TSTP Solution File: SEU337+1 by iProver---3.9

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : iProver---3.9
% Problem  : SEU337+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover %s %d THM

% Computer : n027.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 03:05:51 EDT 2024

% Result   : Theorem 17.41s 3.22s
% Output   : CNFRefutation 17.41s
% Verified : 
% SZS Type : ERROR: Analysing output (Could not find formula named definition)

% Comments : 
%------------------------------------------------------------------------------
fof(f17,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(powerset(the_carrier(X0))))
         => ( open_subsets(X1,X0)
          <=> ! [X2] :
                ( element(X2,powerset(the_carrier(X0)))
               => ( in(X2,X1)
                 => open_subset(X2,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_2) ).

fof(f18,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(powerset(the_carrier(X0))))
         => ( closed_subsets(X1,X0)
          <=> ! [X2] :
                ( element(X2,powerset(the_carrier(X0)))
               => ( in(X2,X1)
                 => closed_subset(X2,X0) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_tops_2) ).

fof(f19,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => ! [X2] :
          ( element(X2,powerset(powerset(X0)))
         => ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( element(X3,powerset(X0))
               => ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8_setfam_1) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => element(subset_complement(X0,X1),powerset(X0)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k7_setfam_1) ).

fof(f30,axiom,
    ! [X0] :
    ? [X1] : element(X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',existence_m1_subset_1) ).

fof(f31,axiom,
    ! [X0] : ~ empty(powerset(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).

fof(f33,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(X0))
     => subset_complement(X0,subset_complement(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).

fof(f34,axiom,
    ! [X0,X1] :
      ( element(X1,powerset(powerset(X0)))
     => complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).

fof(f36,axiom,
    ! [X0] :
      ( ~ empty(X0)
     => ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_subset_1) ).

fof(f39,conjecture,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(powerset(the_carrier(X0))))
         => ( open_subsets(X1,X0)
          <=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_tops_2) ).

fof(f40,negated_conjecture,
    ~ ! [X0] :
        ( top_str(X0)
       => ! [X1] :
            ( element(X1,powerset(powerset(the_carrier(X0))))
           => ( open_subsets(X1,X0)
            <=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
    inference(negated_conjecture,[],[f39]) ).

fof(f41,axiom,
    ! [X0,X1] :
      ( in(X0,X1)
     => element(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1_subset) ).

fof(f42,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/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).

fof(f43,axiom,
    ! [X0,X1] :
      ( element(X0,X1)
     => ( in(X0,X1)
        | empty(X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_subset) ).

fof(f44,axiom,
    ! [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/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).

fof(f46,axiom,
    ! [X0,X1,X2] :
      ( ( element(X1,powerset(X2))
        & in(X0,X1) )
     => element(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t4_subset) ).

fof(f47,axiom,
    ! [X0,X1,X2] :
      ~ ( empty(X2)
        & element(X1,powerset(X2))
        & in(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).

fof(f48,axiom,
    ! [X0] :
      ( empty(X0)
     => empty_set = X0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).

fof(f81,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( open_subsets(X1,X0)
          <=> ! [X2] :
                ( open_subset(X2,X0)
                | ~ in(X2,X1)
                | ~ element(X2,powerset(the_carrier(X0))) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f82,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( open_subsets(X1,X0)
          <=> ! [X2] :
                ( open_subset(X2,X0)
                | ~ in(X2,X1)
                | ~ element(X2,powerset(the_carrier(X0))) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(flattening,[],[f81]) ).

fof(f83,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( closed_subsets(X1,X0)
          <=> ! [X2] :
                ( closed_subset(X2,X0)
                | ~ in(X2,X1)
                | ~ element(X2,powerset(the_carrier(X0))) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f84,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( closed_subsets(X1,X0)
          <=> ! [X2] :
                ( closed_subset(X2,X0)
                | ~ in(X2,X1)
                | ~ element(X2,powerset(the_carrier(X0))) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(flattening,[],[f83]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( complements_of_subsets(X0,X1) = X2
          <=> ! [X3] :
                ( ( in(X3,X2)
                <=> in(subset_complement(X0,X3),X1) )
                | ~ element(X3,powerset(X0)) ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f88,plain,
    ! [X0,X1] :
      ( subset_complement(X0,subset_complement(X0,X1)) = X1
      | ~ element(X1,powerset(X0)) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(ennf_transformation,[],[f34]) ).

fof(f90,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
      | empty(X0) ),
    inference(ennf_transformation,[],[f36]) ).

fof(f91,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( open_subsets(X1,X0)
          <~> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
          & element(X1,powerset(powerset(the_carrier(X0)))) )
      & top_str(X0) ),
    inference(ennf_transformation,[],[f40]) ).

fof(f92,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f41]) ).

fof(f93,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,[],[f42]) ).

fof(f94,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f95,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(flattening,[],[f94]) ).

fof(f96,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,[],[f44]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f46]) ).

fof(f99,plain,
    ! [X0,X1,X2] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(flattening,[],[f98]) ).

fof(f100,plain,
    ! [X0,X1,X2] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(ennf_transformation,[],[f47]) ).

fof(f101,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(ennf_transformation,[],[f48]) ).

fof(f104,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( open_subsets(X1,X0)
              | ? [X2] :
                  ( ~ open_subset(X2,X0)
                  & in(X2,X1)
                  & element(X2,powerset(the_carrier(X0))) ) )
            & ( ! [X2] :
                  ( open_subset(X2,X0)
                  | ~ in(X2,X1)
                  | ~ element(X2,powerset(the_carrier(X0))) )
              | ~ open_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(nnf_transformation,[],[f82]) ).

fof(f105,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( open_subsets(X1,X0)
              | ? [X2] :
                  ( ~ open_subset(X2,X0)
                  & in(X2,X1)
                  & element(X2,powerset(the_carrier(X0))) ) )
            & ( ! [X3] :
                  ( open_subset(X3,X0)
                  | ~ in(X3,X1)
                  | ~ element(X3,powerset(the_carrier(X0))) )
              | ~ open_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(rectify,[],[f104]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ open_subset(X2,X0)
          & in(X2,X1)
          & element(X2,powerset(the_carrier(X0))) )
     => ( ~ open_subset(sK0(X0,X1),X0)
        & in(sK0(X0,X1),X1)
        & element(sK0(X0,X1),powerset(the_carrier(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f107,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( open_subsets(X1,X0)
              | ( ~ open_subset(sK0(X0,X1),X0)
                & in(sK0(X0,X1),X1)
                & element(sK0(X0,X1),powerset(the_carrier(X0))) ) )
            & ( ! [X3] :
                  ( open_subset(X3,X0)
                  | ~ in(X3,X1)
                  | ~ element(X3,powerset(the_carrier(X0))) )
              | ~ open_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f105,f106]) ).

