%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n022.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 : Tue Apr 30 20:41:58 EDT 2024

% Result   : Theorem 0.12s 0.32s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   53 (   6 unt;   0 def)
%            Number of atoms       :  123 (  47 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  125 (  55   ~;  43   |;  16   &)
%                                         (   5 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    9 (   7 usr;   6 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   35 (  31   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f167,axiom,
    ! [A,B] :
      ( element(B,powerset(powerset(A)))
     => element(complements_of_subsets(A,B),powerset(powerset(A))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f258,axiom,
    ! [A,B] :
      ( element(B,powerset(powerset(A)))
     => complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f360,conjecture,
    ! [A,B] :
      ( element(B,powerset(powerset(A)))
     => ( ~ ( B != empty_set
            & complements_of_subsets(A,B) = empty_set )
        & ~ ( complements_of_subsets(A,B) != empty_set
            & B = empty_set ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f361,negated_conjecture,
    ~ ! [A,B] :
        ( element(B,powerset(powerset(A)))
       => ( ~ ( B != empty_set
              & complements_of_subsets(A,B) = empty_set )
          & ~ ( complements_of_subsets(A,B) != empty_set
              & B = empty_set ) ) ),
    inference(negated_conjecture,[status(cth)],[f360]) ).

fof(f476,lemma,
    ! [A,B] :
      ( element(B,powerset(powerset(A)))
     => ~ ( B != empty_set
          & complements_of_subsets(A,B) = empty_set ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f1274,plain,
    ! [A,B] :
      ( ~ element(B,powerset(powerset(A)))
      | element(complements_of_subsets(A,B),powerset(powerset(A))) ),
    inference(pre_NNF_transformation,[status(esa)],[f167]) ).

fof(f1275,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(powerset(X1)))
      | element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
    inference(cnf_transformation,[status(esa)],[f1274]) ).

fof(f1542,plain,
    ! [A,B] :
      ( ~ element(B,powerset(powerset(A)))
      | complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
    inference(pre_NNF_transformation,[status(esa)],[f258]) ).

fof(f1543,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(powerset(X1)))
      | complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
    inference(cnf_transformation,[status(esa)],[f1542]) ).

fof(f2155,plain,
    ? [A,B] :
      ( element(B,powerset(powerset(A)))
      & ( ( B != empty_set
          & complements_of_subsets(A,B) = empty_set )
        | ( complements_of_subsets(A,B) != empty_set
          & B = empty_set ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f361]) ).

fof(f2156,plain,
    ! [A,B] :
      ( pd0_24(B,A)
     => ( B != empty_set
        & complements_of_subsets(A,B) = empty_set ) ),
    introduced(predicate_definition,[f2155]) ).

fof(f2157,plain,
    ? [A,B] :
      ( element(B,powerset(powerset(A)))
      & ( pd0_24(B,A)
        | ( complements_of_subsets(A,B) != empty_set
          & B = empty_set ) ) ),
    inference(formula_renaming,[status(thm)],[f2155,f2156]) ).

fof(f2158,plain,
    ( element(sk0_277,powerset(powerset(sk0_276)))
    & ( pd0_24(sk0_277,sk0_276)
      | ( complements_of_subsets(sk0_276,sk0_277) != empty_set
        & sk0_277 = empty_set ) ) ),
    inference(skolemization,[status(esa)],[f2157]) ).

fof(f2159,plain,
    element(sk0_277,powerset(powerset(sk0_276))),
    inference(cnf_transformation,[status(esa)],[f2158]) ).

fof(f2160,plain,
    ( pd0_24(sk0_277,sk0_276)
    | complements_of_subsets(sk0_276,sk0_277) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f2158]) ).

fof(f2161,plain,
    ( pd0_24(sk0_277,sk0_276)
    | sk0_277 = empty_set ),
    inference(cnf_transformation,[status(esa)],[f2158]) ).

fof(f2544,plain,
    ! [A,B] :
      ( ~ element(B,powerset(powerset(A)))
      | B = empty_set
      | complements_of_subsets(A,B) != empty_set ),
    inference(pre_NNF_transformation,[status(esa)],[f476]) ).

fof(f2545,plain,
    ! [X0,X1] :
      ( ~ element(X0,powerset(powerset(X1)))
      | X0 = empty_set
      | complements_of_subsets(X1,X0) != empty_set ),
    inference(cnf_transformation,[status(esa)],[f2544]) ).

fof(f2948,plain,
    ! [A,B] :
      ( ~ pd0_24(B,A)
      | ( B != empty_set
        & complements_of_subsets(A,B) = empty_set ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2156]) ).

fof(f2949,plain,
    ! [X0,X1] :
      ( ~ pd0_24(X0,X1)
      | X0 != empty_set ),
    inference(cnf_transformation,[status(esa)],[f2948]) ).

fof(f2950,plain,
    ! [X0,X1] :
      ( ~ pd0_24(X0,X1)
      | complements_of_subsets(X1,X0) = empty_set ),
    inference(cnf_transformation,[status(esa)],[f2948]) ).

fof(f3116,plain,
    ( spl0_31
  <=> pd0_24(sk0_277,sk0_276) ),
    introduced(split_symbol_definition) ).

fof(f3117,plain,
    ( pd0_24(sk0_277,sk0_276)
    | ~ spl0_31 ),
    inference(component_clause,[status(thm)],[f3116]) ).

fof(f3119,plain,
    ( spl0_32
  <=> complements_of_subsets(sk0_276,sk0_277) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f3121,plain,
    ( complements_of_subsets(sk0_276,sk0_277) != empty_set
    | spl0_32 ),
    inference(component_clause,[status(thm)],[f3119]) ).

