TSTP Solution File: SEU320+1 by Drodi---3.5.1

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%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 : Wed May 31 12:36:41 EDT 2023

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   55 (  12 unt;   0 def)
%            Number of atoms       :  132 (   4 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  123 (  46   ~;  49   |;   9   &)
%                                         (  10 <=>;   8  =>;   0  <=;   1 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of predicates  :   12 (  10 usr;   7 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   36 (;  31   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => element(subset_complement(A,B),powerset(A)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [A] :
    ? [B] : element(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [A,B] :
      ( element(B,powerset(A))
     => subset_complement(A,subset_complement(A,B)) = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => ( closed_subset(B,A)
          <=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,conjecture,
    ! [A] :
      ( top_str(A)
     => ! [B] :
          ( element(B,powerset(the_carrier(A)))
         => ( open_subset(B,A)
          <=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,negated_conjecture,
    ~ ! [A] :
        ( top_str(A)
       => ! [B] :
            ( element(B,powerset(the_carrier(A)))
           => ( open_subset(B,A)
            <=> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    inference(negated_conjecture,[status(cth)],[f13]) ).

fof(f16,plain,
    ! [A,B] :
      ( ~ element(B,powerset(A))
      | element(subset_complement(A,B),powerset(A)) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f17,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | element(subset_complement(X1,X0),powerset(X1)) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f24,plain,
    ! [A] : element(sk0_2(A),A),
    inference(skolemization,[status(esa)],[f9]) ).

fof(f25,plain,
    ! [X0] : element(sk0_2(X0),X0),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f26,plain,
    ! [A,B] :
      ( ~ element(B,powerset(A))
      | subset_complement(A,subset_complement(A,B)) = B ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(X1))
      | subset_complement(X1,subset_complement(X1,X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f30,plain,
    ! [A] :
      ( ~ top_str(A)
      | ! [B] :
          ( ~ element(B,powerset(the_carrier(A)))
          | ( closed_subset(B,A)
          <=> open_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f31,plain,
    ! [A] :
      ( ~ top_str(A)
      | ! [B] :
          ( ~ element(B,powerset(the_carrier(A)))
          | ( ( ~ closed_subset(B,A)
              | open_subset(subset_complement(the_carrier(A),B),A) )
            & ( closed_subset(B,A)
              | ~ open_subset(subset_complement(the_carrier(A),B),A) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | ~ closed_subset(X1,X0)
      | open_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( ~ top_str(X0)
      | ~ element(X1,powerset(the_carrier(X0)))
      | closed_subset(X1,X0)
      | ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ? [A] :
      ( top_str(A)
      & ? [B] :
          ( element(B,powerset(the_carrier(A)))
          & ( open_subset(B,A)
          <~> closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f35,plain,
    ? [A] :
      ( top_str(A)
      & ? [B] :
          ( element(B,powerset(the_carrier(A)))
          & ( open_subset(B,A)
            | closed_subset(subset_complement(the_carrier(A),B),A) )
          & ( ~ open_subset(B,A)
            | ~ closed_subset(subset_complement(the_carrier(A),B),A) ) ) ),
    inference(NNF_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ( top_str(sk0_3)
    & element(sk0_4,powerset(the_carrier(sk0_3)))
    & ( open_subset(sk0_4,sk0_3)
      | closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) )
    & ( ~ open_subset(sk0_4,sk0_3)
      | ~ closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ) ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f37,plain,
    top_str(sk0_3),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    element(sk0_4,powerset(the_carrier(sk0_3))),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    ( open_subset(sk0_4,sk0_3)
    | closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f40,plain,
    ( ~ open_subset(sk0_4,sk0_3)
    | ~ closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f45,plain,
    ( spl0_0
  <=> open_subset(sk0_4,sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f47,plain,
    ( ~ open_subset(sk0_4,sk0_3)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f45]) ).

fof(f48,plain,
    ( spl0_1
  <=> closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f49,plain,
    ( closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3)
    | ~ spl0_1 ),
    inference(component_clause,[status(thm)],[f48]) ).

fof(f51,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f39,f45,f48]) ).

fof(f52,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f40,f45,f48]) ).

fof(f53,plain,
    subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)) = sk0_4,
    inference(resolution,[status(thm)],[f27,f38]) ).

