SEU320+2 by iProver---3.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.8
% Problem  : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n024.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 17:05:46 EDT 2023

% Result   : Theorem 195.55s 26.85s
% Output   : CNFRefutation 195.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  135 (  39 unt;   0 def)
%            Number of atoms       :  449 (  93 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  528 ( 214   ~; 212   |;  73   &)
%                                         (   9 <=>;  19  =>;   0  <=;   1 <~>)
%            Maximal formula depth :   15 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   3 con; 0-3 aty)
%            Number of variables   :  215 (   1 sgn; 107   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f35,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_xboole_0) ).

fof(f89,axiom,
    ! [X0] : cast_to_subset(X0) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_subset_1) ).

fof(f98,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => set_difference(X0,X1) = subset_complement(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_subset_1) ).

fof(f138,axiom,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_subset_1) ).

fof(f145,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => element(subset_complement(X0,X1),powerset(X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_subset_1) ).

fof(f247,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => subset_complement(X0,subset_complement(X0,X1)) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

fof(f342,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(the_carrier(X0)))
        & top_str(X0)
        & topological_space(X0) )
     => ? [X2] :
          ( ! [X3] :
              ( element(X3,powerset(the_carrier(X0)))
             => ( in(X3,X2)
              <=> ? [X4] :
                    ( subset(X1,X3)
                    & closed_subset(X4,X0)
                    & X3 = X4
                    & element(X4,powerset(the_carrier(X0))) ) ) )
          & element(X2,powerset(powerset(the_carrier(X0)))) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',s3_subset_1__e1_40__pre_topc) ).

fof(f418,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ( closed_subset(X1,X0)
          <=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t29_tops_1) ).

fof(f425,conjecture,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ( open_subset(X1,X0)
          <=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t30_tops_1) ).

fof(f426,negated_conjecture,
    ~ ! [X0] :
        ( top_str(X0)
       => ! [X1] :
            ( element(X1,powerset(the_carrier(X0)))
           => ( open_subset(X1,X0)
            <=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
    inference(negated_conjecture,[],[f425]) ).

fof(f436,axiom,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t36_xboole_1) ).

fof(f438,axiom,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t37_xboole_1) ).

fof(f444,axiom,
    ! [X0] : set_difference(X0,empty_set) = X0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_boole) ).

fof(f446,axiom,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
    <=> subset(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).

fof(f468,axiom,
    ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t48_xboole_1) ).

fof(f475,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => ( ( ( topstr_closure(X0,X1) = X1
                & topological_space(X0) )
             => closed_subset(X1,X0) )
            & ( closed_subset(X1,X0)
             => topstr_closure(X0,X1) = X1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_pre_topc) ).

fof(f672,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) = subset_complement(X0,X1)
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f98]) ).

fof(f705,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f145]) ).

fof(f794,plain,
    ! [X0,X1] :
      ( subset_complement(X0,subset_complement(X0,X1)) = X1
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f247]) ).

fof(f892,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ( in(X3,X2)
              <=> ? [X4] :
                    ( subset(X1,X3)
                    & closed_subset(X4,X0)
                    & X3 = X4
                    & element(X4,powerset(the_carrier(X0))) ) )
              | ~ element(X3,powerset(the_carrier(X0))) )
          & element(X2,powerset(powerset(the_carrier(X0)))) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(ennf_transformation,[],[f342]) ).

fof(f893,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ( in(X3,X2)
              <=> ? [X4] :
                    ( subset(X1,X3)
                    & closed_subset(X4,X0)
                    & X3 = X4
                    & element(X4,powerset(the_carrier(X0))) ) )
              | ~ element(X3,powerset(the_carrier(X0))) )
          & element(X2,powerset(powerset(the_carrier(X0)))) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(flattening,[],[f892]) ).

fof(f993,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( closed_subset(X1,X0)
          <=> open_subset(subset_complement(the_carrier(X0),X1),X0) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f418]) ).

fof(f999,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( open_subset(X1,X0)
          <~> closed_subset(subset_complement(the_carrier(X0),X1),X0) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0) ),
    inference(ennf_transformation,[],[f426]) ).