fof(f108,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subsets(X1,X0)
              | ? [X2] :
                  ( ~ closed_subset(X2,X0)
                  & in(X2,X1)
                  & element(X2,powerset(the_carrier(X0))) ) )
            & ( ! [X2] :
                  ( closed_subset(X2,X0)
                  | ~ in(X2,X1)
                  | ~ element(X2,powerset(the_carrier(X0))) )
              | ~ closed_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(nnf_transformation,[],[f84]) ).

fof(f109,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subsets(X1,X0)
              | ? [X2] :
                  ( ~ closed_subset(X2,X0)
                  & in(X2,X1)
                  & element(X2,powerset(the_carrier(X0))) ) )
            & ( ! [X3] :
                  ( closed_subset(X3,X0)
                  | ~ in(X3,X1)
                  | ~ element(X3,powerset(the_carrier(X0))) )
              | ~ closed_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(rectify,[],[f108]) ).

fof(f110,plain,
    ! [X0,X1] :
      ( ? [X2] :
          ( ~ closed_subset(X2,X0)
          & in(X2,X1)
          & element(X2,powerset(the_carrier(X0))) )
     => ( ~ closed_subset(sK1(X0,X1),X0)
        & in(sK1(X0,X1),X1)
        & element(sK1(X0,X1),powerset(the_carrier(X0))) ) ),
    introduced(choice_axiom,[]) ).

fof(f111,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( closed_subsets(X1,X0)
              | ( ~ closed_subset(sK1(X0,X1),X0)
                & in(sK1(X0,X1),X1)
                & element(sK1(X0,X1),powerset(the_carrier(X0))) ) )
            & ( ! [X3] :
                  ( closed_subset(X3,X0)
                  | ~ in(X3,X1)
                  | ~ element(X3,powerset(the_carrier(X0))) )
              | ~ closed_subsets(X1,X0) ) )
          | ~ element(X1,powerset(powerset(the_carrier(X0)))) )
      | ~ top_str(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f109,f110]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X3] :
                  ( ( ( in(X3,X2)
                      | ~ in(subset_complement(X0,X3),X1) )
                    & ( in(subset_complement(X0,X3),X1)
                      | ~ in(X3,X2) ) )
                  | ~ element(X3,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(nnf_transformation,[],[f85]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X3] :
                  ( ( ( in(X3,X2)
                      | ~ in(subset_complement(X0,X3),X1) )
                    & ( in(subset_complement(X0,X3),X1)
                      | ~ in(X3,X2) ) )
                  | ~ element(X3,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(flattening,[],[f112]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ? [X3] :
                  ( ( ~ in(subset_complement(X0,X3),X1)
                    | ~ in(X3,X2) )
                  & ( in(subset_complement(X0,X3),X1)
                    | in(X3,X2) )
                  & element(X3,powerset(X0)) ) )
            & ( ! [X4] :
                  ( ( ( in(X4,X2)
                      | ~ in(subset_complement(X0,X4),X1) )
                    & ( in(subset_complement(X0,X4),X1)
                      | ~ in(X4,X2) ) )
                  | ~ element(X4,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(rectify,[],[f113]) ).

fof(f115,plain,
    ! [X0,X1,X2] :
      ( ? [X3] :
          ( ( ~ in(subset_complement(X0,X3),X1)
            | ~ in(X3,X2) )
          & ( in(subset_complement(X0,X3),X1)
            | in(X3,X2) )
          & element(X3,powerset(X0)) )
     => ( ( ~ in(subset_complement(X0,sK2(X0,X1,X2)),X1)
          | ~ in(sK2(X0,X1,X2),X2) )
        & ( in(subset_complement(X0,sK2(X0,X1,X2)),X1)
          | in(sK2(X0,X1,X2),X2) )
        & element(sK2(X0,X1,X2),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f116,plain,
    ! [X0,X1] :
      ( ! [X2] :
          ( ( ( complements_of_subsets(X0,X1) = X2
              | ( ( ~ in(subset_complement(X0,sK2(X0,X1,X2)),X1)
                  | ~ in(sK2(X0,X1,X2),X2) )
                & ( in(subset_complement(X0,sK2(X0,X1,X2)),X1)
                  | in(sK2(X0,X1,X2),X2) )
                & element(sK2(X0,X1,X2),powerset(X0)) ) )
            & ( ! [X4] :
                  ( ( ( in(X4,X2)
                      | ~ in(subset_complement(X0,X4),X1) )
                    & ( in(subset_complement(X0,X4),X1)
                      | ~ in(X4,X2) ) )
                  | ~ element(X4,powerset(X0)) )
              | complements_of_subsets(X0,X1) != X2 ) )
          | ~ element(X2,powerset(powerset(X0))) )
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f114,f115]) ).

fof(f119,plain,
    ! [X0] :
      ( ? [X1] : element(X1,X0)
     => element(sK4(X0),X0) ),
    introduced(choice_axiom,[]) ).

fof(f120,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f119]) ).

fof(f123,plain,
    ! [X0] :
      ( ? [X1] :
          ( ~ empty(X1)
          & element(X1,powerset(X0)) )
     => ( ~ empty(sK6(X0))
        & element(sK6(X0),powerset(X0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f124,plain,
    ! [X0] :
      ( ( ~ empty(sK6(X0))
        & element(sK6(X0),powerset(X0)) )
      | empty(X0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f90,f123]) ).

fof(f127,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
            | ~ open_subsets(X1,X0) )
          & ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
            | open_subsets(X1,X0) )
          & element(X1,powerset(powerset(the_carrier(X0)))) )
      & top_str(X0) ),
    inference(nnf_transformation,[],[f91]) ).

fof(f128,plain,
    ? [X0] :
      ( ? [X1] :
          ( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
            | ~ open_subsets(X1,X0) )
          & ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
            | open_subsets(X1,X0) )
          & element(X1,powerset(powerset(the_carrier(X0)))) )
      & top_str(X0) ),
    inference(flattening,[],[f127]) ).

fof(f129,plain,
    ( ? [X0] :
        ( ? [X1] :
            ( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
              | ~ open_subsets(X1,X0) )
            & ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
              | open_subsets(X1,X0) )
            & element(X1,powerset(powerset(the_carrier(X0)))) )
        & top_str(X0) )
   => ( ? [X1] :
          ( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),X1),sK8)
            | ~ open_subsets(X1,sK8) )
          & ( closed_subsets(complements_of_subsets(the_carrier(sK8),X1),sK8)
            | open_subsets(X1,sK8) )
          & element(X1,powerset(powerset(the_carrier(sK8)))) )
      & top_str(sK8) ) ),
    introduced(choice_axiom,[]) ).

