%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : KLE001+1 : TPTP v5.0.0. Released v4.0.0.
% 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 : Sat Dec 25 11:36:49 EST 2010

% Result   : Theorem 0.17s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   17 (   8 unt;   0 def)
%            Number of atoms       :   30 (   9 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   23 (  10   ~;   5   |;   5   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   24 (   0 sgn  14   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] : addition(X1,X1) = X1,
    file('/tmp/tmpQdkUsL/sel_KLE001+1.p_1',additive_idempotence) ).

fof(7,axiom,
    ! [X1,X2] :
      ( leq(X1,X2)
    <=> addition(X1,X2) = X2 ),
    file('/tmp/tmpQdkUsL/sel_KLE001+1.p_1',order) ).

fof(8,conjecture,
    ! [X4,X5,X6] :
      ( leq(X4,X5)
     => leq(addition(X4,X6),addition(X4,X6)) ),
    file('/tmp/tmpQdkUsL/sel_KLE001+1.p_1',goals) ).

fof(9,negated_conjecture,
    ~ ! [X4,X5,X6] :
        ( leq(X4,X5)
       => leq(addition(X4,X6),addition(X4,X6)) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(14,plain,
    ! [X2] : addition(X2,X2) = X2,
    inference(variable_rename,[status(thm)],[3]) ).

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

fof(22,plain,
    ! [X1,X2] :
      ( ( ~ leq(X1,X2)
        | addition(X1,X2) = X2 )
      & ( addition(X1,X2) != X2
        | leq(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(23,plain,
    ! [X3,X4] :
      ( ( ~ leq(X3,X4)
        | addition(X3,X4) = X4 )
      & ( addition(X3,X4) != X4
        | leq(X3,X4) ) ),
    inference(variable_rename,[status(thm)],[22]) ).

cnf(24,plain,
    ( leq(X1,X2)
    | addition(X1,X2) != X2 ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(26,negated_conjecture,
    ? [X4,X5,X6] :
      ( leq(X4,X5)
      & ~ leq(addition(X4,X6),addition(X4,X6)) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(27,negated_conjecture,
    ? [X7,X8,X9] :
      ( leq(X7,X8)
      & ~ leq(addition(X7,X9),addition(X7,X9)) ),
    inference(variable_rename,[status(thm)],[26]) ).

fof(28,negated_conjecture,
    ( leq(esk1_0,esk2_0)
    & ~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)) ),
    inference(skolemize,[status(esa)],[27]) ).

cnf(29,negated_conjecture,
    ~ leq(addition(esk1_0,esk3_0),addition(esk1_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[28]) ).

cnf(35,plain,
    leq(X1,X1),
    inference(spm,[status(thm)],[24,15,theory(equality)]) ).

cnf(83,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[29,35,theory(equality)]) ).

cnf(84,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[83,theory(equality)]) ).

cnf(85,negated_conjecture,
    $false,
    84,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/KLE/KLE001+1.p
% --creating new selector for [KLE001+0.ax]
% -running prover on /tmp/tmpQdkUsL/sel_KLE001+1.p_1 with time limit 29
% -prover status Theorem
% Problem KLE001+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/KLE/KLE001+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/KLE/KLE001+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
% 
%------------------------------------------------------------------------------