TSTP Solution File: SET597+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SET597+3 : TPTP v5.0.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 03:04:20 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   63 (  16 unt;   0 def)
%            Number of atoms       :  220 (  54 equ)
%            Maximal formula atoms :   20 (   3 avg)
%            Number of connectives :  256 (  99   ~; 112   |;  39   &)
%                                         (   3 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   60 (   2 sgn  38   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,conjecture,
    ! [X1,X2,X3] :
      ( X1 = union(X2,X3)
    <=> ( subset(X2,X1)
        & subset(X3,X1)
        & ! [X4] :
            ( ( subset(X2,X4)
              & subset(X3,X4) )
           => subset(X1,X4) ) ) ),
    file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',prove_th56) ).

fof(3,axiom,
    ! [X1,X2] :
      ( X1 = X2
    <=> ( subset(X1,X2)
        & subset(X2,X1) ) ),
    file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',equal_defn) ).

fof(6,axiom,
    ! [X1,X2,X3] :
      ( ( subset(X1,X2)
        & subset(X3,X2) )
     => subset(union(X1,X3),X2) ),
    file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',union_subset) ).

fof(7,axiom,
    ! [X1,X2] : union(X1,X2) = union(X2,X1),
    file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',commutativity_of_union) ).

fof(9,axiom,
    ! [X1,X2] : subset(X1,union(X1,X2)),
    file('/tmp/tmpMnkTUX/sel_SET597+3.p_1',subset_of_union) ).

fof(10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( X1 = union(X2,X3)
      <=> ( subset(X2,X1)
          & subset(X3,X1)
          & ! [X4] :
              ( ( subset(X2,X4)
                & subset(X3,X4) )
             => subset(X1,X4) ) ) ),
    inference(assume_negation,[status(cth)],[1]) ).

fof(11,negated_conjecture,
    ? [X1,X2,X3] :
      ( ( X1 != union(X2,X3)
        | ~ subset(X2,X1)
        | ~ subset(X3,X1)
        | ? [X4] :
            ( subset(X2,X4)
            & subset(X3,X4)
            & ~ subset(X1,X4) ) )
      & ( X1 = union(X2,X3)
        | ( subset(X2,X1)
          & subset(X3,X1)
          & ! [X4] :
              ( ~ subset(X2,X4)
              | ~ subset(X3,X4)
              | subset(X1,X4) ) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(12,negated_conjecture,
    ? [X5,X6,X7] :
      ( ( X5 != union(X6,X7)
        | ~ subset(X6,X5)
        | ~ subset(X7,X5)
        | ? [X8] :
            ( subset(X6,X8)
            & subset(X7,X8)
            & ~ subset(X5,X8) ) )
      & ( X5 = union(X6,X7)
        | ( subset(X6,X5)
          & subset(X7,X5)
          & ! [X9] :
              ( ~ subset(X6,X9)
              | ~ subset(X7,X9)
              | subset(X5,X9) ) ) ) ),
    inference(variable_rename,[status(thm)],[11]) ).

fof(13,negated_conjecture,
    ( ( esk1_0 != union(esk2_0,esk3_0)
      | ~ subset(esk2_0,esk1_0)
      | ~ subset(esk3_0,esk1_0)
      | ( subset(esk2_0,esk4_0)
        & subset(esk3_0,esk4_0)
        & ~ subset(esk1_0,esk4_0) ) )
    & ( esk1_0 = union(esk2_0,esk3_0)
      | ( subset(esk2_0,esk1_0)
        & subset(esk3_0,esk1_0)
        & ! [X9] :
            ( ~ subset(esk2_0,X9)
            | ~ subset(esk3_0,X9)
            | subset(esk1_0,X9) ) ) ) ),
    inference(skolemize,[status(esa)],[12]) ).

fof(14,negated_conjecture,
    ! [X9] :
      ( ( ( ( ~ subset(esk2_0,X9)
            | ~ subset(esk3_0,X9)
            | subset(esk1_0,X9) )
          & subset(esk2_0,esk1_0)
          & subset(esk3_0,esk1_0) )
        | esk1_0 = union(esk2_0,esk3_0) )
      & ( esk1_0 != union(esk2_0,esk3_0)
        | ~ subset(esk2_0,esk1_0)
        | ~ subset(esk3_0,esk1_0)
        | ( subset(esk2_0,esk4_0)
          & subset(esk3_0,esk4_0)
          & ~ subset(esk1_0,esk4_0) ) ) ),
    inference(shift_quantors,[status(thm)],[13]) ).

