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iProver---3.9.4.THM-CRf.s

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%------------------------------------------------------------------------------
% File     : iProver---3.9.4
% Problem  : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri Sep 25 02:56:52 PM UTC 2026

% Result   : Theorem 1.11s 1.73s
% Output   : CNFRefutation 1.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   83 (  21 unt;   0 def)
%            Number of atoms       :  256 (  58 equ)
%            Maximal formula atoms :    9 (   3 avg)
%            Number of connectives :  287 ( 114   ~; 112   |;  35   &)
%                                         (   2 <=>;  24  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   99 (   0 sgn  91   !;   8   ?;  33   :)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X0] :
      ( top_str(X0)
     => ! [X1] :
          ( element(X1,powerset(the_carrier(X0)))
         => interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_tops_1) ).

fof(f4,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(f15,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(the_carrier(X0)))
        & open_subset(X1,X0)
        & top_str(X0)
        & topological_space(X0) )
     => closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc4_tops_1) ).

fof(f16,axiom,
    ! [X0,X1] :
      ( ( element(X1,powerset(the_carrier(X0)))
        & top_str(X0)
        & topological_space(X0) )
     => open_subset(interior(X0,X1),X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc6_tops_1) ).

fof(f17,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(f22,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(f24,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/sandbox2/benchmark/theBenchmark.p',t52_pre_topc) ).

fof(f25,conjecture,
    ! [X0] :
      ( ( top_str(X0)
        & topological_space(X0) )
     => ! [X1] :
          ( top_str(X1)
         => ! [X2] :
              ( element(X2,powerset(the_carrier(X0)))
             => ! [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                 => ( ( interior(X0,X2) = X2
                     => open_subset(X2,X0) )
                    & ( open_subset(X3,X1)
                     => interior(X1,X3) = X3 ) ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t55_tops_1) ).

fof(f26,negated_conjecture,
    ~ ! [X0] :
        ( ( top_str(X0)
          & topological_space(X0) )
       => ! [X1] :
            ( top_str(X1)
           => ! [X2] :
                ( element(X2,powerset(the_carrier(X0)))
               => ! [X3] :
                    ( element(X3,powerset(the_carrier(X1)))
                   => ( ( interior(X0,X2) = X2
                       => open_subset(X2,X0) )
                      & ( open_subset(X3,X1)
                       => interior(X1,X3) = X3 ) ) ) ) ) ),
    inference(negated_conjecture,[status(cth)],[f25]) ).

fof(f27,plain,
    ? [X0] :
      ( top_str(X0)
      & topological_space(X0)
      & ? [X1] :
          ( top_str(X1)
          & ? [X2] :
              ( element(X2,powerset(the_carrier(X0)))
              & ? [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                  & ( ( interior(X0,X2) = X2
                      & ~ open_subset(X2,X0) )
                    | ( open_subset(X3,X1)
                      & interior(X1,X3) != X3 ) ) ) ) ) ),
    inference(ennf_transformation,[],[f26]) ).

fof(f28,plain,
    ? [X0] :
      ( top_str(X0)
      & topological_space(X0)
      & ? [X1] :
          ( top_str(X1)
          & ? [X2] :
              ( element(X2,powerset(the_carrier(X0)))
              & ? [X3] :
                  ( element(X3,powerset(the_carrier(X1)))
                  & ( ( interior(X0,X2) = X2
                      & ~ open_subset(X2,X0) )
                    | ( open_subset(X3,X1)
                      & interior(X1,X3) != X3 ) ) ) ) ) ),
    inference(flattening,[],[f27]) ).

fof(f29,plain,
    ! [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 ) ) ) ),
    inference(ennf_transformation,[],[f24]) ).

fof(f30,plain,
    ! [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 ) ) ) ),
    inference(flattening,[],[f29]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | subset_complement(X0,subset_complement(X0,X1)) = X1 ),
    inference(ennf_transformation,[],[f17]) ).

fof(f32,plain,
    ! [X0] :
      ( ~ top_str(X0)
      | ! [X1] :
          ( ~ element(X1,powerset(the_carrier(X0)))
          | interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | open_subset(interior(X0,X1),X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f34,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | open_subset(interior(X0,X1),X0) ),
    inference(flattening,[],[f33]) ).

