%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET891+1 : TPTP v5.0.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 03:44:28 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   16 (  16 unt;   0 def)
%            Number of atoms       :   16 (  13 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    5 (   5   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   22 (   0 sgn  12   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
    file('/tmp/tmpOhcRM6/sel_SET891+1.p_1',t32_zfmisc_1) ).

fof(4,axiom,
    ! [X1,X2] : union(unordered_pair(X1,X2)) = set_union2(X1,X2),
    file('/tmp/tmpOhcRM6/sel_SET891+1.p_1',l52_zfmisc_1) ).

fof(7,axiom,
    ! [X1,X2] : unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    file('/tmp/tmpOhcRM6/sel_SET891+1.p_1',t41_enumset1) ).

fof(11,negated_conjecture,
    ~ ! [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
    inference(assume_negation,[status(cth)],[1]) ).

fof(15,negated_conjecture,
    ? [X1,X2] : union(unordered_pair(singleton(X1),singleton(X2))) != unordered_pair(X1,X2),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(16,negated_conjecture,
    ? [X3,X4] : union(unordered_pair(singleton(X3),singleton(X4))) != unordered_pair(X3,X4),
    inference(variable_rename,[status(thm)],[15]) ).

fof(17,negated_conjecture,
    union(unordered_pair(singleton(esk1_0),singleton(esk2_0))) != unordered_pair(esk1_0,esk2_0),
    inference(skolemize,[status(esa)],[16]) ).

cnf(18,negated_conjecture,
    union(unordered_pair(singleton(esk1_0),singleton(esk2_0))) != unordered_pair(esk1_0,esk2_0),
    inference(split_conjunct,[status(thm)],[17]) ).

fof(24,plain,
    ! [X3,X4] : union(unordered_pair(X3,X4)) = set_union2(X3,X4),
    inference(variable_rename,[status(thm)],[4]) ).

cnf(25,plain,
    union(unordered_pair(X1,X2)) = set_union2(X1,X2),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(31,plain,
    ! [X3,X4] : unordered_pair(X3,X4) = set_union2(singleton(X3),singleton(X4)),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(32,plain,
    unordered_pair(X1,X2) = set_union2(singleton(X1),singleton(X2)),
    inference(split_conjunct,[status(thm)],[31]) ).

cnf(43,plain,
    union(unordered_pair(singleton(X1),singleton(X2))) = unordered_pair(X1,X2),
    inference(rw,[status(thm)],[32,25,theory(equality)]),
    [unfolding] ).

cnf(53,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[18,43,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/SET/SET891+1.p
% --creating new selector for []
% -running prover on /tmp/tmpOhcRM6/sel_SET891+1.p_1 with time limit 29
% -prover status Theorem
% Problem SET891+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET891+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET891+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
% 
%------------------------------------------------------------------------------