TSTP Solution File: SEU172+2 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SEU172+2 : TPTP v5.0.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 05:05:20 EST 2010

% Result   : Theorem 0.55s
% Output   : CNFRefutation 0.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   27 (   9 unt;   0 def)
%            Number of atoms       :  121 (  22 equ)
%            Maximal formula atoms :   20 (   4 avg)
%            Number of connectives :  146 (  52   ~;  52   |;  35   &)
%                                         (   4 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   3 con; 0-3 aty)
%            Number of variables   :   57 (   2 sgn  40   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(46,conjecture,
    ! [X1,X2,X3] :
      ( element(X3,powerset(X1))
     => ~ ( in(X2,subset_complement(X1,X3))
          & in(X2,X3) ) ),
    file('/tmp/tmp3QkK-8/sel_SEU172+2.p_1',t54_subset_1) ).

fof(73,axiom,
    ! [X1,X2] :
      ( element(X2,powerset(X1))
     => subset_complement(X1,X2) = set_difference(X1,X2) ),
    file('/tmp/tmp3QkK-8/sel_SEU172+2.p_1',d5_subset_1) ).

fof(98,axiom,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    file('/tmp/tmp3QkK-8/sel_SEU172+2.p_1',d4_xboole_0) ).

fof(113,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( element(X3,powerset(X1))
       => ~ ( in(X2,subset_complement(X1,X3))
            & in(X2,X3) ) ),
    inference(assume_negation,[status(cth)],[46]) ).

fof(132,plain,
    ! [X1,X2,X3] :
      ( X3 = set_difference(X1,X2)
    <=> ! [X4] :
          ( in(X4,X3)
        <=> ( in(X4,X1)
            & ~ in(X4,X2) ) ) ),
    inference(fof_simplification,[status(thm)],[98,theory(equality)]) ).

fof(276,negated_conjecture,
    ? [X1,X2,X3] :
      ( element(X3,powerset(X1))
      & in(X2,subset_complement(X1,X3))
      & in(X2,X3) ),
    inference(fof_nnf,[status(thm)],[113]) ).

fof(277,negated_conjecture,
    ? [X4,X5,X6] :
      ( element(X6,powerset(X4))
      & in(X5,subset_complement(X4,X6))
      & in(X5,X6) ),
    inference(variable_rename,[status(thm)],[276]) ).

fof(278,negated_conjecture,
    ( element(esk9_0,powerset(esk7_0))
    & in(esk8_0,subset_complement(esk7_0,esk9_0))
    & in(esk8_0,esk9_0) ),
    inference(skolemize,[status(esa)],[277]) ).

cnf(279,negated_conjecture,
    in(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[278]) ).

cnf(280,negated_conjecture,
    in(esk8_0,subset_complement(esk7_0,esk9_0)),
    inference(split_conjunct,[status(thm)],[278]) ).

cnf(281,negated_conjecture,
    element(esk9_0,powerset(esk7_0)),
    inference(split_conjunct,[status(thm)],[278]) ).

fof(382,plain,
    ! [X1,X2] :
      ( ~ element(X2,powerset(X1))
      | subset_complement(X1,X2) = set_difference(X1,X2) ),
    inference(fof_nnf,[status(thm)],[73]) ).

fof(383,plain,
    ! [X3,X4] :
      ( ~ element(X4,powerset(X3))
      | subset_complement(X3,X4) = set_difference(X3,X4) ),
    inference(variable_rename,[status(thm)],[382]) ).

cnf(384,plain,
    ( subset_complement(X1,X2) = set_difference(X1,X2)
    | ~ element(X2,powerset(X1)) ),
    inference(split_conjunct,[status(thm)],[383]) ).

fof(473,plain,
    ! [X1,X2,X3] :
      ( ( X3 != set_difference(X1,X2)
        | ! [X4] :
            ( ( ~ in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) )
            & ( ~ in(X4,X1)
              | in(X4,X2)
              | in(X4,X3) ) ) )
      & ( ? [X4] :
            ( ( ~ in(X4,X3)
              | ~ in(X4,X1)
              | in(X4,X2) )
            & ( in(X4,X3)
              | ( in(X4,X1)
                & ~ in(X4,X2) ) ) )
        | X3 = set_difference(X1,X2) ) ),
    inference(fof_nnf,[status(thm)],[132]) ).