fof(f43,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ open_subset(X1,X0)
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f44,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ open_subset(X1,X0)
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(flattening,[],[f43]) ).

fof(f47,plain,
    ! [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(ennf_transformation,[],[f22]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | element(subset_complement(X0,X1),powerset(X0)) ),
    inference(ennf_transformation,[],[f4]) ).

fof(f53,plain,
    ( top_str(sK0)
    & topological_space(sK0)
    & top_str(sK1)
    & element(sK2,powerset(the_carrier(sK0)))
    & element(sK3,powerset(the_carrier(sK1)))
    & ( ( sK2 = interior(sK0,sK2)
        & ~ open_subset(sK2,sK0) )
      | ( open_subset(sK3,sK1)
        & sK3 != interior(sK1,sK3) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f28]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ top_str(X0)
      | ! [X1] :
          ( ~ element(X1,powerset(the_carrier(X0)))
          | ( ( ~ 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) ) ) ) ),
    inference(nnf_transformation,[],[f47]) ).

fof(f60,plain,
    top_str(sK0),
    inference(cnf_transformation,[],[f53]) ).

fof(f61,plain,
    topological_space(sK0),
    inference(cnf_transformation,[],[f53]) ).

fof(f62,plain,
    top_str(sK1),
    inference(cnf_transformation,[],[f53]) ).

fof(f63,plain,
    element(sK2,powerset(the_carrier(sK0))),
    inference(cnf_transformation,[],[f53]) ).

fof(f64,plain,
    element(sK3,powerset(the_carrier(sK1))),
    inference(cnf_transformation,[],[f53]) ).

fof(f65,plain,
    ( sK2 = interior(sK0,sK2)
    | open_subset(sK3,sK1) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f66,plain,
    ( ~ open_subset(sK2,sK0)
    | open_subset(sK3,sK1) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f67,plain,
    ( sK2 = interior(sK0,sK2)
    | sK3 != interior(sK1,sK3) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f68,plain,
    ( ~ open_subset(sK2,sK0)
    | sK3 != interior(sK1,sK3) ),
    inference(cnf_transformation,[],[f53]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ closed_subset(X1,X0)
      | topstr_closure(X0,X1) = X1 ),
    inference(cnf_transformation,[],[f30]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | subset_complement(X0,subset_complement(X0,X1)) = X1 ),
    inference(cnf_transformation,[],[f31]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | interior(X0,X1) = subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) ),
    inference(cnf_transformation,[],[f32]) ).

fof(f75,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | open_subset(interior(X0,X1),X0) ),
    inference(cnf_transformation,[],[f34]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(the_carrier(X0)))
      | ~ open_subset(X1,X0)
      | ~ top_str(X0)
      | ~ topological_space(X0)
      | closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(cnf_transformation,[],[f44]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ open_subset(X1,X0)
      | closed_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ element(X1,powerset(X0))
      | element(subset_complement(X0,X1),powerset(X0)) ),
    inference(cnf_transformation,[],[f52]) ).

tcf(c_49,negated_conjecture,
    ( ~ open_subset(sK2,sK0)
    | ( interior(sK1,sK3) != sK3 ) ),
    inference(cnf_transformation,[],[f68]) ).

tcf(c_50,negated_conjecture,
    ( ( interior(sK0,sK2) = sK2 )
    | ( interior(sK1,sK3) != sK3 ) ),
    inference(cnf_transformation,[],[f67]) ).

tcf(c_51,negated_conjecture,
    ( open_subset(sK3,sK1)
    | ~ open_subset(sK2,sK0) ),
    inference(cnf_transformation,[],[f66]) ).

tcf(c_52,negated_conjecture,
    ( open_subset(sK3,sK1)
    | ( interior(sK0,sK2) = sK2 ) ),
    inference(cnf_transformation,[],[f65]) ).

tcf(c_53,negated_conjecture,
    element(sK3,powerset(the_carrier(sK1))),
    inference(cnf_transformation,[],[f64]) ).

tcf(c_54,negated_conjecture,
    element(sK2,powerset(the_carrier(sK0))),
    inference(cnf_transformation,[],[f63]) ).