fof(f1054,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subset(X1,X0)
              | topstr_closure(X0,X1) != X1
              | ~ topological_space(X0) )
            & ( topstr_closure(X0,X1) = X1
              | ~ closed_subset(X1,X0) ) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f475]) ).

fof(f1055,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subset(X1,X0)
              | topstr_closure(X0,X1) != X1
              | ~ topological_space(X0) )
            & ( topstr_closure(X0,X1) = X1
              | ~ closed_subset(X1,X0) ) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(flattening,[],[f1054]) ).

fof(f1865,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ( ( in(X3,X2)
                  | ! [X4] :
                      ( ~ subset(X1,X3)
                      | ~ closed_subset(X4,X0)
                      | X3 != X4
                      | ~ element(X4,powerset(the_carrier(X0))) ) )
                & ( ? [X4] :
                      ( subset(X1,X3)
                      & closed_subset(X4,X0)
                      & X3 = X4
                      & element(X4,powerset(the_carrier(X0))) )
                  | ~ in(X3,X2) ) )
              | ~ element(X3,powerset(the_carrier(X0))) )
          & element(X2,powerset(powerset(the_carrier(X0)))) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(nnf_transformation,[],[f893]) ).

fof(f1866,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ( ( in(X3,X2)
                  | ! [X4] :
                      ( ~ subset(X1,X3)
                      | ~ closed_subset(X4,X0)
                      | X3 != X4
                      | ~ element(X4,powerset(the_carrier(X0))) ) )
                & ( ? [X5] :
                      ( subset(X1,X3)
                      & closed_subset(X5,X0)
                      & X3 = X5
                      & element(X5,powerset(the_carrier(X0))) )
                  | ~ in(X3,X2) ) )
              | ~ element(X3,powerset(the_carrier(X0))) )
          & element(X2,powerset(powerset(the_carrier(X0)))) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(rectify,[],[f1865]) ).

fof(f1867,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ! [X3] :
              ( ( ( in(X3,X2)
                  | ! [X4] :
                      ( ~ subset(X1,X3)
                      | ~ closed_subset(X4,X0)
                      | X3 != X4
                      | ~ element(X4,powerset(the_carrier(X0))) ) )
                & ( ? [X5] :
                      ( subset(X1,X3)
                      & closed_subset(X5,X0)
                      & X3 = X5
                      & element(X5,powerset(the_carrier(X0))) )
                  | ~ in(X3,X2) ) )
              | ~ element(X3,powerset(the_carrier(X0))) )
          & element(X2,powerset(powerset(the_carrier(X0)))) )
     => ( ! [X3] :
            ( ( ( in(X3,sK359(X0,X1))
                | ! [X4] :
                    ( ~ subset(X1,X3)
                    | ~ closed_subset(X4,X0)
                    | X3 != X4
                    | ~ element(X4,powerset(the_carrier(X0))) ) )
              & ( ? [X5] :
                    ( subset(X1,X3)
                    & closed_subset(X5,X0)
                    & X3 = X5
                    & element(X5,powerset(the_carrier(X0))) )
                | ~ in(X3,sK359(X0,X1)) ) )
            | ~ element(X3,powerset(the_carrier(X0))) )
        & element(sK359(X0,X1),powerset(powerset(the_carrier(X0)))) ) ),
    introduced(choice_axiom,[]) ).

fof(f1868,plain,
    ! [X0,X1,X3] :
      ( ? [X5] :
          ( subset(X1,X3)
          & closed_subset(X5,X0)
          & X3 = X5
          & element(X5,powerset(the_carrier(X0))) )
     => ( subset(X1,X3)
        & closed_subset(sK360(X0,X1,X3),X0)
        & sK360(X0,X1,X3) = X3
        & element(sK360(X0,X1,X3),powerset(the_carrier(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f1869,plain,
    ! [X0,X1] :
      ( ( ! [X3] :
            ( ( ( in(X3,sK359(X0,X1))
                | ! [X4] :
                    ( ~ subset(X1,X3)
                    | ~ closed_subset(X4,X0)
                    | X3 != X4
                    | ~ element(X4,powerset(the_carrier(X0))) ) )
              & ( ( subset(X1,X3)
                  & closed_subset(sK360(X0,X1,X3),X0)
                  & sK360(X0,X1,X3) = X3
                  & element(sK360(X0,X1,X3),powerset(the_carrier(X0))) )
                | ~ in(X3,sK359(X0,X1)) ) )
            | ~ element(X3,powerset(the_carrier(X0))) )
        & element(sK359(X0,X1),powerset(powerset(the_carrier(X0)))) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK359,sK360])],[f1866,f1868,f1867]) ).

