%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET987+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 03:59:31 EST 2010

% Result   : Theorem 0.28s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   20 (   9 unt;   0 def)
%            Number of atoms       :   35 (  18 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   35 (  20   ~;   5   |;   5   &)
%                                         (   2 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   26 (   0 sgn  18   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    file('/tmp/tmpT41ipa/sel_SET987+1.p_1',t65_zfmisc_1) ).

fof(9,conjecture,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => set_difference(set_union2(X2,singleton(X1)),singleton(X1)) = X2 ),
    file('/tmp/tmpT41ipa/sel_SET987+1.p_1',t141_zfmisc_1) ).

fof(10,axiom,
    ! [X1,X2] : set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
    file('/tmp/tmpT41ipa/sel_SET987+1.p_1',t40_xboole_1) ).

fof(11,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ in(X1,X2)
       => set_difference(set_union2(X2,singleton(X1)),singleton(X1)) = X2 ),
    inference(assume_negation,[status(cth)],[9]) ).

fof(12,plain,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[1,theory(equality)]) ).

fof(17,negated_conjecture,
    ~ ! [X1,X2] :
        ( ~ in(X1,X2)
       => set_difference(set_union2(X2,singleton(X1)),singleton(X1)) = X2 ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(18,plain,
    ! [X1,X2] :
      ( ( set_difference(X1,singleton(X2)) != X1
        | ~ in(X2,X1) )
      & ( in(X2,X1)
        | set_difference(X1,singleton(X2)) = X1 ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(19,plain,
    ! [X3,X4] :
      ( ( set_difference(X3,singleton(X4)) != X3
        | ~ in(X4,X3) )
      & ( in(X4,X3)
        | set_difference(X3,singleton(X4)) = X3 ) ),
    inference(variable_rename,[status(thm)],[18]) ).

cnf(20,plain,
    ( set_difference(X1,singleton(X2)) = X1
    | in(X2,X1) ),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(41,negated_conjecture,
    ? [X1,X2] :
      ( ~ in(X1,X2)
      & set_difference(set_union2(X2,singleton(X1)),singleton(X1)) != X2 ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(42,negated_conjecture,
    ? [X3,X4] :
      ( ~ in(X3,X4)
      & set_difference(set_union2(X4,singleton(X3)),singleton(X3)) != X4 ),
    inference(variable_rename,[status(thm)],[41]) ).

fof(43,negated_conjecture,
    ( ~ in(esk3_0,esk4_0)
    & set_difference(set_union2(esk4_0,singleton(esk3_0)),singleton(esk3_0)) != esk4_0 ),
    inference(skolemize,[status(esa)],[42]) ).

cnf(44,negated_conjecture,
    set_difference(set_union2(esk4_0,singleton(esk3_0)),singleton(esk3_0)) != esk4_0,
    inference(split_conjunct,[status(thm)],[43]) ).

cnf(45,negated_conjecture,
    ~ in(esk3_0,esk4_0),
    inference(split_conjunct,[status(thm)],[43]) ).

fof(46,plain,
    ! [X3,X4] : set_difference(set_union2(X3,X4),X4) = set_difference(X3,X4),
    inference(variable_rename,[status(thm)],[10]) ).

cnf(47,plain,
    set_difference(set_union2(X1,X2),X2) = set_difference(X1,X2),
    inference(split_conjunct,[status(thm)],[46]) ).

cnf(60,negated_conjecture,
    set_difference(esk4_0,singleton(esk3_0)) != esk4_0,
    inference(rw,[status(thm)],[44,47,theory(equality)]) ).

cnf(61,negated_conjecture,
    in(esk3_0,esk4_0),
    inference(spm,[status(thm)],[60,20,theory(equality)]) ).

cnf(62,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[61,45,theory(equality)]) ).

cnf(63,negated_conjecture,
    $false,
    62,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET987+1.p
% --creating new selector for []
% -running prover on /tmp/tmpT41ipa/sel_SET987+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET987+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET987+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET987+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
% 
%------------------------------------------------------------------------------