TSTP Solution File: GEO284+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : GEO284+1 : TPTP v5.0.0. Released v4.1.0.
% 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 : Sat Dec 25 09:22:32 EST 2010

% Result   : Theorem 0.51s
% Output   : CNFRefutation 0.51s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   80 (  20 unt;   0 def)
%            Number of atoms       :  362 ( 118 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives :  473 ( 191   ~; 226   |;  52   &)
%                                         (   2 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   3 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   8 con; 0-2 aty)
%            Number of variables   :  134 (   0 sgn  50   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    vd1123 = vd1129,
    file('/tmp/tmprztlLg/sel_GEO284+1.p_1','holds(258, 1150, 0)') ).

fof(8,axiom,
    ! [X46,X47] :
      ( ( X46 != X47
        & ? [X48] :
            ( X47 = X48
            & rpoint(X48) )
        & ? [X49] :
            ( X46 = X49
            & rpoint(X49) ) )
     => ? [X50] :
          ( ron(X47,X50)
          & rcenter(X46,X50)
          & rcircle(X50) ) ),
    file('/tmp/tmprztlLg/sel_GEO284+1.p_1','qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))') ).

fof(32,axiom,
    ! [X252,X253] :
      ( ( X252 != X253
        & ? [X254] :
            ( X253 = X254
            & rpoint(X254) )
        & ? [X255] :
            ( X252 = X255
            & rpoint(X255) ) )
     => ? [X256] :
          ( ron(X253,X256)
          & ron(X252,X256)
          & rline(X256) ) ),
    file('/tmp/tmprztlLg/sel_GEO284+1.p_1','qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))') ).

fof(58,axiom,
    ( rless(vf(vd1127,vd1129),vf(vd1123,vd1125))
    & vd1127 != vd1129
    & vd1123 != vd1125
    & vd1129 = vd1130
    & rpoint(vd1130)
    & vd1127 = vd1128
    & rpoint(vd1128)
    & vd1125 = vd1126
    & rpoint(vd1126)
    & vd1123 = vd1124
    & rpoint(vd1124) ),
    file('/tmp/tmprztlLg/sel_GEO284+1.p_1','and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))') ).

fof(61,conjecture,
    ? [X437,X438] :
      ( ron(vd1127,X438)
      & rcenter(vd1123,X438)
      & rcircle(X438)
      & ron(vd1125,X437)
      & ron(vd1123,X437)
      & rline(X437) ),
    file('/tmp/tmprztlLg/sel_GEO284+1.p_1','qe(259)') ).

fof(108,negated_conjecture,
    ~ ? [X437,X438] :
        ( ron(vd1127,X438)
        & rcenter(vd1123,X438)
        & rcircle(X438)
        & ron(vd1125,X437)
        & ron(vd1123,X437)
        & rline(X437) ),
    inference(assume_negation,[status(cth)],[61]) ).

cnf(172,plain,
    vd1123 = vd1129,
    inference(split_conjunct,[status(thm)],[6]) ).

fof(177,plain,
    ! [X46,X47] :
      ( X46 = X47
      | ! [X48] :
          ( X47 != X48
          | ~ rpoint(X48) )
      | ! [X49] :
          ( X46 != X49
          | ~ rpoint(X49) )
      | ? [X50] :
          ( ron(X47,X50)
          & rcenter(X46,X50)
          & rcircle(X50) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(178,plain,
    ! [X51,X52] :
      ( X51 = X52
      | ! [X53] :
          ( X52 != X53
          | ~ rpoint(X53) )
      | ! [X54] :
          ( X51 != X54
          | ~ rpoint(X54) )
      | ? [X55] :
          ( ron(X52,X55)
          & rcenter(X51,X55)
          & rcircle(X55) ) ),
    inference(variable_rename,[status(thm)],[177]) ).

fof(179,plain,
    ! [X51,X52] :
      ( X51 = X52
      | ! [X53] :
          ( X52 != X53
          | ~ rpoint(X53) )
      | ! [X54] :
          ( X51 != X54
          | ~ rpoint(X54) )
      | ( ron(X52,esk4_2(X51,X52))
        & rcenter(X51,esk4_2(X51,X52))
        & rcircle(esk4_2(X51,X52)) ) ),
    inference(skolemize,[status(esa)],[178]) ).