fof(f1908,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subset(X1,X0)
              | ~ open_subset(subset_complement(the_carrier(X0),X1),X0) )
            & ( open_subset(subset_complement(the_carrier(X0),X1),X0)
              | ~ closed_subset(X1,X0) ) )
          | ~ element(X1,powerset(the_carrier(X0))) )
      | ~ top_str(X0) ),
    inference(nnf_transformation,[],[f993]) ).

fof(f1912,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
            | ~ open_subset(X1,X0) )
          & ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
            | open_subset(X1,X0) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0) ),
    inference(nnf_transformation,[],[f999]) ).

fof(f1913,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
            | ~ open_subset(X1,X0) )
          & ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
            | open_subset(X1,X0) )
          & element(X1,powerset(the_carrier(X0))) )
      & top_str(X0) ),
    inference(flattening,[],[f1912]) ).

fof(f1914,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
              | ~ open_subset(X1,X0) )
            & ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
              | open_subset(X1,X0) )
            & element(X1,powerset(the_carrier(X0))) )
        & top_str(X0) )
   => ( ? [X1] :
          ( ( ~ closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
            | ~ open_subset(X1,sK374) )
          & ( closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
            | open_subset(X1,sK374) )
          & element(X1,powerset(the_carrier(sK374))) )
      & top_str(sK374) ) ),
    introduced(choice_axiom,[]) ).

fof(f1915,plain,
    ( ? [X1] :
        ( ( ~ closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
          | ~ open_subset(X1,sK374) )
        & ( closed_subset(subset_complement(the_carrier(sK374),X1),sK374)
          | open_subset(X1,sK374) )
        & element(X1,powerset(the_carrier(sK374))) )
   => ( ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
        | ~ open_subset(sK375,sK374) )
      & ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
        | open_subset(sK375,sK374) )
      & element(sK375,powerset(the_carrier(sK374))) ) ),
    introduced(choice_axiom,[]) ).

fof(f1916,plain,
    ( ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
      | ~ open_subset(sK375,sK374) )
    & ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
      | open_subset(sK375,sK374) )
    & element(sK375,powerset(the_carrier(sK374)))
    & top_str(sK374) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK374,sK375])],[f1913,f1915,f1914]) ).

fof(f1927,plain,
    ! [X0,X1] :
      ( ( empty_set = set_difference(X0,X1)
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | empty_set != set_difference(X0,X1) ) ),
    inference(nnf_transformation,[],[f438]) ).

fof(f1933,plain,
    ! [X0,X1] :
      ( ( element(X0,powerset(X1))
        | ~ subset(X0,X1) )
      & ( subset(X0,X1)
        | ~ element(X0,powerset(X1)) ) ),
    inference(nnf_transformation,[],[f446]) ).

fof(f2045,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
    inference(cnf_transformation,[],[f35]) ).

fof(f2278,plain,
    ! [X0] : cast_to_subset(X0) = X0,
    inference(cnf_transformation,[],[f89]) ).

fof(f2323,plain,
    ! [X0,X1] :
      ( set_difference(X0,X1) = subset_complement(X0,X1)
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f672]) ).

fof(f2402,plain,
    ! [X0] : element(cast_to_subset(X0),powerset(X0)),
    inference(cnf_transformation,[],[f138]) ).

fof(f2404,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f705]) ).

fof(f2577,plain,
    ! [X0,X1] :
      ( subset_complement(X0,subset_complement(X0,X1)) = X1
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f794]) ).

fof(f3076,plain,
    ! [X3,X0,X1] :
      ( subset(X1,X3)
      | ~ in(X3,sK359(X0,X1))
      | ~ element(X3,powerset(the_carrier(X0)))
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0) ),
    inference(cnf_transformation,[],[f1869]) ).