fof(474,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ? [X9] :
            ( ( ~ in(X9,X7)
              | ~ in(X9,X5)
              | in(X9,X6) )
            & ( in(X9,X7)
              | ( in(X9,X5)
                & ~ in(X9,X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(variable_rename,[status(thm)],[473]) ).

fof(475,plain,
    ! [X5,X6,X7] :
      ( ( X7 != set_difference(X5,X6)
        | ! [X8] :
            ( ( ~ in(X8,X7)
              | ( in(X8,X5)
                & ~ in(X8,X6) ) )
            & ( ~ in(X8,X5)
              | in(X8,X6)
              | in(X8,X7) ) ) )
      & ( ( ( ~ in(esk22_3(X5,X6,X7),X7)
            | ~ in(esk22_3(X5,X6,X7),X5)
            | in(esk22_3(X5,X6,X7),X6) )
          & ( in(esk22_3(X5,X6,X7),X7)
            | ( in(esk22_3(X5,X6,X7),X5)
              & ~ in(esk22_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(skolemize,[status(esa)],[474]) ).

fof(476,plain,
    ! [X5,X6,X7,X8] :
      ( ( ( ( ~ in(X8,X7)
            | ( in(X8,X5)
              & ~ in(X8,X6) ) )
          & ( ~ in(X8,X5)
            | in(X8,X6)
            | in(X8,X7) ) )
        | X7 != set_difference(X5,X6) )
      & ( ( ( ~ in(esk22_3(X5,X6,X7),X7)
            | ~ in(esk22_3(X5,X6,X7),X5)
            | in(esk22_3(X5,X6,X7),X6) )
          & ( in(esk22_3(X5,X6,X7),X7)
            | ( in(esk22_3(X5,X6,X7),X5)
              & ~ in(esk22_3(X5,X6,X7),X6) ) ) )
        | X7 = set_difference(X5,X6) ) ),
    inference(shift_quantors,[status(thm)],[475]) ).

fof(477,plain,
    ! [X5,X6,X7,X8] :
      ( ( in(X8,X5)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X6)
        | ~ in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(X8,X5)
        | in(X8,X6)
        | in(X8,X7)
        | X7 != set_difference(X5,X6) )
      & ( ~ in(esk22_3(X5,X6,X7),X7)
        | ~ in(esk22_3(X5,X6,X7),X5)
        | in(esk22_3(X5,X6,X7),X6)
        | X7 = set_difference(X5,X6) )
      & ( in(esk22_3(X5,X6,X7),X5)
        | in(esk22_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) )
      & ( ~ in(esk22_3(X5,X6,X7),X6)
        | in(esk22_3(X5,X6,X7),X7)
        | X7 = set_difference(X5,X6) ) ),
    inference(distribute,[status(thm)],[476]) ).

cnf(482,plain,
    ( X1 != set_difference(X2,X3)
    | ~ in(X4,X1)
    | ~ in(X4,X3) ),
    inference(split_conjunct,[status(thm)],[477]) ).

cnf(786,negated_conjecture,
    subset_complement(esk7_0,esk9_0) = set_difference(esk7_0,esk9_0),
    inference(spm,[status(thm)],[384,281,theory(equality)]) ).

cnf(859,plain,
    ( ~ in(X1,X2)
    | ~ in(X1,set_difference(X3,X2)) ),
    inference(er,[status(thm)],[482,theory(equality)]) ).

cnf(2333,negated_conjecture,
    in(esk8_0,set_difference(esk7_0,esk9_0)),
    inference(rw,[status(thm)],[280,786,theory(equality)]) ).

cnf(6543,negated_conjecture,
    ~ in(esk8_0,esk9_0),
    inference(spm,[status(thm)],[859,2333,theory(equality)]) ).

cnf(6590,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[6543,279,theory(equality)]) ).

cnf(6591,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[6590,theory(equality)]) ).

cnf(6592,negated_conjecture,
    $false,
    6591,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SEU/SEU172+2.p
% --creating new selector for []
% -running prover on /tmp/tmp3QkK-8/sel_SEU172+2.p_1 with time limit 29
% -prover status Theorem
% Problem SEU172+2.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SEU/SEU172+2.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SEU/SEU172+2.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
% 
%------------------------------------------------------------------------------