TSTP Solution File: SET056+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n031.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 20:38:51 EDT 2024

% Result   : Theorem 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   34 (   5 unt;   0 def)
%            Number of atoms       :  101 (  14 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  108 (  41   ~;  41   |;  19   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   53 (  45   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( member(U,X)
         => member(U,Y) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [X,Y] :
      ( X = Y
    <=> ( subclass(X,Y)
        & subclass(Y,X) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ! [X,Y] :
      ( X = Y
      | ? [U] :
          ( member(U,X)
          & ~ member(U,Y) )
      | ? [W] :
          ( member(W,Y)
          & ~ member(W,X) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ! [X,Y] :
        ( X = Y
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) )
        | ? [W] :
            ( member(W,Y)
            & ~ member(W,X) ) ),
    inference(negated_conjecture,[status(cth)],[f44]) ).

fof(f46,plain,
    ! [X,Y] :
      ( subclass(X,Y)
    <=> ! [U] :
          ( ~ member(U,X)
          | member(U,Y) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f1]) ).

fof(f47,plain,
    ! [X,Y] :
      ( ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
      & ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f46]) ).

fof(f48,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ? [U] :
            ( member(U,X)
            & ~ member(U,Y) ) ) ),
    inference(miniscoping,[status(esa)],[f47]) ).

fof(f49,plain,
    ( ! [X,Y] :
        ( ~ subclass(X,Y)
        | ! [U] :
            ( ~ member(U,X)
            | member(U,Y) ) )
    & ! [X,Y] :
        ( subclass(X,Y)
        | ( member(sk0_0(Y,X),X)
          & ~ member(sk0_0(Y,X),Y) ) ) ),
    inference(skolemization,[status(esa)],[f48]) ).

fof(f51,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | member(sk0_0(X1,X0),X0) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f52,plain,
    ! [X0,X1] :
      ( subclass(X0,X1)
      | ~ member(sk0_0(X1,X0),X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

fof(f54,plain,
    ! [X,Y] :
      ( ( X != Y
        | ( subclass(X,Y)
          & subclass(Y,X) ) )
      & ( X = Y
        | ~ subclass(X,Y)
        | ~ subclass(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f3]) ).

fof(f55,plain,
    ( ! [X,Y] :
        ( X != Y
        | ( subclass(X,Y)
          & subclass(Y,X) ) )
    & ! [X,Y] :
        ( X = Y
        | ~ subclass(X,Y)
        | ~ subclass(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f54]) ).

fof(f58,plain,
    ! [X0,X1] :
      ( X0 = X1
      | ~ subclass(X0,X1)
      | ~ subclass(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f55]) ).

fof(f191,plain,
    ? [X,Y] :
      ( X != Y
      & ! [U] :
          ( ~ member(U,X)
          | member(U,Y) )
      & ! [W] :
          ( ~ member(W,Y)
          | member(W,X) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ( sk0_7 != sk0_8
    & ! [U] :
        ( ~ member(U,sk0_7)
        | member(U,sk0_8) )
    & ! [W] :
        ( ~ member(W,sk0_8)
        | member(W,sk0_7) ) ),
    inference(skolemization,[status(esa)],[f191]) ).

fof(f193,plain,
    sk0_7 != sk0_8,
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f194,plain,
    ! [X0] :
      ( ~ member(X0,sk0_7)
      | member(X0,sk0_8) ),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f195,plain,
    ! [X0] :
      ( ~ member(X0,sk0_8)
      | member(X0,sk0_7) ),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f206,plain,
    ! [X0] :
      ( subclass(sk0_8,X0)
      | member(sk0_0(X0,sk0_8),sk0_7) ),
    inference(resolution,[status(thm)],[f51,f195]) ).

fof(f207,plain,
    ! [X0] :
      ( subclass(sk0_7,X0)
      | member(sk0_0(X0,sk0_7),sk0_8) ),
    inference(resolution,[status(thm)],[f51,f194]) ).

fof(f259,plain,
    ( spl0_8
  <=> subclass(sk0_8,sk0_7) ),
    introduced(split_symbol_definition) ).

fof(f260,plain,
    ( subclass(sk0_8,sk0_7)
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f259]) ).

fof(f262,plain,
    ( subclass(sk0_8,sk0_7)
    | subclass(sk0_8,sk0_7) ),
    inference(resolution,[status(thm)],[f52,f206]) ).

fof(f263,plain,
    spl0_8,
    inference(split_clause,[status(thm)],[f262,f259]) ).

fof(f279,plain,
    ( spl0_9
  <=> sk0_8 = sk0_7 ),
    introduced(split_symbol_definition) ).

fof(f280,plain,
    ( sk0_8 = sk0_7
    | ~ spl0_9 ),
    inference(component_clause,[status(thm)],[f279]) ).

fof(f282,plain,
    ( spl0_10
  <=> subclass(sk0_7,sk0_8) ),
    introduced(split_symbol_definition) ).

fof(f285,plain,
    ( sk0_8 = sk0_7
    | ~ subclass(sk0_7,sk0_8)
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f260,f58]) ).

fof(f286,plain,
    ( spl0_9
    | ~ spl0_10
    | ~ spl0_8 ),
    inference(split_clause,[status(thm)],[f285,f279,f282,f259]) ).

fof(f314,plain,
    ( subclass(sk0_7,sk0_8)
    | subclass(sk0_7,sk0_8) ),
    inference(resolution,[status(thm)],[f207,f52]) ).

fof(f315,plain,
    spl0_10,
    inference(split_clause,[status(thm)],[f314,f282]) ).

fof(f318,plain,
    ( $false
    | ~ spl0_9 ),
    inference(forward_subsumption_resolution,[status(thm)],[f280,f193]) ).

fof(f319,plain,
    ~ spl0_9,
    inference(contradiction_clause,[status(thm)],[f318]) ).

fof(f320,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f263,f286,f315,f319]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.11  % Problem  : SET056+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.09/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n031.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 22:18:13 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.35  % Elapsed time: 0.017920 seconds
% 0.11/0.35  % CPU time: 0.033335 seconds
% 0.11/0.35  % Total memory used: 13.555 MB
% 0.11/0.35  % Net memory used: 13.535 MB
%------------------------------------------------------------------------------