tcf(c_55,negated_conjecture,
    top_str(sK1),
    inference(cnf_transformation,[],[f62]) ).

tcf(c_56,negated_conjecture,
    topological_space(sK0),
    inference(cnf_transformation,[],[f61]) ).

tcf(c_57,negated_conjecture,
    top_str(sK0),
    inference(cnf_transformation,[],[f60]) ).

tcf(c_58,plain,
    ! [X0: $i,X1: $i] :
      ( ( topstr_closure(X1,X0) = X0 )
      | ~ top_str(X1)
      | ~ closed_subset(X0,X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f70]) ).

tcf(c_60,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f71]) ).

tcf(c_61,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset_complement(the_carrier(X1),topstr_closure(X1,subset_complement(the_carrier(X1),X0))) = interior(X1,X0) )
      | ~ top_str(X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f72]) ).

tcf(c_64,plain,
    ! [X0: $i,X1: $i] :
      ( open_subset(interior(X1,X0),X1)
      | ~ topological_space(X1)
      | ~ top_str(X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f75]) ).

tcf(c_73,plain,
    ! [X0: $i,X1: $i] :
      ( closed_subset(subset_complement(the_carrier(X1),X0),X1)
      | ~ topological_space(X1)
      | ~ top_str(X1)
      | ~ open_subset(X0,X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f84]) ).

tcf(c_76,plain,
    ! [X0: $i,X1: $i] :
      ( closed_subset(subset_complement(the_carrier(X1),X0),X1)
      | ~ top_str(X1)
      | ~ open_subset(X0,X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(cnf_transformation,[],[f86]) ).

tcf(c_79,plain,
    ! [X0: $i,X1: $i] :
      ( element(subset_complement(X1,X0),powerset(X1))
      | ~ element(X0,powerset(X1)) ),
    inference(cnf_transformation,[],[f90]) ).

tcf(c_100,plain,
    ! [X0: $i,X1: $i] :
      ( closed_subset(subset_complement(the_carrier(X1),X0),X1)
      | ~ element(X0,powerset(the_carrier(X1)))
      | ~ open_subset(X0,X1)
      | ~ top_str(X1) ),
    inference(global_subsumption_just,[status(thm)],[c_73,c_76]) ).

tcf(c_101,plain,
    ! [X0: $i,X1: $i] :
      ( closed_subset(subset_complement(the_carrier(X1),X0),X1)
      | ~ top_str(X1)
      | ~ open_subset(X0,X1)
      | ~ element(X0,powerset(the_carrier(X1))) ),
    inference(renaming,[status(thm)],[c_100]) ).

tcf(c_506,plain,
    ! [X0: $i,X1: $i] :
      ( open_subset(interior(X0,X1),X0)
      | ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ( X0 != sK0 ) ),
    inference(resolution_lifted,[status(thm)],[c_56,c_64]) ).

tcf(c_507,plain,
    ! [X0: $i] :
      ( open_subset(interior(sK0,X0),sK0)
      | ~ top_str(sK0)
      | ~ element(X0,powerset(the_carrier(sK0))) ),
    inference(unflattening,[status(thm)],[c_506]) ).

tcf(c_509,plain,
    ! [X0: $i] :
      ( open_subset(interior(sK0,X0),sK0)
      | ~ element(X0,powerset(the_carrier(sK0))) ),
    inference(global_subsumption_just,[status(thm)],[c_507,c_57,c_507]) ).

tcf(c_556,plain,
    ! [X0: $i,X1: $i] :
      ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
      | ~ open_subset(X1,X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_101]) ).

tcf(c_557,plain,
    ! [X0: $i] :
      ( closed_subset(subset_complement(the_carrier(sK1),X0),sK1)
      | ~ open_subset(X0,sK1)
      | ~ element(X0,powerset(the_carrier(sK1))) ),
    inference(unflattening,[status(thm)],[c_556]) ).

tcf(c_577,plain,
    ! [X0: $i,X1: $i] :
      ( ( subset_complement(the_carrier(X0),topstr_closure(X0,subset_complement(the_carrier(X0),X1))) = interior(X0,X1) )
      | ~ element(X1,powerset(the_carrier(X0)))
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_61]) ).