fof(f3190,plain,
    ! [X0,X1] :
      ( open_subset(subset_complement(the_carrier(X0),X1),X0)
      | ~ closed_subset(X1,X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f1908]) ).

fof(f3191,plain,
    ! [X0,X1] :
      ( closed_subset(X1,X0)
      | ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f1908]) ).

fof(f3200,plain,
    top_str(sK374),
    inference(cnf_transformation,[],[f1916]) ).

fof(f3201,plain,
    element(sK375,powerset(the_carrier(sK374))),
    inference(cnf_transformation,[],[f1916]) ).

fof(f3202,plain,
    ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
    | open_subset(sK375,sK374) ),
    inference(cnf_transformation,[],[f1916]) ).

fof(f3203,plain,
    ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
    | ~ open_subset(sK375,sK374) ),
    inference(cnf_transformation,[],[f1916]) ).

fof(f3221,plain,
    ! [X0,X1] : subset(set_difference(X0,X1),X0),
    inference(cnf_transformation,[],[f436]) ).

fof(f3225,plain,
    ! [X0,X1] :
      ( empty_set = set_difference(X0,X1)
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f1927]) ).

fof(f3236,plain,
    ! [X0] : set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f444]) ).

fof(f3238,plain,
    ! [X0,X1] :
      ( subset(X0,X1)
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f1933]) ).

fof(f3239,plain,
    ! [X0,X1] :
      ( element(X0,powerset(X1))
      | ~ subset(X0,X1) ),
    inference(cnf_transformation,[],[f1933]) ).

fof(f3281,plain,
    ! [X0,X1] : set_intersection2(X0,X1) = set_difference(X0,set_difference(X0,X1)),
    inference(cnf_transformation,[],[f468]) ).

fof(f3289,plain,
    ! [X0,X1] :
      ( topstr_closure(X0,X1) = X1
      | ~ closed_subset(X1,X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f1055]) ).

fof(f3386,plain,
    ! [X0,X1] : set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
    inference(definition_unfolding,[],[f2045,f3281,f3281]) ).

cnf(c_103,plain,
    set_difference(X0,set_difference(X0,X1)) = set_difference(X1,set_difference(X1,X0)),
    inference(cnf_transformation,[],[f3386]) ).

cnf(c_335,plain,
    cast_to_subset(X0) = X0,
    inference(cnf_transformation,[],[f2278]) ).

cnf(c_380,plain,
    ( ~ element(X0,powerset(X1))
    | set_difference(X1,X0) = subset_complement(X1,X0) ),
    inference(cnf_transformation,[],[f2323]) ).

cnf(c_458,plain,
    element(cast_to_subset(X0),powerset(X0)),
    inference(cnf_transformation,[],[f2402]) ).

cnf(c_460,plain,
    ( ~ element(X0,powerset(X1))
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(cnf_transformation,[],[f2404]) ).

cnf(c_633,plain,
    ( ~ element(X0,powerset(X1))
    | subset_complement(X1,subset_complement(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f2577]) ).

cnf(c_1129,plain,
    ( ~ in(X0,sK359(X1,X2))
    | ~ element(X0,powerset(the_carrier(X1)))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ top_str(X1)
    | ~ topological_space(X1)
    | subset(X2,X0) ),
    inference(cnf_transformation,[],[f3076]) ).

cnf(c_1246,plain,
    ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ top_str(X0)
    | closed_subset(X1,X0) ),
    inference(cnf_transformation,[],[f3191]) ).

cnf(c_1247,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ closed_subset(X0,X1)
    | ~ top_str(X1)
    | open_subset(subset_complement(the_carrier(X1),X0),X1) ),
    inference(cnf_transformation,[],[f3190]) ).

cnf(c_1256,negated_conjecture,
    ( ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
    | ~ open_subset(sK375,sK374) ),
    inference(cnf_transformation,[],[f3203]) ).

cnf(c_1257,negated_conjecture,
    ( closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
    | open_subset(sK375,sK374) ),
    inference(cnf_transformation,[],[f3202]) ).

cnf(c_1258,negated_conjecture,
    element(sK375,powerset(the_carrier(sK374))),
    inference(cnf_transformation,[],[f3201]) ).