fof(180,plain,
    ! [X51,X52,X53,X54] :
      ( X51 != X54
      | ~ rpoint(X54)
      | X52 != X53
      | ~ rpoint(X53)
      | X51 = X52
      | ( ron(X52,esk4_2(X51,X52))
        & rcenter(X51,esk4_2(X51,X52))
        & rcircle(esk4_2(X51,X52)) ) ),
    inference(shift_quantors,[status(thm)],[179]) ).

fof(181,plain,
    ! [X51,X52,X53,X54] :
      ( ( ron(X52,esk4_2(X51,X52))
        | X51 != X54
        | ~ rpoint(X54)
        | X52 != X53
        | ~ rpoint(X53)
        | X51 = X52 )
      & ( rcenter(X51,esk4_2(X51,X52))
        | X51 != X54
        | ~ rpoint(X54)
        | X52 != X53
        | ~ rpoint(X53)
        | X51 = X52 )
      & ( rcircle(esk4_2(X51,X52))
        | X51 != X54
        | ~ rpoint(X54)
        | X52 != X53
        | ~ rpoint(X53)
        | X51 = X52 ) ),
    inference(distribute,[status(thm)],[180]) ).

cnf(182,plain,
    ( X1 = X2
    | rcircle(esk4_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[181]) ).

cnf(183,plain,
    ( X1 = X2
    | rcenter(X1,esk4_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[181]) ).

cnf(184,plain,
    ( X1 = X2
    | ron(X2,esk4_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[181]) ).

fof(347,plain,
    ! [X252,X253] :
      ( X252 = X253
      | ! [X254] :
          ( X253 != X254
          | ~ rpoint(X254) )
      | ! [X255] :
          ( X252 != X255
          | ~ rpoint(X255) )
      | ? [X256] :
          ( ron(X253,X256)
          & ron(X252,X256)
          & rline(X256) ) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(348,plain,
    ! [X257,X258] :
      ( X257 = X258
      | ! [X259] :
          ( X258 != X259
          | ~ rpoint(X259) )
      | ! [X260] :
          ( X257 != X260
          | ~ rpoint(X260) )
      | ? [X261] :
          ( ron(X258,X261)
          & ron(X257,X261)
          & rline(X261) ) ),
    inference(variable_rename,[status(thm)],[347]) ).

fof(349,plain,
    ! [X257,X258] :
      ( X257 = X258
      | ! [X259] :
          ( X258 != X259
          | ~ rpoint(X259) )
      | ! [X260] :
          ( X257 != X260
          | ~ rpoint(X260) )
      | ( ron(X258,esk19_2(X257,X258))
        & ron(X257,esk19_2(X257,X258))
        & rline(esk19_2(X257,X258)) ) ),
    inference(skolemize,[status(esa)],[348]) ).

fof(350,plain,
    ! [X257,X258,X259,X260] :
      ( X257 != X260
      | ~ rpoint(X260)
      | X258 != X259
      | ~ rpoint(X259)
      | X257 = X258
      | ( ron(X258,esk19_2(X257,X258))
        & ron(X257,esk19_2(X257,X258))
        & rline(esk19_2(X257,X258)) ) ),
    inference(shift_quantors,[status(thm)],[349]) ).

fof(351,plain,
    ! [X257,X258,X259,X260] :
      ( ( ron(X258,esk19_2(X257,X258))
        | X257 != X260
        | ~ rpoint(X260)
        | X258 != X259
        | ~ rpoint(X259)
        | X257 = X258 )
      & ( ron(X257,esk19_2(X257,X258))
        | X257 != X260
        | ~ rpoint(X260)
        | X258 != X259
        | ~ rpoint(X259)
        | X257 = X258 )
      & ( rline(esk19_2(X257,X258))
        | X257 != X260
        | ~ rpoint(X260)
        | X258 != X259
        | ~ rpoint(X259)
        | X257 = X258 ) ),
    inference(distribute,[status(thm)],[350]) ).

cnf(352,plain,
    ( X1 = X2
    | rline(esk19_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[351]) ).

cnf(353,plain,
    ( X1 = X2
    | ron(X1,esk19_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[351]) ).

cnf(354,plain,
    ( X1 = X2
    | ron(X2,esk19_2(X1,X2))
    | ~ rpoint(X3)
    | X2 != X3
    | ~ rpoint(X4)
    | X1 != X4 ),
    inference(split_conjunct,[status(thm)],[351]) ).