fof(f54,plain,
    element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3))),
    inference(resolution,[status(thm)],[f17,f38]) ).

fof(f58,plain,
    ! [X0] :
      ( ~ element(X0,powerset(the_carrier(sk0_3)))
      | closed_subset(X0,sk0_3)
      | ~ open_subset(subset_complement(the_carrier(sk0_3),X0),sk0_3) ),
    inference(resolution,[status(thm)],[f33,f37]) ).

fof(f59,plain,
    ( spl0_2
  <=> element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3))) ),
    introduced(split_symbol_definition) ).

fof(f61,plain,
    ( ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
    | spl0_2 ),
    inference(component_clause,[status(thm)],[f59]) ).

fof(f62,plain,
    ( ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
    | closed_subset(subset_complement(the_carrier(sk0_3),sk0_4),sk0_3)
    | ~ open_subset(sk0_4,sk0_3) ),
    inference(paramodulation,[status(thm)],[f53,f58]) ).

fof(f63,plain,
    ( ~ spl0_2
    | spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f62,f59,f48,f45]) ).

fof(f64,plain,
    ( $false
    | spl0_2 ),
    inference(forward_subsumption_resolution,[status(thm)],[f61,f54]) ).

fof(f65,plain,
    spl0_2,
    inference(contradiction_clause,[status(thm)],[f64]) ).

fof(f67,plain,
    ! [X0] : element(subset_complement(X0,sk0_2(powerset(X0))),powerset(X0)),
    inference(resolution,[status(thm)],[f25,f17]) ).

fof(f82,plain,
    ( spl0_6
  <=> element(subset_complement(the_carrier(sk0_3),sk0_2(powerset(the_carrier(sk0_3)))),powerset(the_carrier(sk0_3))) ),
    introduced(split_symbol_definition) ).

fof(f84,plain,
    ( ~ element(subset_complement(the_carrier(sk0_3),sk0_2(powerset(the_carrier(sk0_3)))),powerset(the_carrier(sk0_3)))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f82]) ).

fof(f93,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f84,f67]) ).

fof(f94,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f93]) ).

fof(f146,plain,
    ( spl0_15
  <=> top_str(sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f148,plain,
    ( ~ top_str(sk0_3)
    | spl0_15 ),
    inference(component_clause,[status(thm)],[f146]) ).

fof(f149,plain,
    ( spl0_16
  <=> open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3) ),
    introduced(split_symbol_definition) ).

fof(f150,plain,
    ( open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3)
    | ~ spl0_16 ),
    inference(component_clause,[status(thm)],[f149]) ).

fof(f152,plain,
    ( ~ top_str(sk0_3)
    | ~ element(subset_complement(the_carrier(sk0_3),sk0_4),powerset(the_carrier(sk0_3)))
    | open_subset(subset_complement(the_carrier(sk0_3),subset_complement(the_carrier(sk0_3),sk0_4)),sk0_3)
    | ~ spl0_1 ),
    inference(resolution,[status(thm)],[f49,f32]) ).

fof(f153,plain,
    ( ~ spl0_15
    | ~ spl0_2
    | spl0_16
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f152,f146,f59,f149,f48]) ).

fof(f154,plain,
    ( $false
    | spl0_15 ),
    inference(forward_subsumption_resolution,[status(thm)],[f148,f37]) ).

fof(f155,plain,
    spl0_15,
    inference(contradiction_clause,[status(thm)],[f154]) ).

fof(f156,plain,
    ( open_subset(sk0_4,sk0_3)
    | ~ spl0_16 ),
    inference(forward_demodulation,[status(thm)],[f53,f150]) ).

fof(f157,plain,
    ( $false
    | spl0_0
    | ~ spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f156,f47]) ).

fof(f158,plain,
    ( spl0_0
    | ~ spl0_16 ),
    inference(contradiction_clause,[status(thm)],[f157]) ).

fof(f159,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f51,f52,f63,f65,f94,f153,f155,f158]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Tue May 30 09:34:13 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.5.1
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.36  % Elapsed time: 0.020710 seconds
% 0.12/0.36  % CPU time: 0.033284 seconds
% 0.12/0.36  % Memory used: 11.545 MB
%------------------------------------------------------------------------------