cnf(c_1259,negated_conjecture,
    top_str(sK374),
    inference(cnf_transformation,[],[f3200]) ).

cnf(c_1277,plain,
    subset(set_difference(X0,X1),X0),
    inference(cnf_transformation,[],[f3221]) ).

cnf(c_1280,plain,
    ( ~ subset(X0,X1)
    | set_difference(X0,X1) = empty_set ),
    inference(cnf_transformation,[],[f3225]) ).

cnf(c_1292,plain,
    set_difference(X0,empty_set) = X0,
    inference(cnf_transformation,[],[f3236]) ).

cnf(c_1294,plain,
    ( ~ subset(X0,X1)
    | element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f3239]) ).

cnf(c_1295,plain,
    ( ~ element(X0,powerset(X1))
    | subset(X0,X1) ),
    inference(cnf_transformation,[],[f3238]) ).

cnf(c_1345,plain,
    ( ~ element(X0,powerset(the_carrier(X1)))
    | ~ closed_subset(X0,X1)
    | ~ top_str(X1)
    | topstr_closure(X1,X0) = X0 ),
    inference(cnf_transformation,[],[f3289]) ).

cnf(c_2832,plain,
    ( ~ subset(X0,X1)
    | set_difference(X1,X0) = subset_complement(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_1294,c_380]) ).

cnf(c_2834,plain,
    ( ~ subset(X0,X1)
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_1294,c_460]) ).

cnf(c_2836,plain,
    ( ~ subset(X0,X1)
    | subset_complement(X1,subset_complement(X1,X0)) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_1294,c_633]) ).

cnf(c_13791,plain,
    element(X0,powerset(X0)),
    inference(demodulation,[status(thm)],[c_458,c_335]) ).

cnf(c_49436,plain,
    ( X0 != sK374
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ closed_subset(X1,X0)
    | topstr_closure(X0,X1) = X1 ),
    inference(resolution_lifted,[status(thm)],[c_1345,c_1259]) ).

cnf(c_49437,plain,
    ( ~ element(X0,powerset(the_carrier(sK374)))
    | ~ closed_subset(X0,sK374)
    | topstr_closure(sK374,X0) = X0 ),
    inference(unflattening,[status(thm)],[c_49436]) ).

cnf(c_49666,plain,
    ( X0 != sK374
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ closed_subset(X1,X0)
    | open_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(resolution_lifted,[status(thm)],[c_1247,c_1259]) ).

cnf(c_49667,plain,
    ( ~ element(X0,powerset(the_carrier(sK374)))
    | ~ closed_subset(X0,sK374)
    | open_subset(subset_complement(the_carrier(sK374),X0),sK374) ),
    inference(unflattening,[status(thm)],[c_49666]) ).

cnf(c_49774,plain,
    ( X0 != sK374
    | ~ in(X1,sK359(X0,X2))
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ element(X2,powerset(the_carrier(X0)))
    | ~ topological_space(X0)
    | subset(X2,X1) ),
    inference(resolution_lifted,[status(thm)],[c_1129,c_1259]) ).

cnf(c_49775,plain,
    ( ~ in(X0,sK359(sK374,X1))
    | ~ element(X0,powerset(the_carrier(sK374)))
    | ~ element(X1,powerset(the_carrier(sK374)))
    | ~ topological_space(sK374)
    | subset(X1,X0) ),
    inference(unflattening,[status(thm)],[c_49774]) ).

cnf(c_50340,plain,
    ( X0 != sK374
    | ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
    | ~ element(X1,powerset(the_carrier(X0)))
    | closed_subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_1246,c_1259]) ).

cnf(c_50341,plain,
    ( ~ open_subset(subset_complement(the_carrier(sK374),X0),sK374)
    | ~ element(X0,powerset(the_carrier(sK374)))
    | closed_subset(X0,sK374) ),
    inference(unflattening,[status(thm)],[c_50340]) ).

cnf(c_109478,plain,
    ( ~ subset(X0,X1)
    | set_difference(X1,X0) = subset_complement(X1,X0) ),
    inference(prop_impl_just,[status(thm)],[c_2832]) ).