fof(15,negated_conjecture,
    ! [X9] :
      ( ( ~ subset(esk2_0,X9)
        | ~ subset(esk3_0,X9)
        | subset(esk1_0,X9)
        | esk1_0 = union(esk2_0,esk3_0) )
      & ( subset(esk2_0,esk1_0)
        | esk1_0 = union(esk2_0,esk3_0) )
      & ( subset(esk3_0,esk1_0)
        | esk1_0 = union(esk2_0,esk3_0) )
      & ( subset(esk2_0,esk4_0)
        | ~ subset(esk2_0,esk1_0)
        | ~ subset(esk3_0,esk1_0)
        | esk1_0 != union(esk2_0,esk3_0) )
      & ( subset(esk3_0,esk4_0)
        | ~ subset(esk2_0,esk1_0)
        | ~ subset(esk3_0,esk1_0)
        | esk1_0 != union(esk2_0,esk3_0) )
      & ( ~ subset(esk1_0,esk4_0)
        | ~ subset(esk2_0,esk1_0)
        | ~ subset(esk3_0,esk1_0)
        | esk1_0 != union(esk2_0,esk3_0) ) ),
    inference(distribute,[status(thm)],[14]) ).

cnf(16,negated_conjecture,
    ( esk1_0 != union(esk2_0,esk3_0)
    | ~ subset(esk3_0,esk1_0)
    | ~ subset(esk2_0,esk1_0)
    | ~ subset(esk1_0,esk4_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | esk1_0 != union(esk2_0,esk3_0)
    | ~ subset(esk3_0,esk1_0)
    | ~ subset(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | esk1_0 != union(esk2_0,esk3_0)
    | ~ subset(esk3_0,esk1_0)
    | ~ subset(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(19,negated_conjecture,
    ( esk1_0 = union(esk2_0,esk3_0)
    | subset(esk3_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(20,negated_conjecture,
    ( esk1_0 = union(esk2_0,esk3_0)
    | subset(esk2_0,esk1_0) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(21,negated_conjecture,
    ( esk1_0 = union(esk2_0,esk3_0)
    | subset(esk1_0,X1)
    | ~ subset(esk3_0,X1)
    | ~ subset(esk2_0,X1) ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(30,plain,
    ! [X1,X2] :
      ( ( X1 != X2
        | ( subset(X1,X2)
          & subset(X2,X1) ) )
      & ( ~ subset(X1,X2)
        | ~ subset(X2,X1)
        | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(31,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ( subset(X3,X4)
          & subset(X4,X3) ) )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[30]) ).

fof(32,plain,
    ! [X3,X4] :
      ( ( subset(X3,X4)
        | X3 != X4 )
      & ( subset(X4,X3)
        | X3 != X4 )
      & ( ~ subset(X3,X4)
        | ~ subset(X4,X3)
        | X3 = X4 ) ),
    inference(distribute,[status(thm)],[31]) ).

cnf(33,plain,
    ( X1 = X2
    | ~ subset(X2,X1)
    | ~ subset(X1,X2) ),
    inference(split_conjunct,[status(thm)],[32]) ).

fof(44,plain,
    ! [X1,X2,X3] :
      ( ~ subset(X1,X2)
      | ~ subset(X3,X2)
      | subset(union(X1,X3),X2) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(45,plain,
    ! [X4,X5,X6] :
      ( ~ subset(X4,X5)
      | ~ subset(X6,X5)
      | subset(union(X4,X6),X5) ),
    inference(variable_rename,[status(thm)],[44]) ).

cnf(46,plain,
    ( subset(union(X1,X2),X3)
    | ~ subset(X2,X3)
    | ~ subset(X1,X3) ),
    inference(split_conjunct,[status(thm)],[45]) ).

fof(47,plain,
    ! [X3,X4] : union(X3,X4) = union(X4,X3),
    inference(variable_rename,[status(thm)],[7]) ).

cnf(48,plain,
    union(X1,X2) = union(X2,X1),
    inference(split_conjunct,[status(thm)],[47]) ).

fof(58,plain,
    ! [X3,X4] : subset(X3,union(X3,X4)),
    inference(variable_rename,[status(thm)],[9]) ).

cnf(59,plain,
    subset(X1,union(X1,X2)),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(60,negated_conjecture,
    subset(esk2_0,esk1_0),
    inference(spm,[status(thm)],[59,20,theory(equality)]) ).

cnf(66,plain,
    subset(X1,union(X2,X1)),
    inference(spm,[status(thm)],[59,48,theory(equality)]) ).

cnf(88,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | subset(esk1_0,union(esk3_0,X1))
    | ~ subset(esk2_0,union(esk3_0,X1)) ),
    inference(spm,[status(thm)],[21,59,theory(equality)]) ).

cnf(113,negated_conjecture,
    ( union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk4_0)
    | $false
    | ~ subset(esk3_0,esk1_0) ),
    inference(rw,[status(thm)],[16,60,theory(equality)]) ).

cnf(114,negated_conjecture,
    ( union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk4_0)
    | ~ subset(esk3_0,esk1_0) ),
    inference(cn,[status(thm)],[113,theory(equality)]) ).