fof(f130,plain,
    ( ? [X1] :
        ( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),X1),sK8)
          | ~ open_subsets(X1,sK8) )
        & ( closed_subsets(complements_of_subsets(the_carrier(sK8),X1),sK8)
          | open_subsets(X1,sK8) )
        & element(X1,powerset(powerset(the_carrier(sK8)))) )
   => ( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
        | ~ open_subsets(sK9,sK8) )
      & ( closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
        | open_subsets(sK9,sK8) )
      & element(sK9,powerset(powerset(the_carrier(sK8)))) ) ),
    introduced(choice_axiom,[]) ).

fof(f131,plain,
    ( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
      | ~ open_subsets(sK9,sK8) )
    & ( closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
      | open_subsets(sK9,sK8) )
    & element(sK9,powerset(powerset(the_carrier(sK8))))
    & top_str(sK8) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9])],[f128,f130,f129]) ).

fof(f132,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,[],[f93]) ).

fof(f133,plain,
    ! [X0] :
      ( ! [X1] :
          ( ( ( open_subset(X1,X0)
              | ~ closed_subset(subset_complement(the_carrier(X0),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,[],[f96]) ).

fof(f159,plain,
    ! [X3,X0,X1] :
      ( open_subset(X3,X0)
      | ~ in(X3,X1)
      | ~ element(X3,powerset(the_carrier(X0)))
      | ~ open_subsets(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f161,plain,
    ! [X0,X1] :
      ( open_subsets(X1,X0)
      | in(sK0(X0,X1),X1)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f162,plain,
    ! [X0,X1] :
      ( open_subsets(X1,X0)
      | ~ open_subset(sK0(X0,X1),X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f107]) ).

fof(f163,plain,
    ! [X3,X0,X1] :
      ( closed_subset(X3,X0)
      | ~ in(X3,X1)
      | ~ element(X3,powerset(the_carrier(X0)))
      | ~ closed_subsets(X1,X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f164,plain,
    ! [X0,X1] :
      ( closed_subsets(X1,X0)
      | element(sK1(X0,X1),powerset(the_carrier(X0)))
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f165,plain,
    ! [X0,X1] :
      ( closed_subsets(X1,X0)
      | in(sK1(X0,X1),X1)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f166,plain,
    ! [X0,X1] :
      ( closed_subsets(X1,X0)
      | ~ closed_subset(sK1(X0,X1),X0)
      | ~ element(X1,powerset(powerset(the_carrier(X0))))
      | ~ top_str(X0) ),
    inference(cnf_transformation,[],[f111]) ).

fof(f167,plain,
    ! [X2,X0,X1,X4] :
      ( in(subset_complement(X0,X4),X1)
      | ~ in(X4,X2)
      | ~ element(X4,powerset(X0))
      | complements_of_subsets(X0,X1) != X2
      | ~ element(X2,powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f116]) ).

fof(f172,plain,
    ! [X0,X1] :
      ( element(subset_complement(X0,X1),powerset(X0))
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f173,plain,
    ! [X0,X1] :
      ( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f87]) ).

fof(f175,plain,
    ! [X0] : element(sK4(X0),X0),
    inference(cnf_transformation,[],[f120]) ).

fof(f176,plain,
    ! [X0] : ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f31]) ).

fof(f183,plain,
    ! [X0,X1] :
      ( subset_complement(X0,subset_complement(X0,X1)) = X1
      | ~ element(X1,powerset(X0)) ),
    inference(cnf_transformation,[],[f88]) ).

fof(f184,plain,
    ! [X0,X1] :
      ( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f191,plain,
    ! [X0] :
      ( element(sK6(X0),powerset(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ empty(sK6(X0))
      | empty(X0) ),
    inference(cnf_transformation,[],[f124]) ).

fof(f196,plain,
    top_str(sK8),
    inference(cnf_transformation,[],[f131]) ).

fof(f197,plain,
    element(sK9,powerset(powerset(the_carrier(sK8)))),
    inference(cnf_transformation,[],[f131]) ).

fof(f198,plain,
    ( closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | open_subsets(sK9,sK8) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f199,plain,
    ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subsets(sK9,sK8) ),
    inference(cnf_transformation,[],[f131]) ).

fof(f200,plain,
    ! [X0,X1] :
      ( element(X0,X1)
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f92]) ).

fof(f202,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,[],[f132]) ).

fof(f203,plain,
    ! [X0,X1] :
      ( in(X0,X1)
      | empty(X1)
      | ~ element(X0,X1) ),
    inference(cnf_transformation,[],[f95]) ).

fof(f205,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(cnf_transformation,[],[f133]) ).

fof(f207,plain,
    ! [X2,X0,X1] :
      ( element(X0,X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f208,plain,
    ! [X2,X0,X1] :
      ( ~ empty(X2)
      | ~ element(X1,powerset(X2))
      | ~ in(X0,X1) ),
    inference(cnf_transformation,[],[f100]) ).

fof(f209,plain,
    ! [X0] :
      ( empty_set = X0
      | ~ empty(X0) ),
    inference(cnf_transformation,[],[f101]) ).

fof(f213,plain,
    ! [X0,X1,X4] :
      ( in(subset_complement(X0,X4),X1)
      | ~ in(X4,complements_of_subsets(X0,X1))
      | ~ element(X4,powerset(X0))
      | ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
      | ~ element(X1,powerset(powerset(X0))) ),
    inference(equality_resolution,[],[f167]) ).

cnf(c_74,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ open_subset(sK0(X1,X0),X1)
    | ~ top_str(X1)
    | open_subsets(X0,X1) ),
    inference(cnf_transformation,[],[f162]) ).

cnf(c_75,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ top_str(X1)
    | in(sK0(X1,X0),X0)
    | open_subsets(X0,X1) ),
    inference(cnf_transformation,[],[f161]) ).

cnf(c_77,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ in(X2,X0)
    | ~ open_subsets(X0,X1)
    | ~ top_str(X1)
    | open_subset(X2,X1) ),
    inference(cnf_transformation,[],[f159]) ).

cnf(c_78,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ closed_subset(sK1(X1,X0),X1)
    | ~ top_str(X1)
    | closed_subsets(X0,X1) ),
    inference(cnf_transformation,[],[f166]) ).

cnf(c_79,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ top_str(X1)
    | in(sK1(X1,X0),X0)
    | closed_subsets(X0,X1) ),
    inference(cnf_transformation,[],[f165]) ).

cnf(c_80,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ top_str(X1)
    | element(sK1(X1,X0),powerset(the_carrier(X1)))
    | closed_subsets(X0,X1) ),
    inference(cnf_transformation,[],[f164]) ).

cnf(c_81,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ element(X2,powerset(the_carrier(X1)))
    | ~ in(X2,X0)
    | ~ closed_subsets(X0,X1)
    | ~ top_str(X1)
    | closed_subset(X2,X1) ),
    inference(cnf_transformation,[],[f163]) ).