cnf(c_109480,plain,
    ( ~ subset(X0,X1)
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(prop_impl_just,[status(thm)],[c_2834]) ).

cnf(c_109482,plain,
    ( ~ subset(X0,X1)
    | subset_complement(X1,subset_complement(X1,X0)) = X0 ),
    inference(prop_impl_just,[status(thm)],[c_2836]) ).

cnf(c_157955,plain,
    X0 = X0,
    theory(equality) ).

cnf(c_157957,plain,
    ( X0 != X1
    | X2 != X1
    | X2 = X0 ),
    theory(equality) ).

cnf(c_157989,plain,
    ( X0 != X1
    | X2 != X3
    | ~ open_subset(X1,X3)
    | open_subset(X0,X2) ),
    theory(equality) ).

cnf(c_191351,plain,
    ( ~ element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374)))
    | ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374)
    | open_subset(subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)),sK374) ),
    inference(instantiation,[status(thm)],[c_49667]) ).

cnf(c_197545,plain,
    subset(sK375,the_carrier(sK374)),
    inference(superposition,[status(thm)],[c_1258,c_1295]) ).

cnf(c_203459,plain,
    ( ~ subset(sK375,the_carrier(sK374))
    | element(subset_complement(the_carrier(sK374),sK375),powerset(the_carrier(sK374))) ),
    inference(instantiation,[status(thm)],[c_109480]) ).

cnf(c_203641,plain,
    sK374 = sK374,
    inference(instantiation,[status(thm)],[c_157955]) ).

cnf(c_233383,plain,
    ( X0 != sK375
    | X1 != sK374
    | ~ open_subset(sK375,sK374)
    | open_subset(X0,X1) ),
    inference(instantiation,[status(thm)],[c_157989]) ).

cnf(c_247886,plain,
    ( X0 != subset_complement(the_carrier(sK374),X1)
    | X2 != sK374
    | ~ open_subset(subset_complement(the_carrier(sK374),X1),sK374)
    | open_subset(X0,X2) ),
    inference(instantiation,[status(thm)],[c_157989]) ).

cnf(c_253837,plain,
    ( set_difference(sK375,empty_set) != sK375
    | X0 != sK374
    | ~ open_subset(sK375,sK374)
    | open_subset(set_difference(sK375,empty_set),X0) ),
    inference(instantiation,[status(thm)],[c_233383]) ).

cnf(c_253838,plain,
    set_difference(sK375,empty_set) = sK375,
    inference(instantiation,[status(thm)],[c_1292]) ).

cnf(c_253857,plain,
    sK375 = sK375,
    inference(instantiation,[status(thm)],[c_157955]) ).

cnf(c_272890,plain,
    ( set_difference(sK375,empty_set) != sK375
    | sK374 != sK374
    | ~ open_subset(sK375,sK374)
    | open_subset(set_difference(sK375,empty_set),sK374) ),
    inference(instantiation,[status(thm)],[c_253837]) ).

cnf(c_277173,plain,
    ( sK374 != sK374
    | sK375 != subset_complement(the_carrier(sK374),X0)
    | ~ open_subset(subset_complement(the_carrier(sK374),X0),sK374)
    | open_subset(sK375,sK374) ),
    inference(instantiation,[status(thm)],[c_247886]) ).

cnf(c_278864,plain,
    ( sK374 != sK374
    | sK375 != subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375))
    | ~ open_subset(subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)),sK374)
    | open_subset(sK375,sK374) ),
    inference(instantiation,[status(thm)],[c_277173]) ).

cnf(c_349040,plain,
    set_difference(X0,set_difference(X0,X1)) = subset_complement(X0,set_difference(X0,X1)),
    inference(superposition,[status(thm)],[c_1277,c_109478]) ).

cnf(c_427611,plain,
    ( ~ open_subset(set_difference(the_carrier(sK374),set_difference(the_carrier(sK374),X0)),sK374)
    | ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(superposition,[status(thm)],[c_349040,c_50341]) ).

cnf(c_432466,plain,
    ( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
    | ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(superposition,[status(thm)],[c_103,c_427611]) ).

cnf(c_449955,plain,
    ( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
    | ~ subset(set_difference(the_carrier(sK374),X0),the_carrier(sK374))
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(superposition,[status(thm)],[c_1294,c_432466]) ).