cnf(483,plain,
    rpoint(vd1126),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(484,plain,
    vd1125 = vd1126,
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(485,plain,
    rpoint(vd1128),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(486,plain,
    vd1127 = vd1128,
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(487,plain,
    rpoint(vd1130),
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(488,plain,
    vd1129 = vd1130,
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(489,plain,
    vd1123 != vd1125,
    inference(split_conjunct,[status(thm)],[58]) ).

cnf(490,plain,
    vd1127 != vd1129,
    inference(split_conjunct,[status(thm)],[58]) ).

fof(503,negated_conjecture,
    ! [X437,X438] :
      ( ~ ron(vd1127,X438)
      | ~ rcenter(vd1123,X438)
      | ~ rcircle(X438)
      | ~ ron(vd1125,X437)
      | ~ ron(vd1123,X437)
      | ~ rline(X437) ),
    inference(fof_nnf,[status(thm)],[108]) ).

fof(504,negated_conjecture,
    ! [X439,X440] :
      ( ~ ron(vd1127,X440)
      | ~ rcenter(vd1123,X440)
      | ~ rcircle(X440)
      | ~ ron(vd1125,X439)
      | ~ ron(vd1123,X439)
      | ~ rline(X439) ),
    inference(variable_rename,[status(thm)],[503]) ).

cnf(505,negated_conjecture,
    ( ~ rline(X1)
    | ~ ron(vd1123,X1)
    | ~ ron(vd1125,X1)
    | ~ rcircle(X2)
    | ~ rcenter(vd1123,X2)
    | ~ ron(vd1127,X2) ),
    inference(split_conjunct,[status(thm)],[504]) ).

cnf(766,plain,
    vd1130 = vd1123,
    inference(rw,[status(thm)],[488,172,theory(equality)]) ).

cnf(767,plain,
    rpoint(vd1123),
    inference(rw,[status(thm)],[487,766,theory(equality)]) ).

cnf(768,plain,
    vd1127 != vd1123,
    inference(rw,[status(thm)],[490,172,theory(equality)]) ).

cnf(769,plain,
    rpoint(vd1127),
    inference(rw,[status(thm)],[485,486,theory(equality)]) ).

cnf(770,plain,
    rpoint(vd1125),
    inference(rw,[status(thm)],[483,484,theory(equality)]) ).

fof(798,plain,
    ( ~ epred1_0
  <=> ! [X2] :
        ( ~ ron(vd1127,X2)
        | ~ rcircle(X2)
        | ~ rcenter(vd1123,X2) ) ),
    introduced(definition),
    [split] ).

cnf(799,plain,
    ( epred1_0
    | ~ ron(vd1127,X2)
    | ~ rcircle(X2)
    | ~ rcenter(vd1123,X2) ),
    inference(split_equiv,[status(thm)],[798]) ).

fof(800,plain,
    ( ~ epred2_0
  <=> ! [X1] :
        ( ~ ron(vd1125,X1)
        | ~ ron(vd1123,X1)
        | ~ rline(X1) ) ),
    introduced(definition),
    [split] ).

cnf(801,plain,
    ( epred2_0
    | ~ ron(vd1125,X1)
    | ~ ron(vd1123,X1)
    | ~ rline(X1) ),
    inference(split_equiv,[status(thm)],[800]) ).

cnf(802,negated_conjecture,
    ( ~ epred2_0
    | ~ epred1_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[505,798,theory(equality)]),800,theory(equality)]),
    [split] ).

cnf(825,plain,
    ( X1 = X2
    | rline(esk19_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[352,theory(equality)]) ).

cnf(826,plain,
    ( X1 = X2
    | rline(esk19_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[825,theory(equality)]) ).

cnf(827,plain,
    ( X1 = X2
    | rcircle(esk4_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[182,theory(equality)]) ).

cnf(828,plain,
    ( X1 = X2
    | rcircle(esk4_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[827,theory(equality)]) ).

cnf(840,plain,
    ( X1 = X2
    | ron(X2,esk4_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[184,theory(equality)]) ).

cnf(841,plain,
    ( X1 = X2
    | ron(X2,esk4_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[840,theory(equality)]) ).

cnf(842,plain,
    ( X1 = X2
    | ron(X2,esk19_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[354,theory(equality)]) ).

cnf(843,plain,
    ( X1 = X2
    | ron(X2,esk19_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[842,theory(equality)]) ).

cnf(844,plain,
    ( X1 = X2
    | ron(X1,esk19_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[353,theory(equality)]) ).

cnf(845,plain,
    ( X1 = X2
    | ron(X1,esk19_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[844,theory(equality)]) ).

