TSTP Solution File: SEU165+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU165+3 : 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 04:59:44 EST 2010

% Result   : Theorem 0.16s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   33 (   9 unt;   0 def)
%            Number of atoms       :   94 (   3 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  102 (  41   ~;  41   |;  17   &)
%                                         (   3 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   4 con; 0-2 aty)
%            Number of variables   :   62 (   7 sgn  28   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',l55_zfmisc_1) ).

fof(2,axiom,
    ! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',d5_tarski) ).

fof(8,conjecture,
    ! [X1,X2,X3,X4] :
      ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    <=> ( in(X1,X3)
        & in(X2,X4) ) ),
    file('/tmp/tmpIGIK02/sel_SEU165+3.p_1',t106_zfmisc_1) ).

fof(9,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
      <=> ( in(X1,X3)
          & in(X2,X4) ) ),
    inference(assume_negation,[status(cth)],[8]) ).

fof(13,plain,
    ! [X1,X2,X3,X4] :
      ( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
        | ( in(X1,X3)
          & in(X2,X4) ) )
      & ( ~ in(X1,X3)
        | ~ in(X2,X4)
        | in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(14,plain,
    ! [X5,X6,X7,X8] :
      ( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
        | ( in(X5,X7)
          & in(X6,X8) ) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
    inference(variable_rename,[status(thm)],[13]) ).

fof(15,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X5,X7)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( in(X6,X8)
        | ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) )
      & ( ~ in(X5,X7)
        | ~ in(X6,X8)
        | in(ordered_pair(X5,X6),cartesian_product2(X7,X8)) ) ),
    inference(distribute,[status(thm)],[14]) ).

cnf(16,plain,
    ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(17,plain,
    ( in(X2,X4)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[15]) ).

cnf(18,plain,
    ( in(X1,X3)
    | ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4)) ),
    inference(split_conjunct,[status(thm)],[15]) ).

fof(19,plain,
    ! [X3,X4] : ordered_pair(X3,X4) = unordered_pair(unordered_pair(X3,X4),singleton(X3)),
    inference(variable_rename,[status(thm)],[2]) ).

cnf(20,plain,
    ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
    inference(split_conjunct,[status(thm)],[19]) ).

fof(34,negated_conjecture,
    ? [X1,X2,X3,X4] :
      ( ( ~ in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
        | ~ in(X1,X3)
        | ~ in(X2,X4) )
      & ( in(ordered_pair(X1,X2),cartesian_product2(X3,X4))
        | ( in(X1,X3)
          & in(X2,X4) ) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(35,negated_conjecture,
    ? [X5,X6,X7,X8] :
      ( ( ~ in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
        | ~ in(X5,X7)
        | ~ in(X6,X8) )
      & ( in(ordered_pair(X5,X6),cartesian_product2(X7,X8))
        | ( in(X5,X7)
          & in(X6,X8) ) ) ),
    inference(variable_rename,[status(thm)],[34]) ).

fof(36,negated_conjecture,
    ( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
      | ~ in(esk3_0,esk5_0)
      | ~ in(esk4_0,esk6_0) )
    & ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
      | ( in(esk3_0,esk5_0)
        & in(esk4_0,esk6_0) ) ) ),
    inference(skolemize,[status(esa)],[35]) ).

fof(37,negated_conjecture,
    ( ( ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
      | ~ in(esk3_0,esk5_0)
      | ~ in(esk4_0,esk6_0) )
    & ( in(esk3_0,esk5_0)
      | in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) )
    & ( in(esk4_0,esk6_0)
      | in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ) ),
    inference(distribute,[status(thm)],[36]) ).

cnf(38,negated_conjecture,
    ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
    | in(esk4_0,esk6_0) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(39,negated_conjecture,
    ( in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0))
    | in(esk3_0,esk5_0) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(40,negated_conjecture,
    ( ~ in(esk4_0,esk6_0)
    | ~ in(esk3_0,esk5_0)
    | ~ in(ordered_pair(esk3_0,esk4_0),cartesian_product2(esk5_0,esk6_0)) ),
    inference(split_conjunct,[status(thm)],[37]) ).

cnf(41,negated_conjecture,
    ( in(esk3_0,esk5_0)
    | in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
    inference(rw,[status(thm)],[39,20,theory(equality)]),
    [unfolding] ).

cnf(42,negated_conjecture,
    ( in(esk4_0,esk6_0)
    | in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
    inference(rw,[status(thm)],[38,20,theory(equality)]),
    [unfolding] ).

cnf(43,plain,
    ( in(X2,X4)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
    inference(rw,[status(thm)],[17,20,theory(equality)]),
    [unfolding] ).

cnf(44,plain,
    ( in(X1,X3)
    | ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4)) ),
    inference(rw,[status(thm)],[18,20,theory(equality)]),
    [unfolding] ).

cnf(45,plain,
    ( in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),cartesian_product2(X3,X4))
    | ~ in(X2,X4)
    | ~ in(X1,X3) ),
    inference(rw,[status(thm)],[16,20,theory(equality)]),
    [unfolding] ).

cnf(47,negated_conjecture,
    ( ~ in(esk3_0,esk5_0)
    | ~ in(esk4_0,esk6_0)
    | ~ in(unordered_pair(unordered_pair(esk3_0,esk4_0),singleton(esk3_0)),cartesian_product2(esk5_0,esk6_0)) ),
    inference(rw,[status(thm)],[40,20,theory(equality)]),
    [unfolding] ).

cnf(55,negated_conjecture,
    in(esk4_0,esk6_0),
    inference(spm,[status(thm)],[43,42,theory(equality)]) ).

cnf(66,negated_conjecture,
    ( ~ in(esk3_0,esk5_0)
    | ~ in(esk4_0,esk6_0) ),
    inference(csr,[status(thm)],[47,45]) ).

cnf(71,negated_conjecture,
    in(esk3_0,esk5_0),
    inference(spm,[status(thm)],[44,41,theory(equality)]) ).

cnf(83,negated_conjecture,
    ( ~ in(esk3_0,esk5_0)
    | $false ),
    inference(rw,[status(thm)],[66,55,theory(equality)]) ).

cnf(84,negated_conjecture,
    ~ in(esk3_0,esk5_0),
    inference(cn,[status(thm)],[83,theory(equality)]) ).

cnf(93,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[84,71,theory(equality)]) ).

cnf(94,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[93,theory(equality)]) ).

cnf(95,negated_conjecture,
    $false,
    94,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU165+3.p
% --creating new selector for []
% -running prover on /tmp/tmpIGIK02/sel_SEU165+3.p_1 with time limit 29
% -prover status Theorem
% Problem SEU165+3.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU165+3.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU165+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
% 
%------------------------------------------------------------------------------