cnf(c_86,plain,
    ( ~ element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
    | ~ in(X2,complements_of_subsets(X0,X1))
    | ~ element(X1,powerset(powerset(X0)))
    | ~ element(X2,powerset(X0))
    | in(subset_complement(X0,X2),X1) ),
    inference(cnf_transformation,[],[f213]) ).

cnf(c_87,plain,
    ( ~ element(X0,powerset(X1))
    | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(cnf_transformation,[],[f172]) ).

cnf(c_88,plain,
    ( ~ element(X0,powerset(powerset(X1)))
    | element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
    inference(cnf_transformation,[],[f173]) ).

cnf(c_90,plain,
    element(sK4(X0),X0),
    inference(cnf_transformation,[],[f175]) ).

cnf(c_91,plain,
    ~ empty(powerset(X0)),
    inference(cnf_transformation,[],[f176]) ).

cnf(c_98,plain,
    ( ~ element(X0,powerset(X1))
    | subset_complement(X1,subset_complement(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f183]) ).

cnf(c_99,plain,
    ( ~ element(X0,powerset(powerset(X1)))
    | complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
    inference(cnf_transformation,[],[f184]) ).

cnf(c_106,plain,
    ( ~ empty(sK6(X0))
    | empty(X0) ),
    inference(cnf_transformation,[],[f192]) ).

cnf(c_107,plain,
    ( element(sK6(X0),powerset(X0))
    | empty(X0) ),
    inference(cnf_transformation,[],[f191]) ).

cnf(c_111,negated_conjecture,
    ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subsets(sK9,sK8) ),
    inference(cnf_transformation,[],[f199]) ).

cnf(c_112,negated_conjecture,
    ( closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | open_subsets(sK9,sK8) ),
    inference(cnf_transformation,[],[f198]) ).

cnf(c_113,negated_conjecture,
    element(sK9,powerset(powerset(the_carrier(sK8)))),
    inference(cnf_transformation,[],[f197]) ).

cnf(c_114,negated_conjecture,
    top_str(sK8),
    inference(cnf_transformation,[],[f196]) ).

cnf(c_115,plain,
    ( ~ in(X0,X1)
    | element(X0,X1) ),
    inference(cnf_transformation,[],[f200]) ).

cnf(c_116,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,[],[f202]) ).

cnf(c_118,plain,
    ( ~ element(X0,X1)
    | in(X0,X1)
    | empty(X1) ),
    inference(cnf_transformation,[],[f203]) ).

cnf(c_119,plain,
    ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
    | ~ element(X1,powerset(the_carrier(X0)))
    | ~ top_str(X0)
    | open_subset(X1,X0) ),
    inference(cnf_transformation,[],[f205]) ).

cnf(c_122,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | element(X2,X1) ),
    inference(cnf_transformation,[],[f207]) ).

cnf(c_123,plain,
    ( ~ element(X0,powerset(X1))
    | ~ in(X2,X0)
    | ~ empty(X1) ),
    inference(cnf_transformation,[],[f208]) ).

cnf(c_124,plain,
    ( ~ empty(X0)
    | X0 = empty_set ),
    inference(cnf_transformation,[],[f209]) ).

cnf(c_175,plain,
    ( ~ open_subsets(sK9,sK8)
    | ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8) ),
    inference(prop_impl_just,[status(thm)],[c_111]) ).

cnf(c_176,plain,
    ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subsets(sK9,sK8) ),
    inference(renaming,[status(thm)],[c_175]) ).

cnf(c_233,plain,
    ( ~ element(X0,powerset(powerset(X1)))
    | element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
    inference(prop_impl_just,[status(thm)],[c_88]) ).

cnf(c_488,plain,
    ( ~ in(X0,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1)))
    | ~ element(X0,powerset(X1))
    | in(subset_complement(X1,X0),X2) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_86,c_233]) ).

cnf(c_604,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ in(X2,X0)
    | ~ open_subsets(X0,X1)
    | ~ top_str(X1)
    | open_subset(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_77,c_122]) ).

cnf(c_605,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ in(X2,X0)
    | ~ closed_subsets(X0,X1)
    | ~ top_str(X1)
    | closed_subset(X2,X1) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_81,c_122]) ).

cnf(c_1199,plain,
    ( X0 != sK9
    | X1 != sK8
    | ~ element(X0,powerset(powerset(the_carrier(X1))))
    | ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subset(sK0(X1,X0),X1)
    | ~ top_str(X1) ),
    inference(resolution_lifted,[status(thm)],[c_74,c_176]) ).

cnf(c_1200,plain,
    ( ~ element(sK9,powerset(powerset(the_carrier(sK8))))
    | ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subset(sK0(sK8,sK9),sK8)
    | ~ top_str(sK8) ),
    inference(unflattening,[status(thm)],[c_1199]) ).

cnf(c_1201,plain,
    ( ~ open_subset(sK0(sK8,sK9),sK8)
    | ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_1200,c_114,c_113,c_1200]) ).

cnf(c_1202,plain,
    ( ~ closed_subsets(complements_of_subsets(the_carrier(sK8),sK9),sK8)
    | ~ open_subset(sK0(sK8,sK9),sK8) ),
    inference(renaming,[status(thm)],[c_1201]) ).

cnf(c_1913,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ in(X2,X1)
    | ~ closed_subsets(X1,X0)
    | closed_subset(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_605,c_114]) ).

cnf(c_1914,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | ~ in(X1,X0)
    | ~ closed_subsets(X0,sK8)
    | closed_subset(X1,sK8) ),
    inference(unflattening,[status(thm)],[c_1913]) ).

cnf(c_1927,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ in(X2,X1)
    | ~ open_subsets(X1,X0)
    | open_subset(X2,X0) ),
    inference(resolution_lifted,[status(thm)],[c_604,c_114]) ).

cnf(c_1928,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | ~ in(X1,X0)
    | ~ open_subsets(X0,sK8)
    | open_subset(X1,sK8) ),
    inference(unflattening,[status(thm)],[c_1927]) ).

cnf(c_1965,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | element(sK1(X0,X1),powerset(the_carrier(X0)))
    | closed_subsets(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_80,c_114]) ).

cnf(c_1966,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | element(sK1(sK8,X0),powerset(the_carrier(sK8)))
    | closed_subsets(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_1965]) ).

cnf(c_1977,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | in(sK1(X0,X1),X1)
    | closed_subsets(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_79,c_114]) ).

cnf(c_1978,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | in(sK1(sK8,X0),X0)
    | closed_subsets(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_1977]) ).

cnf(c_1989,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | ~ closed_subset(sK1(X0,X1),X0)
    | closed_subsets(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_78,c_114]) ).

cnf(c_1990,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | ~ closed_subset(sK1(sK8,X0),sK8)
    | closed_subsets(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_1989]) ).