cnf(c_449967,plain,
    ( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_449955,c_1277]) ).

cnf(c_505999,plain,
    ( ~ in(X0,sK359(sK374,sK375))
    | ~ element(X0,powerset(the_carrier(sK374)))
    | ~ topological_space(sK374)
    | subset(sK375,X0) ),
    inference(superposition,[status(thm)],[c_1258,c_49775]) ).

cnf(c_507567,plain,
    ( ~ in(the_carrier(sK374),sK359(sK374,sK375))
    | ~ topological_space(sK374)
    | subset(sK375,the_carrier(sK374)) ),
    inference(superposition,[status(thm)],[c_13791,c_505999]) ).

cnf(c_507701,plain,
    subset(sK375,the_carrier(sK374)),
    inference(global_subsumption_just,[status(thm)],[c_507567,c_197545]) ).

cnf(c_542562,plain,
    ( subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) != X0
    | sK375 != X0
    | sK375 = subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) ),
    inference(instantiation,[status(thm)],[c_157957]) ).

cnf(c_556717,plain,
    set_difference(sK375,the_carrier(sK374)) = empty_set,
    inference(superposition,[status(thm)],[c_507701,c_1280]) ).

cnf(c_563396,plain,
    ( ~ closed_subset(subset_complement(the_carrier(sK374),X0),sK374)
    | ~ subset(X0,the_carrier(sK374))
    | topstr_closure(sK374,subset_complement(the_carrier(sK374),X0)) = subset_complement(the_carrier(sK374),X0) ),
    inference(superposition,[status(thm)],[c_109480,c_49437]) ).

cnf(c_573016,plain,
    ( subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) != sK375
    | sK375 != sK375
    | sK375 = subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) ),
    inference(instantiation,[status(thm)],[c_542562]) ).

cnf(c_573017,plain,
    ( ~ subset(sK375,the_carrier(sK374))
    | subset_complement(the_carrier(sK374),subset_complement(the_carrier(sK374),sK375)) = sK375 ),
    inference(instantiation,[status(thm)],[c_109482]) ).

cnf(c_575682,negated_conjecture,
    open_subset(sK375,sK374),
    inference(global_subsumption_just,[status(thm)],[c_1257,c_1257,c_191351,c_197545,c_203459,c_203641,c_253857,c_278864,c_573016,c_573017]) ).

cnf(c_625833,plain,
    ( ~ subset(sK375,the_carrier(sK374))
    | topstr_closure(sK374,subset_complement(the_carrier(sK374),sK375)) = subset_complement(the_carrier(sK374),sK375)
    | open_subset(sK375,sK374) ),
    inference(superposition,[status(thm)],[c_1257,c_563396]) ).

cnf(c_625834,plain,
    ( topstr_closure(sK374,subset_complement(the_carrier(sK374),sK375)) = subset_complement(the_carrier(sK374),sK375)
    | open_subset(sK375,sK374) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_625833,c_507701]) ).

cnf(c_625837,plain,
    open_subset(sK375,sK374),
    inference(global_subsumption_just,[status(thm)],[c_625834,c_575682]) ).

cnf(c_625845,plain,
    ~ closed_subset(subset_complement(the_carrier(sK374),sK375),sK374),
    inference(backward_subsumption_resolution,[status(thm)],[c_1256,c_625837]) ).

cnf(c_645723,plain,
    set_difference(X0,set_difference(X0,X1)) = subset_complement(X0,set_difference(X0,X1)),
    inference(superposition,[status(thm)],[c_1277,c_109478]) ).

cnf(c_645730,plain,
    set_difference(the_carrier(sK374),sK375) = subset_complement(the_carrier(sK374),sK375),
    inference(superposition,[status(thm)],[c_507701,c_109478]) ).

cnf(c_646535,plain,
    ~ closed_subset(set_difference(the_carrier(sK374),sK375),sK374),
    inference(demodulation,[status(thm)],[c_625845,c_645730]) ).

cnf(c_756434,plain,
    ( ~ open_subset(set_difference(the_carrier(sK374),set_difference(the_carrier(sK374),X0)),sK374)
    | ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(superposition,[status(thm)],[c_645723,c_50341]) ).

