%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU152+1 : 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 04:53:42 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (  10 unt;   0 def)
%            Number of atoms       :   44 (  16 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   36 (  17   ~;  10   |;   5   &)
%                                         (   1 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 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   :   34 (   0 sgn  20   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1,X2] : set_union2(X1,X2) = set_union2(X2,X1),
    file('/tmp/tmpfNOtMS/sel_SEU152+1.p_1',commutativity_k2_xboole_0) ).

fof(4,axiom,
    ! [X1,X2] :
      ( subset(singleton(X1),X2)
    <=> in(X1,X2) ),
    file('/tmp/tmpfNOtMS/sel_SEU152+1.p_1',l2_zfmisc_1) ).

fof(5,axiom,
    ! [X1,X2] :
      ( subset(X1,X2)
     => set_union2(X1,X2) = X2 ),
    file('/tmp/tmpfNOtMS/sel_SEU152+1.p_1',t12_xboole_1) ).

fof(8,conjecture,
    ! [X1,X2] :
      ( in(X1,X2)
     => set_union2(singleton(X1),X2) = X2 ),
    file('/tmp/tmpfNOtMS/sel_SEU152+1.p_1',l23_zfmisc_1) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2] :
        ( in(X1,X2)
       => set_union2(singleton(X1),X2) = X2 ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(14,plain,
    ! [X3,X4] : set_union2(X3,X4) = set_union2(X4,X3),
    inference(variable_rename,[status(thm)],[3]) ).

cnf(15,plain,
    set_union2(X1,X2) = set_union2(X2,X1),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(16,plain,
    ! [X1,X2] :
      ( ( ~ subset(singleton(X1),X2)
        | in(X1,X2) )
      & ( ~ in(X1,X2)
        | subset(singleton(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(17,plain,
    ! [X3,X4] :
      ( ( ~ subset(singleton(X3),X4)
        | in(X3,X4) )
      & ( ~ in(X3,X4)
        | subset(singleton(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[16]) ).

cnf(18,plain,
    ( subset(singleton(X1),X2)
    | ~ in(X1,X2) ),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(20,plain,
    ! [X1,X2] :
      ( ~ subset(X1,X2)
      | set_union2(X1,X2) = X2 ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(21,plain,
    ! [X3,X4] :
      ( ~ subset(X3,X4)
      | set_union2(X3,X4) = X4 ),
    inference(variable_rename,[status(thm)],[20]) ).

cnf(22,plain,
    ( set_union2(X1,X2) = X2
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[21]) ).

fof(28,negated_conjecture,
    ? [X1,X2] :
      ( in(X1,X2)
      & set_union2(singleton(X1),X2) != X2 ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(29,negated_conjecture,
    ? [X3,X4] :
      ( in(X3,X4)
      & set_union2(singleton(X3),X4) != X4 ),
    inference(variable_rename,[status(thm)],[28]) ).

fof(30,negated_conjecture,
    ( in(esk1_0,esk2_0)
    & set_union2(singleton(esk1_0),esk2_0) != esk2_0 ),
    inference(skolemize,[status(esa)],[29]) ).

cnf(31,negated_conjecture,
    set_union2(singleton(esk1_0),esk2_0) != esk2_0,
    inference(split_conjunct,[status(thm)],[30]) ).

cnf(32,negated_conjecture,
    in(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[30]) ).

cnf(42,negated_conjecture,
    set_union2(esk2_0,singleton(esk1_0)) != esk2_0,
    inference(rw,[status(thm)],[31,15,theory(equality)]) ).

cnf(44,plain,
    ( set_union2(singleton(X1),X2) = X2
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[22,18,theory(equality)]) ).

cnf(47,plain,
    ( X2 = set_union2(X2,singleton(X1))
    | ~ in(X1,X2) ),
    inference(spm,[status(thm)],[15,44,theory(equality)]) ).

cnf(51,negated_conjecture,
    ~ in(esk1_0,esk2_0),
    inference(spm,[status(thm)],[42,47,theory(equality)]) ).

cnf(53,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[51,32,theory(equality)]) ).

cnf(54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[53,theory(equality)]) ).

cnf(55,negated_conjecture,
    $false,
    54,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU152+1.p
% --creating new selector for []
% -running prover on /tmp/tmpfNOtMS/sel_SEU152+1.p_1 with time limit 29
% -prover status Theorem
% Problem SEU152+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU152+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU152+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
% 
%------------------------------------------------------------------------------