cnf(c_2013,plain,
    ( X0 != sK8
    | ~ element(X1,powerset(powerset(the_carrier(X0))))
    | in(sK0(X0,X1),X1)
    | open_subsets(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_75,c_114]) ).

cnf(c_2014,plain,
    ( ~ element(X0,powerset(powerset(the_carrier(sK8))))
    | in(sK0(sK8,X0),X0)
    | open_subsets(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_2013]) ).

cnf(c_2061,plain,
    ( X0 != sK8
    | ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
    | ~ element(X1,powerset(the_carrier(X0)))
    | open_subset(X1,X0) ),
    inference(resolution_lifted,[status(thm)],[c_114,c_119]) ).

cnf(c_2062,plain,
    ( ~ closed_subset(subset_complement(the_carrier(sK8),X0),sK8)
    | ~ element(X0,powerset(the_carrier(sK8)))
    | open_subset(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_2061]) ).

cnf(c_2073,plain,
    ( X0 != sK8
    | ~ 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_114,c_116]) ).

cnf(c_2074,plain,
    ( ~ open_subset(subset_complement(the_carrier(sK8),X0),sK8)
    | ~ element(X0,powerset(the_carrier(sK8)))
    | closed_subset(X0,sK8) ),
    inference(unflattening,[status(thm)],[c_2073]) ).

cnf(c_7572,plain,
    the_carrier(sK8) = sP0_iProver_def,
    definition ).

cnf(c_7573,plain,
    powerset(sP0_iProver_def) = sP1_iProver_def,
    definition ).

cnf(c_7574,plain,
    powerset(sP1_iProver_def) = sP2_iProver_def,
    definition ).

cnf(c_7575,plain,
    complements_of_subsets(sP0_iProver_def,sK9) = sP3_iProver_def,
    definition ).

cnf(c_7576,negated_conjecture,
    element(sK9,sP2_iProver_def),
    inference(demodulation,[status(thm)],[c_113,c_7572,c_7573,c_7574]) ).

cnf(c_7577,negated_conjecture,
    ( open_subsets(sK9,sK8)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(demodulation,[status(thm)],[c_112,c_7575]) ).

cnf(c_7578,negated_conjecture,
    ( ~ open_subsets(sK9,sK8)
    | ~ closed_subsets(sP3_iProver_def,sK8) ),
    inference(demodulation,[status(thm)],[c_111]) ).

cnf(c_8738,plain,
    ( ~ element(X0,sP2_iProver_def)
    | in(sK1(sK8,X0),X0)
    | closed_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1978,c_7572,c_7573,c_7574]) ).

cnf(c_8745,plain,
    ( ~ element(X0,sP2_iProver_def)
    | in(sK0(sK8,X0),X0)
    | open_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_2014,c_7572,c_7573,c_7574]) ).

cnf(c_8774,plain,
    ~ empty(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7573,c_91]) ).

cnf(c_8968,plain,
    ( in(sK4(X0),X0)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_90,c_118]) ).

cnf(c_9150,plain,
    ( ~ element(X0,powerset(sP1_iProver_def))
    | element(subset_complement(sP1_iProver_def,X0),sP2_iProver_def) ),
    inference(superposition,[status(thm)],[c_7574,c_87]) ).

cnf(c_9152,plain,
    ( ~ element(X0,sP2_iProver_def)
    | element(subset_complement(sP1_iProver_def,X0),sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_9150,c_7574]) ).

cnf(c_9164,plain,
    ( ~ element(sK9,powerset(powerset(the_carrier(sK8))))
    | ~ in(X0,sK9)
    | ~ open_subsets(sK9,sK8)
    | open_subset(X0,sK8) ),
    inference(instantiation,[status(thm)],[c_1928]) ).

cnf(c_9180,plain,
    ( ~ in(X0,subset_complement(X1,X2))
    | ~ element(X2,powerset(X1))
    | element(X0,X1) ),
    inference(superposition,[status(thm)],[c_87,c_122]) ).

cnf(c_9182,plain,
    ( ~ in(X0,sK6(X1))
    | element(X0,X1)
    | empty(X1) ),
    inference(superposition,[status(thm)],[c_107,c_122]) ).

cnf(c_9237,plain,
    ( ~ in(X0,subset_complement(X1,X2))
    | ~ element(X2,powerset(X1))
    | ~ empty(X1) ),
    inference(superposition,[status(thm)],[c_87,c_123]) ).

cnf(c_9246,plain,
    ( ~ in(X0,X1)
    | ~ element(X1,sP1_iProver_def)
    | ~ empty(sP0_iProver_def) ),
    inference(superposition,[status(thm)],[c_7573,c_123]) ).

cnf(c_9388,plain,
    ( ~ element(sK9,powerset(powerset(sP0_iProver_def)))
    | element(sP3_iProver_def,powerset(powerset(sP0_iProver_def))) ),
    inference(superposition,[status(thm)],[c_7575,c_88]) ).

cnf(c_9392,plain,
    ( ~ in(X0,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1)))
    | element(X0,powerset(X1)) ),
    inference(superposition,[status(thm)],[c_88,c_122]) ).

cnf(c_9394,plain,
    ( ~ element(sK9,sP2_iProver_def)
    | element(sP3_iProver_def,sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_9388,c_7573,c_7574]) ).

cnf(c_9395,plain,
    element(sP3_iProver_def,sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_9394,c_7576]) ).

cnf(c_9426,plain,
    ( ~ element(X0,sP2_iProver_def)
    | subset_complement(sP1_iProver_def,subset_complement(sP1_iProver_def,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_7574,c_98]) ).

cnf(c_9522,plain,
    ( ~ element(X2,powerset(powerset(X1)))
    | ~ in(X0,complements_of_subsets(X1,X2))
    | in(subset_complement(X1,X0),X2) ),
    inference(global_subsumption_just,[status(thm)],[c_488,c_488,c_9392]) ).

cnf(c_9523,plain,
    ( ~ in(X0,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1)))
    | in(subset_complement(X1,X0),X2) ),
    inference(renaming,[status(thm)],[c_9522]) ).

cnf(c_10382,plain,
    ~ empty(sP1_iProver_def),
    inference(superposition,[status(thm)],[c_7573,c_91]) ).

cnf(c_12635,plain,
    ( element(sK4(sK6(X0)),X0)
    | empty(sK6(X0))
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_8968,c_9182]) ).

cnf(c_14037,plain,
    ( ~ element(X0,sP1_iProver_def)
    | ~ empty(sP0_iProver_def)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_8968,c_9246]) ).

cnf(c_14960,plain,
    subset_complement(sP1_iProver_def,subset_complement(sP1_iProver_def,sK9)) = sK9,
    inference(superposition,[status(thm)],[c_7576,c_9426]) ).