cnf(c_757064,plain,
    ( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
    | ~ element(set_difference(the_carrier(sK374),X0),powerset(the_carrier(sK374)))
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(superposition,[status(thm)],[c_103,c_756434]) ).

cnf(c_769891,plain,
    ( ~ open_subset(set_difference(X0,set_difference(X0,the_carrier(sK374))),sK374)
    | closed_subset(set_difference(the_carrier(sK374),X0),sK374) ),
    inference(global_subsumption_just,[status(thm)],[c_757064,c_449967]) ).

cnf(c_769906,plain,
    ( ~ open_subset(set_difference(sK375,empty_set),sK374)
    | closed_subset(set_difference(the_carrier(sK374),sK375),sK374) ),
    inference(superposition,[status(thm)],[c_556717,c_769891]) ).

cnf(c_769909,plain,
    ~ open_subset(set_difference(sK375,empty_set),sK374),
    inference(forward_subsumption_resolution,[status(thm)],[c_769906,c_646535]) ).

cnf(c_769921,plain,
    $false,
    inference(prop_impl_just,[status(thm)],[c_769909,c_575682,c_272890,c_253838,c_203641]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SEU320+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n024.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 21:20:54 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.47  Running first-order theorem proving
% 0.19/0.47  Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 195.55/26.85  % SZS status Started for theBenchmark.p
% 195.55/26.85  % SZS status Theorem for theBenchmark.p
% 195.55/26.85  
% 195.55/26.85  %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 195.55/26.85  
% 195.55/26.85  ------  iProver source info
% 195.55/26.85  
% 195.55/26.85  git: date: 2023-05-31 18:12:56 +0000
% 195.55/26.85  git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 195.55/26.85  git: non_committed_changes: false
% 195.55/26.85  git: last_make_outside_of_git: false
% 195.55/26.85  
% 195.55/26.85  ------ Parsing...
% 195.55/26.85  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 195.55/26.85  
% 195.55/26.85  ------ Preprocessing... sup_sim: 95  sf_s  rm: 96 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe:16:0s pe_e  sup_sim: 67  sf_s  rm: 25 0s  sf_e  pe_s  pe_e  sup_sim: 0  sf_s  rm: 25 0s  sf_e  pe_s  pe_e 
% 195.55/26.85  
% 195.55/26.85  ------ Preprocessing... gs_s  sp: 15 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 195.55/26.85  
% 195.55/26.85  ------ Preprocessing... sf_s  rm: 3 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 195.55/26.85  ------ Proving...
% 195.55/26.85  ------ Problem Properties 
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  clauses                                 1285
% 195.55/26.85  conjectures                             3
% 195.55/26.85  EPR                                     173
% 195.55/26.85  Horn                                    959
% 195.55/26.85  unary                                   172
% 195.55/26.85  binary                                  382
% 195.55/26.85  lits                                    3896
% 195.55/26.85  lits eq                                 548
% 195.55/26.85  fd_pure                                 0
% 195.55/26.85  fd_pseudo                               0
% 195.55/26.85  fd_cond                                 44
% 195.55/26.85  fd_pseudo_cond                          117
% 195.55/26.85  AC symbols                              0
% 195.55/26.85  
% 195.55/26.85  ------ Schedule dynamic 5 is on 
% 195.55/26.85  
% 195.55/26.85  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  ------ 
% 195.55/26.85  Current options:
% 195.55/26.85  ------ 
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  ------ Proving...
% 195.55/26.85  Proof_search_loop: time out after: 12171 full_loop iterations
% 195.55/26.85  
% 195.55/26.85  ------ Input Options"--res_lit_sel adaptive --res_lit_sel_side num_symb" Time Limit: 15.
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  ------ 
% 195.55/26.85  Current options:
% 195.55/26.85  ------ 
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  ------ Proving...
% 195.55/26.85  
% 195.55/26.85  
% 195.55/26.85  % SZS status Theorem for theBenchmark.p
% 195.55/26.85  
% 195.55/26.85  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 195.55/26.85  
% 195.55/26.86  
%------------------------------------------------------------------------------