%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : REL049+1 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 01:41:36 EST 2010

% Result   : Theorem 0.23s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   21 (  16 unt;   0 def)
%            Number of atoms       :   31 (  28 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   16 (   6   ~;   0   |;   8   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   28 (   0 sgn  16   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3] : join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    file('/tmp/tmp31eAQ8/sel_REL049+1.p_1',maddux2_join_associativity) ).

fof(2,axiom,
    ! [X1,X2] : join(X1,X2) = join(X2,X1),
    file('/tmp/tmp31eAQ8/sel_REL049+1.p_1',maddux1_join_commutativity) ).

fof(3,conjecture,
    ! [X1,X2,X3] :
      ( ( join(X1,X2) = X2
        & join(X3,X2) = X2 )
     => join(join(X1,X3),X2) = X2 ),
    file('/tmp/tmp31eAQ8/sel_REL049+1.p_1',goals) ).

fof(4,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ( join(X1,X2) = X2
          & join(X3,X2) = X2 )
       => join(join(X1,X3),X2) = X2 ),
    inference(assume_negation,[status(cth)],[3]) ).

fof(5,plain,
    ! [X4,X5,X6] : join(X4,join(X5,X6)) = join(join(X4,X5),X6),
    inference(variable_rename,[status(thm)],[1]) ).

cnf(6,plain,
    join(X1,join(X2,X3)) = join(join(X1,X2),X3),
    inference(split_conjunct,[status(thm)],[5]) ).

fof(7,plain,
    ! [X3,X4] : join(X3,X4) = join(X4,X3),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(8,plain,
    join(X1,X2) = join(X2,X1),
    inference(split_conjunct,[status(thm)],[7]) ).

fof(9,negated_conjecture,
    ? [X1,X2,X3] :
      ( join(X1,X2) = X2
      & join(X3,X2) = X2
      & join(join(X1,X3),X2) != X2 ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(10,negated_conjecture,
    ? [X4,X5,X6] :
      ( join(X4,X5) = X5
      & join(X6,X5) = X5
      & join(join(X4,X6),X5) != X5 ),
    inference(variable_rename,[status(thm)],[9]) ).

fof(11,negated_conjecture,
    ( join(esk1_0,esk2_0) = esk2_0
    & join(esk3_0,esk2_0) = esk2_0
    & join(join(esk1_0,esk3_0),esk2_0) != esk2_0 ),
    inference(skolemize,[status(esa)],[10]) ).

cnf(12,negated_conjecture,
    join(join(esk1_0,esk3_0),esk2_0) != esk2_0,
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(13,negated_conjecture,
    join(esk3_0,esk2_0) = esk2_0,
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(14,negated_conjecture,
    join(esk1_0,esk2_0) = esk2_0,
    inference(split_conjunct,[status(thm)],[11]) ).

cnf(15,negated_conjecture,
    join(esk2_0,esk3_0) = esk2_0,
    inference(rw,[status(thm)],[13,8,theory(equality)]) ).

cnf(16,negated_conjecture,
    join(esk2_0,esk1_0) = esk2_0,
    inference(rw,[status(thm)],[14,8,theory(equality)]) ).

cnf(17,negated_conjecture,
    join(esk2_0,join(esk1_0,esk3_0)) != esk2_0,
    inference(rw,[status(thm)],[12,8,theory(equality)]) ).

cnf(28,negated_conjecture,
    join(esk2_0,X1) = join(esk2_0,join(esk1_0,X1)),
    inference(spm,[status(thm)],[6,16,theory(equality)]) ).

cnf(90,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[17,28,theory(equality)]),15,theory(equality)]) ).

cnf(91,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[90,theory(equality)]) ).

cnf(92,negated_conjecture,
    $false,
    91,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/REL/REL049+1.p
% --creating new selector for [REL001+0.ax]
% -running prover on /tmp/tmp31eAQ8/sel_REL049+1.p_1 with time limit 29
% -prover status Theorem
% Problem REL049+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/REL/REL049+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/REL/REL049+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
% 
%------------------------------------------------------------------------------