cnf(c_14967,plain,
    subset_complement(sP1_iProver_def,subset_complement(sP1_iProver_def,sP3_iProver_def)) = sP3_iProver_def,
    inference(superposition,[status(thm)],[c_9395,c_9426]) ).

cnf(c_16280,plain,
    ( element(sK4(sK6(X0)),X0)
    | empty(X0) ),
    inference(global_subsumption_just,[status(thm)],[c_12635,c_106,c_12635]) ).

cnf(c_16293,plain,
    ( in(sK4(sK6(X0)),X0)
    | empty(X0) ),
    inference(superposition,[status(thm)],[c_16280,c_118]) ).

cnf(c_23000,plain,
    ( ~ element(subset_complement(X0,X1),sP2_iProver_def)
    | ~ element(X1,powerset(X0))
    | element(sK1(sK8,subset_complement(X0,X1)),X0)
    | closed_subsets(subset_complement(X0,X1),sK8) ),
    inference(superposition,[status(thm)],[c_8738,c_9180]) ).

cnf(c_23016,plain,
    ( ~ element(subset_complement(sP1_iProver_def,sK9),powerset(sP1_iProver_def))
    | ~ in(X0,sK9)
    | element(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_14960,c_9180]) ).

cnf(c_23025,plain,
    ( ~ element(subset_complement(sP1_iProver_def,sK9),sP2_iProver_def)
    | ~ in(X0,sK9)
    | element(X0,sP1_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_23016,c_7574]) ).

cnf(c_23255,plain,
    ( ~ element(X0,powerset(X1))
    | ~ empty(X1)
    | empty(subset_complement(X1,X0)) ),
    inference(superposition,[status(thm)],[c_16293,c_9237]) ).

cnf(c_23643,plain,
    ( ~ in(X0,sK9)
    | ~ element(sK9,sP2_iProver_def)
    | element(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_9152,c_23025]) ).

cnf(c_23644,plain,
    ( ~ in(X0,sK9)
    | element(X0,sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23643,c_7576]) ).

cnf(c_23661,plain,
    ( ~ element(sK9,sP2_iProver_def)
    | element(sK0(sK8,sK9),sP1_iProver_def)
    | open_subsets(sK9,sK8) ),
    inference(superposition,[status(thm)],[c_8745,c_23644]) ).

cnf(c_23671,plain,
    ( element(sK0(sK8,sK9),sP1_iProver_def)
    | open_subsets(sK9,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_23661,c_7576]) ).

cnf(c_23726,plain,
    ( ~ empty(sP0_iProver_def)
    | empty(sK0(sK8,sK9))
    | open_subsets(sK9,sK8) ),
    inference(superposition,[status(thm)],[c_23671,c_14037]) ).

cnf(c_37602,plain,
    ( ~ element(subset_complement(sP1_iProver_def,subset_complement(sP1_iProver_def,sP3_iProver_def)),sP2_iProver_def)
    | ~ element(subset_complement(sP1_iProver_def,sP3_iProver_def),powerset(sP1_iProver_def))
    | closed_subsets(subset_complement(sP1_iProver_def,subset_complement(sP1_iProver_def,sP3_iProver_def)),sK8)
    | element(sK1(sK8,sP3_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_14967,c_23000]) ).

cnf(c_37642,plain,
    ( ~ element(subset_complement(sP1_iProver_def,sP3_iProver_def),sP2_iProver_def)
    | ~ element(sP3_iProver_def,sP2_iProver_def)
    | element(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(light_normalisation,[status(thm)],[c_37602,c_7574,c_14967]) ).

cnf(c_37643,plain,
    ( ~ element(subset_complement(sP1_iProver_def,sP3_iProver_def),sP2_iProver_def)
    | element(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_37642,c_9395]) ).

cnf(c_38245,plain,
    ( ~ element(sP3_iProver_def,sP2_iProver_def)
    | element(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(superposition,[status(thm)],[c_9152,c_37643]) ).

cnf(c_38246,plain,
    ( element(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_38245,c_9395]) ).

cnf(c_38255,plain,
    ( in(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8)
    | empty(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_38246,c_118]) ).

cnf(c_38263,plain,
    ( in(sK1(sK8,sP3_iProver_def),sP1_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_38255,c_8774]) ).

cnf(c_38651,plain,
    ( ~ element(X0,sP2_iProver_def)
    | in(sK1(sK8,X0),X0)
    | closed_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1978,c_7572,c_7573,c_7574]) ).

cnf(c_38658,plain,
    ( ~ element(X0,sP2_iProver_def)
    | in(sK0(sK8,X0),X0)
    | open_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_2014,c_7572,c_7573,c_7574]) ).

cnf(c_38679,plain,
    ( ~ closed_subset(sK1(sK8,X0),sK8)
    | ~ element(X0,sP2_iProver_def)
    | closed_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1990,c_7572,c_7573,c_7574]) ).

cnf(c_38698,plain,
    ( ~ closed_subset(subset_complement(sP0_iProver_def,X0),sK8)
    | ~ element(X0,sP1_iProver_def)
    | open_subset(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_2062,c_7572,c_7573]) ).

cnf(c_38706,plain,
    ( ~ open_subset(subset_complement(sP0_iProver_def,X0),sK8)
    | ~ element(X0,sP1_iProver_def)
    | closed_subset(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_2074,c_7572,c_7573]) ).

cnf(c_38714,plain,
    ( ~ element(X0,sP2_iProver_def)
    | element(sK1(sK8,X0),sP1_iProver_def)
    | closed_subsets(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1966,c_7572,c_7573,c_7574]) ).

cnf(c_38728,plain,
    ( ~ in(X0,X1)
    | ~ element(X1,sP2_iProver_def)
    | ~ closed_subsets(X1,sK8)
    | closed_subset(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1914,c_7572,c_7573,c_7574]) ).

cnf(c_38743,plain,
    ( ~ in(X0,X1)
    | ~ element(X1,sP2_iProver_def)
    | ~ open_subsets(X1,sK8)
    | open_subset(X0,sK8) ),
    inference(light_normalisation,[status(thm)],[c_1928,c_7572,c_7573,c_7574]) ).

cnf(c_39034,plain,
    ( ~ in(X0,X1)
    | ~ element(X1,sP2_iProver_def)
    | element(X0,sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_7574,c_122]) ).

cnf(c_39096,plain,
    ( ~ element(sK9,powerset(powerset(sP0_iProver_def)))
    | element(sP3_iProver_def,powerset(powerset(sP0_iProver_def))) ),
    inference(superposition,[status(thm)],[c_7575,c_88]) ).

cnf(c_39102,plain,
    ( ~ element(sK9,sP2_iProver_def)
    | element(sP3_iProver_def,sP2_iProver_def) ),
    inference(light_normalisation,[status(thm)],[c_39096,c_7573,c_7574]) ).

