%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET067+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n024.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 20:38:57 EDT 2024

% Result   : Theorem 0.16s 0.32s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   46 (  13 unt;   0 def)
%            Number of atoms       :  113 (  20 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  112 (  45   ~;  47   |;  13   &)
%                                         (   6 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   71 (  67   !;   4   ?)

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

fof(f2,axiom,
    ! [X] : subclass(X,universal_class),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [U,X,Y] :
      ( member(U,unordered_pair(X,Y))
    <=> ( member(U,universal_class)
        & ( U = X
          | U = Y ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X] : singleton(X) = unordered_pair(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f44,conjecture,
    ! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f45,negated_conjecture,
    ~ ! [X,Y] : subclass(unordered_pair(X,X),unordered_pair(X,Y)),
    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(f50,plain,
    ! [X0,X1,X2] :
      ( ~ subclass(X0,X1)
      | ~ member(X2,X0)
      | member(X2,X1) ),
    inference(cnf_transformation,[status(esa)],[f49]) ).

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(f53,plain,
    ! [X0] : subclass(X0,universal_class),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f59,plain,
    ! [U,X,Y] :
      ( ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
      & ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f60,plain,
    ( ! [U,X,Y] :
        ( ~ member(U,unordered_pair(X,Y))
        | ( member(U,universal_class)
          & ( U = X
            | U = Y ) ) )
    & ! [U,X,Y] :
        ( member(U,unordered_pair(X,Y))
        | ~ member(U,universal_class)
        | ( U != X
          & U != Y ) ) ),
    inference(miniscoping,[status(esa)],[f59]) ).

fof(f62,plain,
    ! [X0,X1,X2] :
      ( ~ member(X0,unordered_pair(X1,X2))
      | X0 = X1
      | X0 = X2 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X1,X2))
      | ~ member(X0,universal_class)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f60]) ).

fof(f66,plain,
    ! [X0] : singleton(X0) = unordered_pair(X0,X0),
    inference(cnf_transformation,[status(esa)],[f6]) ).

fof(f191,plain,
    ? [X,Y] : ~ subclass(unordered_pair(X,X),unordered_pair(X,Y)),
    inference(pre_NNF_transformation,[status(esa)],[f45]) ).

fof(f192,plain,
    ~ subclass(unordered_pair(sk0_7,sk0_7),unordered_pair(sk0_7,sk0_8)),
    inference(skolemization,[status(esa)],[f191]) ).

fof(f193,plain,
    ~ subclass(unordered_pair(sk0_7,sk0_7),unordered_pair(sk0_7,sk0_8)),
    inference(cnf_transformation,[status(esa)],[f192]) ).

fof(f196,plain,
    ! [X0,X1] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,universal_class) ),
    inference(destructive_equality_resolution,[status(esa)],[f63]) ).

fof(f204,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ subclass(X2,universal_class)
      | ~ member(X0,X2) ),
    inference(resolution,[status(thm)],[f196,f50]) ).

fof(f205,plain,
    ! [X0,X1,X2] :
      ( member(X0,unordered_pair(X0,X1))
      | ~ member(X0,X2) ),
    inference(forward_subsumption_resolution,[status(thm)],[f204,f53]) ).

fof(f213,plain,
    ~ subclass(singleton(sk0_7),unordered_pair(sk0_7,sk0_8)),
    inference(backward_demodulation,[status(thm)],[f66,f193]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1
      | X0 = X1 ),
    inference(paramodulation,[status(thm)],[f66,f62]) ).

fof(f224,plain,
    ! [X0,X1] :
      ( ~ member(X0,singleton(X1))
      | X0 = X1 ),
    inference(duplicate_literals_removal,[status(esa)],[f223]) ).

fof(f228,plain,
    ! [X0,X1] :
      ( sk0_0(X0,singleton(X1)) = X1
      | subclass(singleton(X1),X0) ),
    inference(resolution,[status(thm)],[f224,f51]) ).

fof(f308,plain,
    sk0_0(unordered_pair(sk0_7,sk0_8),singleton(sk0_7)) = sk0_7,
    inference(resolution,[status(thm)],[f228,f213]) ).

fof(f315,plain,
    ( spl0_0
  <=> subclass(singleton(sk0_7),unordered_pair(sk0_7,sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f316,plain,
    ( subclass(singleton(sk0_7),unordered_pair(sk0_7,sk0_8))
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f315]) ).

fof(f318,plain,
    ( spl0_1
  <=> member(sk0_7,unordered_pair(sk0_7,sk0_8)) ),
    introduced(split_symbol_definition) ).

fof(f320,plain,
    ( ~ member(sk0_7,unordered_pair(sk0_7,sk0_8))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f318]) ).

fof(f321,plain,
    ( subclass(singleton(sk0_7),unordered_pair(sk0_7,sk0_8))
    | ~ member(sk0_7,unordered_pair(sk0_7,sk0_8)) ),
    inference(paramodulation,[status(thm)],[f308,f52]) ).

fof(f322,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f321,f315,f318]) ).

fof(f323,plain,
    ( spl0_2
  <=> member(sk0_7,singleton(sk0_7)) ),
    introduced(split_symbol_definition) ).

fof(f324,plain,
    ( member(sk0_7,singleton(sk0_7))
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f323]) ).

fof(f326,plain,
    ( subclass(singleton(sk0_7),unordered_pair(sk0_7,sk0_8))
    | member(sk0_7,singleton(sk0_7)) ),
    inference(paramodulation,[status(thm)],[f308,f51]) ).

fof(f327,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f326,f315,f323]) ).

fof(f328,plain,
    ( $false
    | ~ spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f316,f213]) ).

fof(f329,plain,
    ~ spl0_0,
    inference(contradiction_clause,[status(thm)],[f328]) ).

fof(f330,plain,
    ! [X0] :
      ( ~ member(sk0_7,X0)
      | spl0_1 ),
    inference(resolution,[status(thm)],[f320,f205]) ).

fof(f332,plain,
    ( $false
    | spl0_1
    | ~ spl0_2 ),
    inference(backward_subsumption_resolution,[status(thm)],[f324,f330]) ).

fof(f333,plain,
    ( spl0_1
    | ~ spl0_2 ),
    inference(contradiction_clause,[status(thm)],[f332]) ).

fof(f334,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f322,f327,f329,f333]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.09  % Problem  : SET067+1 : TPTP v8.1.2. Bugfixed v5.4.0.
% 0.08/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.30  % Computer : n024.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit : 300
% 0.10/0.30  % WCLimit  : 300
% 0.10/0.30  % DateTime : Mon Apr 29 21:35:21 EDT 2024
% 0.10/0.30  % CPUTime  : 
% 0.10/0.31  % Drodi V3.6.0
% 0.16/0.32  % Refutation found
% 0.16/0.32  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.32  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.32  % Elapsed time: 0.018459 seconds
% 0.16/0.32  % CPU time: 0.036988 seconds
% 0.16/0.32  % Total memory used: 13.705 MB
% 0.16/0.32  % Net memory used: 13.671 MB
%------------------------------------------------------------------------------