fof(f3122,plain,
    ( spl0_31
    | ~ spl0_32 ),
    inference(split_clause,[status(thm)],[f2160,f3116,f3119]) ).

fof(f3123,plain,
    ( spl0_33
  <=> sk0_277 = empty_set ),
    introduced(split_symbol_definition) ).

fof(f3124,plain,
    ( sk0_277 = empty_set
    | ~ spl0_33 ),
    inference(component_clause,[status(thm)],[f3123]) ).

fof(f3126,plain,
    ( spl0_31
    | spl0_33 ),
    inference(split_clause,[status(thm)],[f2161,f3116,f3123]) ).

fof(f3385,plain,
    ! [X0] : ~ pd0_24(empty_set,X0),
    inference(destructive_equality_resolution,[status(esa)],[f2949]) ).

fof(f3393,plain,
    complements_of_subsets(sk0_276,complements_of_subsets(sk0_276,sk0_277)) = sk0_277,
    inference(resolution,[status(thm)],[f1543,f2159]) ).

fof(f3403,plain,
    ( complements_of_subsets(sk0_276,sk0_277) = empty_set
    | ~ spl0_31 ),
    inference(resolution,[status(thm)],[f3117,f2950]) ).

fof(f3404,plain,
    ( $false
    | spl0_32
    | ~ spl0_31 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3403,f3121]) ).

fof(f3405,plain,
    ( spl0_32
    | ~ spl0_31 ),
    inference(contradiction_clause,[status(thm)],[f3404]) ).

fof(f3418,plain,
    ( spl0_58
  <=> element(sk0_277,powerset(powerset(sk0_276))) ),
    introduced(split_symbol_definition) ).

fof(f3420,plain,
    ( ~ element(sk0_277,powerset(powerset(sk0_276)))
    | spl0_58 ),
    inference(component_clause,[status(thm)],[f3418]) ).

fof(f3467,plain,
    ( $false
    | spl0_58 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3420,f2159]) ).

fof(f3468,plain,
    spl0_58,
    inference(contradiction_clause,[status(thm)],[f3467]) ).

fof(f3472,plain,
    element(complements_of_subsets(sk0_276,sk0_277),powerset(powerset(sk0_276))),
    inference(resolution,[status(thm)],[f1275,f2159]) ).

fof(f3495,plain,
    ( spl0_71
  <=> complements_of_subsets(sk0_276,complements_of_subsets(sk0_276,sk0_277)) = empty_set ),
    introduced(split_symbol_definition) ).

fof(f3497,plain,
    ( complements_of_subsets(sk0_276,complements_of_subsets(sk0_276,sk0_277)) != empty_set
    | spl0_71 ),
    inference(component_clause,[status(thm)],[f3495]) ).

fof(f3498,plain,
    ( complements_of_subsets(sk0_276,sk0_277) = empty_set
    | complements_of_subsets(sk0_276,complements_of_subsets(sk0_276,sk0_277)) != empty_set ),
    inference(resolution,[status(thm)],[f2545,f3472]) ).

fof(f3499,plain,
    ( spl0_32
    | ~ spl0_71 ),
    inference(split_clause,[status(thm)],[f3498,f3119,f3495]) ).

fof(f3500,plain,
    ( sk0_277 = empty_set
    | complements_of_subsets(sk0_276,sk0_277) != empty_set ),
    inference(resolution,[status(thm)],[f2545,f2159]) ).

fof(f3501,plain,
    ( spl0_33
    | ~ spl0_32 ),
    inference(split_clause,[status(thm)],[f3500,f3123,f3119]) ).

fof(f3502,plain,
    ( sk0_277 != empty_set
    | spl0_71 ),
    inference(forward_demodulation,[status(thm)],[f3393,f3497]) ).

fof(f3565,plain,
    ( pd0_24(empty_set,sk0_276)
    | ~ spl0_33
    | ~ spl0_31 ),
    inference(forward_demodulation,[status(thm)],[f3124,f3117]) ).

fof(f3566,plain,
    ( $false
    | ~ spl0_33
    | ~ spl0_31 ),
    inference(forward_subsumption_resolution,[status(thm)],[f3565,f3385]) ).

fof(f3567,plain,
    ( ~ spl0_33
    | ~ spl0_31 ),
    inference(contradiction_clause,[status(thm)],[f3566]) ).

fof(f3568,plain,
    ( empty_set != empty_set
    | ~ spl0_33
    | spl0_71 ),
    inference(forward_demodulation,[status(thm)],[f3124,f3502]) ).

fof(f3569,plain,
    ( $false
    | ~ spl0_33
    | spl0_71 ),
    inference(trivial_equality_resolution,[status(esa)],[f3568]) ).

fof(f3570,plain,
    ( ~ spl0_33
    | spl0_71 ),
    inference(contradiction_clause,[status(thm)],[f3569]) ).

fof(f3571,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f3122,f3126,f3405,f3468,f3499,f3501,f3567,f3570]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08  % Problem  : SEU326+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.08  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.27  % Computer : n022.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 300
% 0.07/0.27  % DateTime : Mon Apr 29 19:40:43 EDT 2024
% 0.07/0.27  % CPUTime  : 
% 0.12/0.31  % Drodi V3.6.0
% 0.12/0.32  % Refutation found
% 0.12/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.33  % Elapsed time: 0.053971 seconds
% 0.12/0.33  % CPU time: 0.106802 seconds
% 0.12/0.33  % Total memory used: 31.904 MB
% 0.12/0.33  % Net memory used: 31.646 MB
%------------------------------------------------------------------------------