%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET900+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 03:45:12 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   23 (   5 unt;   0 def)
%            Number of atoms       :   69 (  54 equ)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :   84 (  38   ~;  25   |;  21   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   36 (   0 sgn  21   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ~ ( X1 != singleton(X2)
        & X1 != empty_set
        & ! [X3] :
            ~ ( in(X3,X1)
              & X3 != X2 ) ),
    file('/tmp/tmp34fb1G/sel_SET900+1.p_1',l45_zfmisc_1) ).

fof(2,conjecture,
    ! [X1,X2] :
      ~ ( X1 != singleton(X2)
        & X1 != empty_set
        & ! [X3] :
            ~ ( in(X3,X1)
              & X3 != X2 ) ),
    file('/tmp/tmp34fb1G/sel_SET900+1.p_1',t41_zfmisc_1) ).

fof(7,negated_conjecture,
    ~ ! [X1,X2] :
        ~ ( X1 != singleton(X2)
          & X1 != empty_set
          & ! [X3] :
              ~ ( in(X3,X1)
                & X3 != X2 ) ),
    inference(assume_negation,[status(cth)],[2]) ).

fof(10,plain,
    ! [X1,X2] :
      ( X1 = singleton(X2)
      | X1 = empty_set
      | ? [X3] :
          ( in(X3,X1)
          & X3 != X2 ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(11,plain,
    ! [X4,X5] :
      ( X4 = singleton(X5)
      | X4 = empty_set
      | ? [X6] :
          ( in(X6,X4)
          & X6 != X5 ) ),
    inference(variable_rename,[status(thm)],[10]) ).

fof(12,plain,
    ! [X4,X5] :
      ( X4 = singleton(X5)
      | X4 = empty_set
      | ( in(esk1_2(X4,X5),X4)
        & esk1_2(X4,X5) != X5 ) ),
    inference(skolemize,[status(esa)],[11]) ).

fof(13,plain,
    ! [X4,X5] :
      ( ( in(esk1_2(X4,X5),X4)
        | X4 = singleton(X5)
        | X4 = empty_set )
      & ( esk1_2(X4,X5) != X5
        | X4 = singleton(X5)
        | X4 = empty_set ) ),
    inference(distribute,[status(thm)],[12]) ).

cnf(14,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | esk1_2(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[13]) ).

cnf(15,plain,
    ( X1 = empty_set
    | X1 = singleton(X2)
    | in(esk1_2(X1,X2),X1) ),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(16,negated_conjecture,
    ? [X1,X2] :
      ( X1 != singleton(X2)
      & X1 != empty_set
      & ! [X3] :
          ( ~ in(X3,X1)
          | X3 = X2 ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(17,negated_conjecture,
    ? [X4,X5] :
      ( X4 != singleton(X5)
      & X4 != empty_set
      & ! [X6] :
          ( ~ in(X6,X4)
          | X6 = X5 ) ),
    inference(variable_rename,[status(thm)],[16]) ).

fof(18,negated_conjecture,
    ( esk2_0 != singleton(esk3_0)
    & esk2_0 != empty_set
    & ! [X6] :
        ( ~ in(X6,esk2_0)
        | X6 = esk3_0 ) ),
    inference(skolemize,[status(esa)],[17]) ).

fof(19,negated_conjecture,
    ! [X6] :
      ( ( ~ in(X6,esk2_0)
        | X6 = esk3_0 )
      & esk2_0 != singleton(esk3_0)
      & esk2_0 != empty_set ),
    inference(shift_quantors,[status(thm)],[18]) ).

cnf(20,negated_conjecture,
    esk2_0 != empty_set,
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(21,negated_conjecture,
    esk2_0 != singleton(esk3_0),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(22,negated_conjecture,
    ( X1 = esk3_0
    | ~ in(X1,esk2_0) ),
    inference(split_conjunct,[status(thm)],[19]) ).

cnf(34,negated_conjecture,
    ( esk3_0 = esk1_2(esk2_0,X1)
    | singleton(X1) = esk2_0
    | empty_set = esk2_0 ),
    inference(spm,[status(thm)],[22,15,theory(equality)]) ).

cnf(35,negated_conjecture,
    ( esk1_2(esk2_0,X1) = esk3_0
    | singleton(X1) = esk2_0 ),
    inference(sr,[status(thm)],[34,20,theory(equality)]) ).

cnf(37,negated_conjecture,
    ( singleton(X1) = esk2_0
    | empty_set = esk2_0
    | esk3_0 != X1 ),
    inference(spm,[status(thm)],[14,35,theory(equality)]) ).

cnf(39,negated_conjecture,
    ( singleton(X1) = esk2_0
    | esk3_0 != X1 ),
    inference(sr,[status(thm)],[37,20,theory(equality)]) ).

cnf(40,negated_conjecture,
    singleton(esk3_0) = esk2_0,
    inference(er,[status(thm)],[39,theory(equality)]) ).

cnf(41,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[40,21,theory(equality)]) ).

cnf(42,negated_conjecture,
    $false,
    41,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET900+1.p
% --creating new selector for []
% -running prover on /tmp/tmp34fb1G/sel_SET900+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET900+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET900+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET900+1.p
% Solved 1 out of 1.
% # Problem is unsatisfiable (or provable), constructing proof object
% # SZS status Theorem
% # SZS output start CNFRefutation.
% See solution above
% # SZS output end CNFRefutation
% 
%------------------------------------------------------------------------------