cnf(c_39103,plain,
    element(sP3_iProver_def,sP2_iProver_def),
    inference(forward_subsumption_resolution,[status(thm)],[c_39102,c_7576]) ).

cnf(c_39190,plain,
    ( ~ element(X0,sP1_iProver_def)
    | subset_complement(sP0_iProver_def,subset_complement(sP0_iProver_def,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_7573,c_98]) ).

cnf(c_39220,plain,
    ( ~ element(X0,powerset(sP1_iProver_def))
    | complements_of_subsets(sP0_iProver_def,complements_of_subsets(sP0_iProver_def,X0)) = X0 ),
    inference(superposition,[status(thm)],[c_7573,c_99]) ).

cnf(c_39224,plain,
    ( ~ element(X0,sP2_iProver_def)
    | complements_of_subsets(sP0_iProver_def,complements_of_subsets(sP0_iProver_def,X0)) = X0 ),
    inference(light_normalisation,[status(thm)],[c_39220,c_7574]) ).

cnf(c_39238,plain,
    ( ~ element(X2,powerset(powerset(X1)))
    | ~ in(X0,complements_of_subsets(X1,X2))
    | in(subset_complement(X1,X0),X2) ),
    inference(global_subsumption_just,[status(thm)],[c_488,c_9523]) ).

cnf(c_39239,plain,
    ( ~ in(X0,complements_of_subsets(X1,X2))
    | ~ element(X2,powerset(powerset(X1)))
    | in(subset_complement(X1,X0),X2) ),
    inference(renaming,[status(thm)],[c_39238]) ).

cnf(c_39254,plain,
    ( ~ in(X0,complements_of_subsets(sP0_iProver_def,X1))
    | ~ element(X1,powerset(sP1_iProver_def))
    | in(subset_complement(sP0_iProver_def,X0),X1) ),
    inference(superposition,[status(thm)],[c_7573,c_39239]) ).

cnf(c_39262,plain,
    ( ~ in(X0,complements_of_subsets(sP0_iProver_def,X1))
    | ~ element(X1,sP2_iProver_def)
    | in(subset_complement(sP0_iProver_def,X0),X1) ),
    inference(light_normalisation,[status(thm)],[c_39254,c_7574]) ).

cnf(c_40378,plain,
    ( ~ element(X0,sP2_iProver_def)
    | subset_complement(sP0_iProver_def,subset_complement(sP0_iProver_def,sK1(sK8,X0))) = sK1(sK8,X0)
    | closed_subsets(X0,sK8) ),
    inference(superposition,[status(thm)],[c_38714,c_39190]) ).

cnf(c_40417,plain,
    complements_of_subsets(sP0_iProver_def,complements_of_subsets(sP0_iProver_def,sK9)) = sK9,
    inference(superposition,[status(thm)],[c_7576,c_39224]) ).

cnf(c_40424,plain,
    complements_of_subsets(sP0_iProver_def,sP3_iProver_def) = sK9,
    inference(light_normalisation,[status(thm)],[c_40417,c_7575]) ).

cnf(c_40737,plain,
    ( subset_complement(sP0_iProver_def,subset_complement(sP0_iProver_def,sK1(sK8,sP3_iProver_def))) = sK1(sK8,sP3_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(superposition,[status(thm)],[c_39103,c_40378]) ).

cnf(c_41195,plain,
    ( ~ in(X0,sP3_iProver_def)
    | ~ element(sK9,sP2_iProver_def)
    | in(subset_complement(sP0_iProver_def,X0),sK9) ),
    inference(superposition,[status(thm)],[c_7575,c_39262]) ).

cnf(c_41197,plain,
    ( ~ in(X0,sK9)
    | ~ element(sP3_iProver_def,sP2_iProver_def)
    | in(subset_complement(sP0_iProver_def,X0),sP3_iProver_def) ),
    inference(superposition,[status(thm)],[c_40424,c_39262]) ).

cnf(c_41198,plain,
    ( ~ in(X0,sK9)
    | in(subset_complement(sP0_iProver_def,X0),sP3_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41197,c_39103]) ).

cnf(c_41201,plain,
    ( ~ in(X0,sP3_iProver_def)
    | in(subset_complement(sP0_iProver_def,X0),sK9) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41195,c_7576]) ).

cnf(c_41271,plain,
    ( ~ in(X0,sP3_iProver_def)
    | ~ element(sK9,sP2_iProver_def)
    | ~ open_subsets(sK9,sK8)
    | open_subset(subset_complement(sP0_iProver_def,X0),sK8) ),
    inference(superposition,[status(thm)],[c_41201,c_38743]) ).

cnf(c_41298,plain,
    ( ~ in(X0,sP3_iProver_def)
    | ~ open_subsets(sK9,sK8)
    | open_subset(subset_complement(sP0_iProver_def,X0),sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41271,c_7576]) ).

cnf(c_41358,plain,
    ( ~ in(X0,sP3_iProver_def)
    | ~ element(X0,sP1_iProver_def)
    | ~ open_subsets(sK9,sK8)
    | closed_subset(X0,sK8) ),
    inference(superposition,[status(thm)],[c_41298,c_38706]) ).

cnf(c_41423,plain,
    ( ~ in(X0,sK9)
    | ~ element(sP3_iProver_def,sP2_iProver_def)
    | element(subset_complement(sP0_iProver_def,X0),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_41198,c_39034]) ).

cnf(c_41429,plain,
    ( ~ in(X0,sK9)
    | ~ element(sP3_iProver_def,sP2_iProver_def)
    | ~ closed_subsets(sP3_iProver_def,sK8)
    | closed_subset(subset_complement(sP0_iProver_def,X0),sK8) ),
    inference(superposition,[status(thm)],[c_41198,c_38728]) ).

cnf(c_41447,plain,
    ( ~ in(X0,sK9)
    | element(subset_complement(sP0_iProver_def,X0),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41423,c_39103]) ).

cnf(c_41450,plain,
    ( ~ in(X0,sK9)
    | ~ closed_subsets(sP3_iProver_def,sK8)
    | closed_subset(subset_complement(sP0_iProver_def,X0),sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41429,c_39103]) ).

cnf(c_41680,plain,
    ( ~ in(X0,sK9)
    | in(subset_complement(sP0_iProver_def,X0),sP1_iProver_def)
    | empty(sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_41447,c_118]) ).

cnf(c_41682,plain,
    ( ~ in(X0,sK9)
    | in(subset_complement(sP0_iProver_def,X0),sP1_iProver_def) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_41680,c_10382]) ).

cnf(c_42284,plain,
    ( ~ in(X0,sK9)
    | ~ element(X0,sP1_iProver_def)
    | ~ closed_subsets(sP3_iProver_def,sK8)
    | open_subset(X0,sK8) ),
    inference(superposition,[status(thm)],[c_41450,c_38698]) ).

