%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET019+4 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 02:38:06 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   18 (   5 unt;   0 def)
%            Number of atoms       :   51 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   53 (  20   ~;  15   |;  15   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    2 (   2 usr;   2 con; 0-0 aty)
%            Number of variables   :   18 (   0 sgn  12   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1,X2] :
      ( equal_set(X1,X2)
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpLXnkUY/sel_SET019+4.p_1',equal_set) ).

fof(3,conjecture,
    ! [X1,X2] :
      ( ( subset(X1,X2)
        & subset(X2,X1) )
     => equal_set(X1,X2) ),
    file('/tmp/tmpLXnkUY/sel_SET019+4.p_1',thI02) ).

fof(4,negated_conjecture,
    ~ ! [X1,X2] :
        ( ( subset(X1,X2)
          & subset(X2,X1) )
       => equal_set(X1,X2) ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(13,plain,
    ! [X1,X2] :
      ( ( ~ equal_set(X1,X2)
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | equal_set(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(14,plain,
    ! [X3,X4] :
      ( ( ~ equal_set(X3,X4)
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | ~ equal_set(X3,X4) )
      & ( subset(X4,X3)
        | ~ equal_set(X3,X4) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | equal_set(X3,X4) ) ),
    inference(distribute,[status(thm)],[14]) ).

cnf(16,plain,
    ( equal_set(X1,X2)
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(19,negated_conjecture,
    ? [X1,X2] :
      ( subset(X1,X2)
      & subset(X2,X1)
      & ~ equal_set(X1,X2) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(20,negated_conjecture,
    ? [X3,X4] :
      ( subset(X3,X4)
      & subset(X4,X3)
      & ~ equal_set(X3,X4) ),
    inference(variable_rename,[status(thm)],[19]) ).

fof(21,negated_conjecture,
    ( subset(esk2_0,esk3_0)
    & subset(esk3_0,esk2_0)
    & ~ equal_set(esk2_0,esk3_0) ),
    inference(skolemize,[status(esa)],[20]) ).

cnf(22,negated_conjecture,
    ~ equal_set(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(23,negated_conjecture,
    subset(esk3_0,esk2_0),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(24,negated_conjecture,
    subset(esk2_0,esk3_0),
    inference(split_conjunct,[status(thm)],[21]) ).

cnf(25,negated_conjecture,
    ( ~ subset(esk3_0,esk2_0)
    | ~ subset(esk2_0,esk3_0) ),
    inference(spm,[status(thm)],[22,16,theory(equality)]) ).

cnf(28,negated_conjecture,
    ( $false
    | ~ subset(esk2_0,esk3_0) ),
    inference(rw,[status(thm)],[25,23,theory(equality)]) ).

cnf(29,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[28,24,theory(equality)]) ).

cnf(30,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[29,theory(equality)]) ).

cnf(31,negated_conjecture,
    $false,
    30,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET019+4.p
% --creating new selector for [SET006+0.ax]
% -running prover on /tmp/tmpLXnkUY/sel_SET019+4.p_1 with time limit 29
% -prover status Theorem
% Problem SET019+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET019+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET019+4.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
% 
%------------------------------------------------------------------------------