%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU162+1 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 04:57:24 EST 2010

% Result   : Theorem 0.19s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   15
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   37 (   8 unt;   0 def)
%            Number of atoms       :   76 (  21 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   71 (  32   ~;  26   |;   6   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   50 (   0 sgn  32   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2] :
      ( set_difference(X1,singleton(X2)) = X1
    <=> ~ in(X2,X1) ),
    file('/tmp/tmp1US2I-/sel_SEU162+1.p_1',t65_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] :
      ~ ( disjoint(singleton(X1),X2)
        & in(X1,X2) ),
    file('/tmp/tmp1US2I-/sel_SEU162+1.p_1',l25_zfmisc_1) ).

fof(5,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
     => disjoint(X2,X1) ),
    file('/tmp/tmp1US2I-/sel_SEU162+1.p_1',symmetry_r1_xboole_0) ).

fof(6,axiom,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    file('/tmp/tmp1US2I-/sel_SEU162+1.p_1',l28_zfmisc_1) ).

fof(8,axiom,
    ! [X1,X2] :
      ( disjoint(X1,X2)
    <=> set_difference(X1,X2) = X1 ),
    file('/tmp/tmp1US2I-/sel_SEU162+1.p_1',t83_xboole_1) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(X1,singleton(X2)) = X1
      <=> ~ in(X2,X1) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( set_difference(X1,singleton(X2)) = X1
      <=> ~ in(X2,X1) ),
    inference(fof_simplification,[status(thm)],[9,theory(equality)]) ).

fof(11,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
     => disjoint(singleton(X1),X2) ),
    inference(fof_simplification,[status(thm)],[6,theory(equality)]) ).

fof(13,negated_conjecture,
    ? [X1,X2] :
      ( ( set_difference(X1,singleton(X2)) != X1
        | in(X2,X1) )
      & ( set_difference(X1,singleton(X2)) = X1
        | ~ in(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(14,negated_conjecture,
    ? [X3,X4] :
      ( ( set_difference(X3,singleton(X4)) != X3
        | in(X4,X3) )
      & ( set_difference(X3,singleton(X4)) = X3
        | ~ in(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ( ( set_difference(esk1_0,singleton(esk2_0)) != esk1_0
      | in(esk2_0,esk1_0) )
    & ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
      | ~ in(esk2_0,esk1_0) ) ),
    inference(skolemize,[status(esa)],[14]) ).

cnf(16,negated_conjecture,
    ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
    | ~ in(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    ( in(esk2_0,esk1_0)
    | set_difference(esk1_0,singleton(esk2_0)) != esk1_0 ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(20,plain,
    ! [X1,X2] :
      ( ~ disjoint(singleton(X1),X2)
      | ~ in(X1,X2) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(21,plain,
    ! [X3,X4] :
      ( ~ disjoint(singleton(X3),X4)
      | ~ in(X3,X4) ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(22,plain,
    ( ~ in(X1,X2)
    | ~ disjoint(singleton(X1),X2) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(23,plain,
    ! [X1,X2] :
      ( ~ disjoint(X1,X2)
      | disjoint(X2,X1) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(24,plain,
    ! [X3,X4] :
      ( ~ disjoint(X3,X4)
      | disjoint(X4,X3) ),
    inference(variable_rename,[status(thm)],[23]) ).

cnf(25,plain,
    ( disjoint(X1,X2)
    | ~ disjoint(X2,X1) ),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(26,plain,
    ! [X1,X2] :
      ( in(X1,X2)
      | disjoint(singleton(X1),X2) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(27,plain,
    ! [X3,X4] :
      ( in(X3,X4)
      | disjoint(singleton(X3),X4) ),
    inference(variable_rename,[status(thm)],[26]) ).

cnf(28,plain,
    ( disjoint(singleton(X1),X2)
    | in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[27]) ).

fof(32,plain,
    ! [X1,X2] :
      ( ( ~ disjoint(X1,X2)
        | set_difference(X1,X2) = X1 )
      & ( set_difference(X1,X2) != X1
        | disjoint(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(33,plain,
    ! [X3,X4] :
      ( ( ~ disjoint(X3,X4)
        | set_difference(X3,X4) = X3 )
      & ( set_difference(X3,X4) != X3
        | disjoint(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[32]) ).

cnf(34,plain,
    ( disjoint(X1,X2)
    | set_difference(X1,X2) != X1 ),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(35,plain,
    ( set_difference(X1,X2) = X1
    | ~ disjoint(X1,X2) ),
    inference(split_conjunct,[status(thm)],[33]) ).

cnf(38,plain,
    ( disjoint(X1,singleton(X2))
    | in(X2,X1) ),
    inference(spm,[status(thm)],[25,28,theory(equality)]) ).

cnf(40,plain,
    ( set_difference(X1,singleton(X2)) = X1
    | in(X2,X1) ),
    inference(spm,[status(thm)],[35,38,theory(equality)]) ).

cnf(42,negated_conjecture,
    in(esk2_0,esk1_0),
    inference(spm,[status(thm)],[17,40,theory(equality)]) ).

cnf(46,negated_conjecture,
    ( set_difference(esk1_0,singleton(esk2_0)) = esk1_0
    | $false ),
    inference(rw,[status(thm)],[16,42,theory(equality)]) ).

cnf(47,negated_conjecture,
    set_difference(esk1_0,singleton(esk2_0)) = esk1_0,
    inference(cn,[status(thm)],[46,theory(equality)]) ).

cnf(48,negated_conjecture,
    disjoint(esk1_0,singleton(esk2_0)),
    inference(spm,[status(thm)],[34,47,theory(equality)]) ).

cnf(50,negated_conjecture,
    disjoint(singleton(esk2_0),esk1_0),
    inference(spm,[status(thm)],[25,48,theory(equality)]) ).

cnf(52,negated_conjecture,
    ~ in(esk2_0,esk1_0),
    inference(spm,[status(thm)],[22,50,theory(equality)]) ).

cnf(55,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[52,42,theory(equality)]) ).

cnf(56,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[55,theory(equality)]) ).

cnf(57,negated_conjecture,
    $false,
    56,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU162+1.p
% --creating new selector for []
% -running prover on /tmp/tmp1US2I-/sel_SEU162+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU162+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU162+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU162+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
% 
%------------------------------------------------------------------------------