cnf(c_59755,plain,
    ( ~ empty(X0)
    | empty(subset_complement(X0,sK4(powerset(X0)))) ),
    inference(superposition,[status(thm)],[c_90,c_23255]) ).

cnf(c_61706,plain,
    ( ~ empty(X0)
    | subset_complement(X0,sK4(powerset(X0))) = empty_set ),
    inference(superposition,[status(thm)],[c_59755,c_124]) ).

cnf(c_64882,plain,
    ( ~ empty(sP0_iProver_def)
    | subset_complement(sK0(sK8,sK9),sK4(powerset(sK0(sK8,sK9)))) = empty_set
    | open_subsets(sK9,sK8) ),
    inference(superposition,[status(thm)],[c_23726,c_61706]) ).

cnf(c_66011,plain,
    ( ~ in(X0,sK9)
    | open_subset(X0,sK8) ),
    inference(global_subsumption_just,[status(thm)],[c_42284,c_113,c_7577,c_9164,c_23644,c_42284]) ).

cnf(c_66021,plain,
    ( ~ element(sK9,sP2_iProver_def)
    | open_subset(sK0(sK8,sK9),sK8)
    | open_subsets(sK9,sK8) ),
    inference(superposition,[status(thm)],[c_38658,c_66011]) ).

cnf(c_66032,plain,
    ( open_subset(sK0(sK8,sK9),sK8)
    | open_subsets(sK9,sK8) ),
    inference(forward_subsumption_resolution,[status(thm)],[c_66021,c_7576]) ).

cnf(c_68228,plain,
    open_subsets(sK9,sK8),
    inference(global_subsumption_just,[status(thm)],[c_64882,c_112,c_1202,c_66032]) ).

cnf(c_70402,plain,
    open_subsets(sK9,sK8),
    inference(global_subsumption_just,[status(thm)],[c_66032,c_68228]) ).

cnf(c_70405,plain,
    ( ~ in(X0,sP3_iProver_def)
    | ~ element(X0,sP1_iProver_def)
    | closed_subset(X0,sK8) ),
    inference(backward_subsumption_resolution,[status(thm)],[c_41358,c_70402]) ).

cnf(c_70409,plain,
    ~ closed_subsets(sP3_iProver_def,sK8),
    inference(backward_subsumption_resolution,[status(thm)],[c_7578,c_70402]) ).

cnf(c_70419,plain,
    subset_complement(sP0_iProver_def,subset_complement(sP0_iProver_def,sK1(sK8,sP3_iProver_def))) = sK1(sK8,sP3_iProver_def),
    inference(backward_subsumption_resolution,[status(thm)],[c_40737,c_70409]) ).

cnf(c_72162,plain,
    ( ~ in(subset_complement(sP0_iProver_def,sK1(sK8,sP3_iProver_def)),sK9)
    | in(sK1(sK8,sP3_iProver_def),sP1_iProver_def) ),
    inference(superposition,[status(thm)],[c_70419,c_41682]) ).

cnf(c_74016,plain,
    in(sK1(sK8,sP3_iProver_def),sP1_iProver_def),
    inference(global_subsumption_just,[status(thm)],[c_72162,c_7578,c_38263,c_68228]) ).

cnf(c_74023,plain,
    element(sK1(sK8,sP3_iProver_def),sP1_iProver_def),
    inference(superposition,[status(thm)],[c_74016,c_115]) ).

cnf(c_74492,plain,
    ( ~ in(sK1(sK8,sP3_iProver_def),sP3_iProver_def)
    | closed_subset(sK1(sK8,sP3_iProver_def),sK8) ),
    inference(superposition,[status(thm)],[c_74023,c_70405]) ).

cnf(c_75512,plain,
    ( ~ element(sP3_iProver_def,sP2_iProver_def)
    | closed_subset(sK1(sK8,sP3_iProver_def),sK8)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(superposition,[status(thm)],[c_38651,c_74492]) ).

cnf(c_75513,plain,
    closed_subset(sK1(sK8,sP3_iProver_def),sK8),
    inference(forward_subsumption_resolution,[status(thm)],[c_75512,c_70409,c_39103]) ).

cnf(c_75514,plain,
    ( ~ element(sP3_iProver_def,sP2_iProver_def)
    | closed_subsets(sP3_iProver_def,sK8) ),
    inference(superposition,[status(thm)],[c_75513,c_38679]) ).

cnf(c_75515,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_75514,c_70409,c_39103]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU337+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13  % Command  : run_iprover %s %d THM
% 0.12/0.34  % Computer : n027.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 : Thu May  2 18:21:35 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.20/0.47  Running first-order theorem proving
% 0.20/0.47  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
% 17.41/3.22  % SZS status Started for theBenchmark.p
% 17.41/3.22  % SZS status Theorem for theBenchmark.p
% 17.41/3.22  
% 17.41/3.22  %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 17.41/3.22  
% 17.41/3.22  ------  iProver source info
% 17.41/3.22  
% 17.41/3.22  git: date: 2024-05-02 19:28:25 +0000
% 17.41/3.22  git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 17.41/3.22  git: non_committed_changes: false
% 17.41/3.22  
% 17.41/3.22  ------ Parsing...
% 17.41/3.22  ------ Clausification by vclausify_rel  & Parsing by iProver...
% 17.41/3.22  
% 17.41/3.22  ------ Preprocessing... sup_sim: 0  sf_s  rm: 40 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e  sup_sim: 0  sf_s  rm: 7 0s  sf_e  pe_s  pe_e 
% 17.41/3.22  
% 17.41/3.22  ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e 
% 17.41/3.22  
% 17.41/3.22  ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 17.41/3.22  ------ Proving...
% 17.41/3.22  ------ Problem Properties 
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  clauses                                 57
% 17.41/3.22  conjectures                             3
% 17.41/3.22  EPR                                     11
% 17.41/3.22  Horn                                    44
% 17.41/3.22  unary                                   12
% 17.41/3.22  binary                                  12
% 17.41/3.22  lits                                    146
% 17.41/3.22  lits eq                                 11
% 17.41/3.22  fd_pure                                 0
% 17.41/3.22  fd_pseudo                               0
% 17.41/3.22  fd_cond                                 1
% 17.41/3.22  fd_pseudo_cond                          4
% 17.41/3.22  AC symbols                              0
% 17.41/3.22  
% 17.41/3.22  ------ Schedule dynamic 5 is on 
% 17.41/3.22  
% 17.41/3.22  ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  ------ 
% 17.41/3.22  Current options:
% 17.41/3.22  ------ 
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  ------ Proving...
% 17.41/3.22  
% 17.41/3.22  
% 17.41/3.22  % SZS status Theorem for theBenchmark.p
% 17.41/3.22  
% 17.41/3.22  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.41/3.22  
% 17.41/3.22  
%------------------------------------------------------------------------------