cnf(115,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | $false
    | ~ subset(esk3_0,esk1_0) ),
    inference(rw,[status(thm)],[17,60,theory(equality)]) ).

cnf(116,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk3_0,esk1_0) ),
    inference(cn,[status(thm)],[115,theory(equality)]) ).

cnf(117,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | $false
    | ~ subset(esk3_0,esk1_0) ),
    inference(rw,[status(thm)],[18,60,theory(equality)]) ).

cnf(118,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk3_0,esk1_0) ),
    inference(cn,[status(thm)],[117,theory(equality)]) ).

cnf(135,negated_conjecture,
    subset(esk3_0,esk1_0),
    inference(spm,[status(thm)],[66,19,theory(equality)]) ).

cnf(145,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | $false ),
    inference(rw,[status(thm)],[118,135,theory(equality)]) ).

cnf(146,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0 ),
    inference(cn,[status(thm)],[145,theory(equality)]) ).

cnf(147,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0
    | $false ),
    inference(rw,[status(thm)],[116,135,theory(equality)]) ).

cnf(148,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | union(esk2_0,esk3_0) != esk1_0 ),
    inference(cn,[status(thm)],[147,theory(equality)]) ).

cnf(149,negated_conjecture,
    ( union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[114,135,theory(equality)]) ).

cnf(150,negated_conjecture,
    ( union(esk2_0,esk3_0) != esk1_0
    | ~ subset(esk1_0,esk4_0) ),
    inference(cn,[status(thm)],[149,theory(equality)]) ).

cnf(403,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | subset(esk1_0,union(esk3_0,esk2_0)) ),
    inference(spm,[status(thm)],[88,66,theory(equality)]) ).

cnf(410,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | subset(esk1_0,union(esk2_0,esk3_0)) ),
    inference(rw,[status(thm)],[403,48,theory(equality)]) ).

cnf(413,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | ~ subset(union(esk2_0,esk3_0),esk1_0) ),
    inference(spm,[status(thm)],[33,410,theory(equality)]) ).

cnf(420,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | ~ subset(esk3_0,esk1_0)
    | ~ subset(esk2_0,esk1_0) ),
    inference(spm,[status(thm)],[413,46,theory(equality)]) ).

cnf(423,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | $false
    | ~ subset(esk2_0,esk1_0) ),
    inference(rw,[status(thm)],[420,135,theory(equality)]) ).

cnf(424,negated_conjecture,
    ( union(esk2_0,esk3_0) = esk1_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[423,60,theory(equality)]) ).

cnf(425,negated_conjecture,
    union(esk2_0,esk3_0) = esk1_0,
    inference(cn,[status(thm)],[424,theory(equality)]) ).

cnf(434,negated_conjecture,
    ( subset(esk1_0,X1)
    | ~ subset(esk3_0,X1)
    | ~ subset(esk2_0,X1) ),
    inference(spm,[status(thm)],[46,425,theory(equality)]) ).

cnf(451,negated_conjecture,
    ( $false
    | ~ subset(esk1_0,esk4_0) ),
    inference(rw,[status(thm)],[150,425,theory(equality)]) ).

cnf(452,negated_conjecture,
    ~ subset(esk1_0,esk4_0),
    inference(cn,[status(thm)],[451,theory(equality)]) ).

cnf(453,negated_conjecture,
    ( subset(esk3_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[148,425,theory(equality)]) ).

cnf(454,negated_conjecture,
    subset(esk3_0,esk4_0),
    inference(cn,[status(thm)],[453,theory(equality)]) ).

cnf(455,negated_conjecture,
    ( subset(esk2_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[146,425,theory(equality)]) ).

cnf(456,negated_conjecture,
    subset(esk2_0,esk4_0),
    inference(cn,[status(thm)],[455,theory(equality)]) ).

cnf(604,negated_conjecture,
    ( subset(esk1_0,esk4_0)
    | ~ subset(esk2_0,esk4_0) ),
    inference(spm,[status(thm)],[434,454,theory(equality)]) ).

cnf(616,negated_conjecture,
    ( subset(esk1_0,esk4_0)
    | $false ),
    inference(rw,[status(thm)],[604,456,theory(equality)]) ).

cnf(617,negated_conjecture,
    subset(esk1_0,esk4_0),
    inference(cn,[status(thm)],[616,theory(equality)]) ).

cnf(618,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[617,452,theory(equality)]) ).

cnf(619,negated_conjecture,
    $false,
    618,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SET/SET597+3.p
% --creating new selector for []
% -running prover on /tmp/tmpMnkTUX/sel_SET597+3.p_1 with time limit 29
% -prover status Theorem
% Problem SET597+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SET/SET597+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SET/SET597+3.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
% 
%------------------------------------------------------------------------------