tcf(c_578,plain,
    ! [X0: $i] :
      ( ( subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),X0))) = interior(sK1,X0) )
      | ~ element(X0,powerset(the_carrier(sK1))) ),
    inference(unflattening,[status(thm)],[c_577]) ).

tcf(c_586,plain,
    ! [X0: $i,X1: $i] :
      ( ( topstr_closure(X0,X1) = X1 )
      | ~ closed_subset(X1,X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ( X0 != sK1 ) ),
    inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).

tcf(c_587,plain,
    ! [X0: $i] :
      ( ( topstr_closure(sK1,X0) = X0 )
      | ~ closed_subset(X0,sK1)
      | ~ element(X0,powerset(the_carrier(sK1))) ),
    inference(unflattening,[status(thm)],[c_586]) ).

tcf(c_2212,plain,
    subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK3)) = sK3,
    inference(superposition,[status(thm)],[c_53,c_60]) ).

tcf(c_2242,plain,
    open_subset(interior(sK0,sK2),sK0),
    inference(superposition,[status(thm)],[c_54,c_509]) ).

tcf(c_2361,plain,
    ! [X0: $i] :
      ( ( topstr_closure(sK1,subset_complement(the_carrier(sK1),X0)) = subset_complement(the_carrier(sK1),X0) )
      | ~ element(X0,powerset(the_carrier(sK1)))
      | ~ closed_subset(subset_complement(the_carrier(sK1),X0),sK1) ),
    inference(superposition,[status(thm)],[c_79,c_587]) ).

tcf(c_2530,plain,
    subset_complement(the_carrier(sK1),topstr_closure(sK1,subset_complement(the_carrier(sK1),sK3))) = interior(sK1,sK3),
    inference(superposition,[status(thm)],[c_53,c_578]) ).

tcf(c_5311,plain,
    ! [X0: $i] :
      ( ( topstr_closure(sK1,subset_complement(the_carrier(sK1),X0)) = subset_complement(the_carrier(sK1),X0) )
      | ~ open_subset(X0,sK1)
      | ~ element(X0,powerset(the_carrier(sK1))) ),
    inference(superposition,[status(thm)],[c_557,c_2361]) ).

tcf(c_5373,plain,
    ( ( topstr_closure(sK1,subset_complement(the_carrier(sK1),sK3)) = subset_complement(the_carrier(sK1),sK3) )
    | ~ open_subset(sK3,sK1) ),
    inference(superposition,[status(thm)],[c_53,c_5311]) ).

tcf(c_5420,plain,
    ( ( interior(sK0,sK2) = sK2 )
    | ( topstr_closure(sK1,subset_complement(the_carrier(sK1),sK3)) = subset_complement(the_carrier(sK1),sK3) ) ),
    inference(superposition,[status(thm)],[c_52,c_5373]) ).

tcf(c_5437,plain,
    ( ( interior(sK0,sK2) = sK2 )
    | ( subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK3)) = interior(sK1,sK3) ) ),
    inference(superposition,[status(thm)],[c_5420,c_2530]) ).

tcf(c_5438,plain,
    ( ( interior(sK0,sK2) = sK2 )
    | ( interior(sK1,sK3) = sK3 ) ),
    inference(light_normalisation,[status(thm)],[c_5437,c_2212]) ).

tcf(c_5540,plain,
    interior(sK0,sK2) = sK2,
    inference(global_subsumption_just,[status(thm)],[c_5438,c_50,c_5438]) ).

tcf(c_5558,plain,
    open_subset(sK2,sK0),
    inference(demodulation,[status(thm)],[c_2242,c_5540]) ).

tcf(c_5560,plain,
    open_subset(sK3,sK1),
    inference(backward_subsumption_resolution,[status(thm)],[c_51,c_5558]) ).

tcf(c_5561,plain,
    interior(sK1,sK3) != sK3,
    inference(backward_subsumption_resolution,[status(thm)],[c_49,c_5558]) ).

tcf(c_5562,plain,
    topstr_closure(sK1,subset_complement(the_carrier(sK1),sK3)) = subset_complement(the_carrier(sK1),sK3),
    inference(backward_subsumption_resolution,[status(thm)],[c_5373,c_5560]) ).

tcf(c_5563,plain,
    subset_complement(the_carrier(sK1),subset_complement(the_carrier(sK1),sK3)) = interior(sK1,sK3),
    inference(demodulation,[status(thm)],[c_2530,c_5562]) ).

tcf(c_5564,plain,
    interior(sK1,sK3) = sK3,
    inference(light_normalisation,[status(thm)],[c_5563,c_2212]) ).

tcf(c_5575,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[c_5561,c_5564]) ).


