%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU161+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art02.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 04:57:15 EST 2010

% Result   : Theorem 0.28s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (  15 unt;   0 def)
%            Number of atoms       :   35 (  21 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   21 (  11   ~;   4   |;   3   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    3 (   1 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   :   27 (   0 sgn  16   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(34,conjecture,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/tmp/tmpE6x7UX/sel_SEU161+2.p_1',t46_zfmisc_1) ).

fof(48,axiom,
    ! [X1] : unordered_pair(X1,X1) = singleton(X1),
    file('/tmp/tmpE6x7UX/sel_SEU161+2.p_1',t69_enumset1) ).

fof(50,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmpE6x7UX/sel_SEU161+2.p_1',commutativity_k2_xboole_0) ).

fof(55,axiom,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/tmp/tmpE6x7UX/sel_SEU161+2.p_1',l23_zfmisc_1) ).

fof(92,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,X2)
       => set_union2(singleton(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[34]) ).

fof(207,negated_conjecture,
    ? [X1,X2] :
      ( in(X1,X2)
      & set_union2(singleton(X1),X2) != X2 ),
    inference(fof_nnf,[status(thm)],[92]) ).

fof(208,negated_conjecture,
    ? [X3,X4] :
      ( in(X3,X4)
      & set_union2(singleton(X3),X4) != X4 ),
    inference(variable_rename,[status(thm)],[207]) ).

fof(209,negated_conjecture,
    ( in(esk4_0,esk5_0)
    & set_union2(singleton(esk4_0),esk5_0) != esk5_0 ),
    inference(skolemize,[status(esa)],[208]) ).

cnf(210,negated_conjecture,
    set_union2(singleton(esk4_0),esk5_0) != esk5_0,
    inference(split_conjunct,[status(thm)],[209]) ).

cnf(211,negated_conjecture,
    in(esk4_0,esk5_0),
    inference(split_conjunct,[status(thm)],[209]) ).

fof(264,plain,
    ! [X2] : unordered_pair(X2,X2) = singleton(X2),
    inference(variable_rename,[status(thm)],[48]) ).

cnf(265,plain,
    unordered_pair(X1,X1) = singleton(X1),
    inference(split_conjunct,[status(thm)],[264]) ).

fof(268,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[50]) ).

cnf(269,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[268]) ).

fof(285,plain,
    ! [X1,X2] :
      ( ~ in(X1,X2)
      | set_union2(singleton(X1),X2) = X2 ),
    inference(fof_nnf,[status(thm)],[55]) ).

fof(286,plain,
    ! [X3,X4] :
      ( ~ in(X3,X4)
      | set_union2(singleton(X3),X4) = X4 ),
    inference(variable_rename,[status(thm)],[285]) ).

cnf(287,plain,
    ( set_union2(singleton(X1),X2) = X2
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[286]) ).

cnf(452,plain,
    ( set_union2(unordered_pair(X1,X1),X2) = X2
    | ~ in(X1,X2) ),
    inference(rw,[status(thm)],[287,265,theory(equality)]),
    [unfolding] ).

cnf(464,negated_conjecture,
    set_union2(unordered_pair(esk4_0,esk4_0),esk5_0) != esk5_0,
    inference(rw,[status(thm)],[210,265,theory(equality)]),
    [unfolding] ).

cnf(656,negated_conjecture,
    set_union2(esk5_0,unordered_pair(esk4_0,esk4_0)) != esk5_0,
    inference(rw,[status(thm)],[464,269,theory(equality)]) ).

cnf(702,negated_conjecture,
    set_union2(unordered_pair(esk4_0,esk4_0),esk5_0) = esk5_0,
    inference(spm,[status(thm)],[452,211,theory(equality)]) ).

cnf(707,negated_conjecture,
    set_union2(esk5_0,unordered_pair(esk4_0,esk4_0)) = esk5_0,
    inference(rw,[status(thm)],[702,269,theory(equality)]) ).

cnf(2133,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[656,707,theory(equality)]) ).

cnf(2134,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[2133,theory(equality)]) ).

cnf(2135,negated_conjecture,
    $false,
    2134,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU161+2.p
% --creating new selector for []
% -running prover on /tmp/tmpE6x7UX/sel_SEU161+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU161+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU161+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU161+2.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
% 
%------------------------------------------------------------------------------