%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SEU324+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04  % Command  : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.37  % Computer : n009.cluster.edu
% 0.11/0.37  % Model    : x86_64 x86_64
% 0.11/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37  % Memory   : 8046.5625MB
% 0.11/0.37  % OS       : Linux 6.8.0-71-generic
% 0.11/0.37  % CPULimit : 300
% 0.11/0.37  % WCLimit  : 300
% 0.11/0.37  % DateTime : Thu Sep 24 13:42:30 UTC 2026
% 0.11/0.37  % CPUTime  : 
% 0.11/0.37  Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.40  Running first-order theorem proving
% 0.11/0.40  Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.41  
% 0.14/0.41  % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41  
% 0.14/0.41  % Detected problem language: tptp
% 0.14/0.43  % Proving...
% 1.11/1.73  % SZS status Started for theBenchmark.p
% 1.11/1.73  % SZS status Theorem for theBenchmark.p
% 1.11/1.73  
% 1.11/1.73  %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.11/1.73  
% 1.11/1.73  % ------  iProver source info
% 1.11/1.73  
% 1.11/1.73  % git: date: 2026-07-19 20:42:38 +0200
% 1.11/1.73  % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.11/1.73  % git: non_committed_changes: false
% 1.11/1.73  
% 1.11/1.73  % ------ Parsing...
% 1.11/1.73  % ------ Clausification by vclausify_rel  & Parsing by iProver...% 
% 1.11/1.73  
% 1.11/1.73  % ------ Preprocessing... sup_sim: 0  sf_s  rm: 1 0s  sf_e  pe_s  pe:1:0s pe:2:0s pe_e % 
% 1.11/1.73  
% 1.11/1.73  % ------ Preprocessing... gs_s  sp: 0 0s  gs_e  snvd_s sp: 0 0s snvd_e % 
% 1.11/1.73  
% 1.11/1.73  % ------ Preprocessing... sf_s  rm: 1 0s  sf_e  sf_s  rm: 0 0s  sf_e 
% 1.11/1.73  % ------ Proving...
% 1.11/1.73  % ------ Problem Properties 
% 1.11/1.73  
% 1.11/1.73  % 
% 1.11/1.73  % clauses                               38
% 1.11/1.73  % conjectures                           6
% 1.11/1.73  % EPR                                   1
% 1.11/1.73  % Horn                                  37
% 1.11/1.73  % unary                                 10
% 1.11/1.73  % binary                                17
% 1.11/1.73  % lits                                  77
% 1.11/1.73  % lits eq                               12
% 1.11/1.73  % fd_pure                               0
% 1.11/1.73  % fd_pseudo                             0
% 1.11/1.73  % fd_cond                               0
% 1.11/1.73  % fd_pseudo_cond                        0
% 1.11/1.73  % AC symbols                            0
% 1.11/1.73  
% 1.11/1.73  % ------ Schedule dynamic 5 is on 
% 1.11/1.73  
% 1.11/1.73  % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.11/1.73  
% 1.11/1.73  
% 1.11/1.73  % ------ 
% 1.11/1.73  % Current options:
% 1.11/1.73  % ------ 
% 1.11/1.73  
% 1.11/1.73  
% 1.11/1.73  % 
% 1.11/1.73  
% 1.11/1.73  % ------ Proving...
% 1.11/1.73  % 
% 1.11/1.73  
% 1.11/1.73  % SZS status Theorem for theBenchmark.p
% 1.11/1.73  
% 1.11/1.73  % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.11/1.74  
% 1.11/1.74  
%------------------------------------------------------------------------------