cnf(846,plain,
    ( X1 = X2
    | rcenter(X1,esk4_2(X1,X2))
    | X1 != X3
    | ~ rpoint(X3)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[183,theory(equality)]) ).

cnf(847,plain,
    ( X1 = X2
    | rcenter(X1,esk4_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(er,[status(thm)],[846,theory(equality)]) ).

cnf(1883,negated_conjecture,
    ( epred2_0
    | X1 = X2
    | ~ ron(vd1125,esk19_2(X1,X2))
    | ~ ron(vd1123,esk19_2(X1,X2))
    | ~ rpoint(X1)
    | ~ rpoint(X2) ),
    inference(spm,[status(thm)],[801,826,theory(equality)]) ).

cnf(1908,negated_conjecture,
    ( X1 = vd1125
    | epred2_0
    | ~ rpoint(X1)
    | ~ rpoint(vd1125)
    | ~ ron(vd1123,esk19_2(X1,vd1125)) ),
    inference(spm,[status(thm)],[1883,843,theory(equality)]) ).

cnf(1909,negated_conjecture,
    ( X1 = vd1125
    | epred2_0
    | ~ rpoint(X1)
    | $false
    | ~ ron(vd1123,esk19_2(X1,vd1125)) ),
    inference(rw,[status(thm)],[1908,770,theory(equality)]) ).

cnf(1910,negated_conjecture,
    ( X1 = vd1125
    | epred2_0
    | ~ rpoint(X1)
    | ~ ron(vd1123,esk19_2(X1,vd1125)) ),
    inference(cn,[status(thm)],[1909,theory(equality)]) ).

cnf(1916,negated_conjecture,
    ( vd1123 = vd1125
    | epred2_0
    | ~ rpoint(vd1123)
    | ~ rpoint(vd1125) ),
    inference(spm,[status(thm)],[1910,845,theory(equality)]) ).

cnf(1919,negated_conjecture,
    ( vd1123 = vd1125
    | epred2_0
    | $false
    | ~ rpoint(vd1125) ),
    inference(rw,[status(thm)],[1916,767,theory(equality)]) ).

cnf(1920,negated_conjecture,
    ( vd1123 = vd1125
    | epred2_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[1919,770,theory(equality)]) ).

cnf(1921,negated_conjecture,
    ( vd1123 = vd1125
    | epred2_0 ),
    inference(cn,[status(thm)],[1920,theory(equality)]) ).

cnf(1922,negated_conjecture,
    epred2_0,
    inference(sr,[status(thm)],[1921,489,theory(equality)]) ).

cnf(1926,negated_conjecture,
    ( $false
    | ~ epred1_0 ),
    inference(rw,[status(thm)],[802,1922,theory(equality)]) ).

cnf(1927,negated_conjecture,
    ~ epred1_0,
    inference(cn,[status(thm)],[1926,theory(equality)]) ).

cnf(1929,negated_conjecture,
    ( epred1_0
    | vd1123 = X1
    | ~ rcircle(esk4_2(vd1123,X1))
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | ~ rpoint(vd1123)
    | ~ rpoint(X1) ),
    inference(spm,[status(thm)],[799,847,theory(equality)]) ).

cnf(1933,negated_conjecture,
    ( epred1_0
    | vd1123 = X1
    | ~ rcircle(esk4_2(vd1123,X1))
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | $false
    | ~ rpoint(X1) ),
    inference(rw,[status(thm)],[1929,767,theory(equality)]) ).

cnf(1934,negated_conjecture,
    ( epred1_0
    | vd1123 = X1
    | ~ rcircle(esk4_2(vd1123,X1))
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | ~ rpoint(X1) ),
    inference(cn,[status(thm)],[1933,theory(equality)]) ).

cnf(1935,negated_conjecture,
    ( vd1123 = X1
    | ~ rcircle(esk4_2(vd1123,X1))
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | ~ rpoint(X1) ),
    inference(sr,[status(thm)],[1934,1927,theory(equality)]) ).

cnf(1936,negated_conjecture,
    ( vd1123 = X1
    | ~ rpoint(X1)
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | ~ rpoint(vd1123) ),
    inference(spm,[status(thm)],[1935,828,theory(equality)]) ).

cnf(1937,negated_conjecture,
    ( vd1123 = X1
    | ~ rpoint(X1)
    | ~ ron(vd1127,esk4_2(vd1123,X1))
    | $false ),
    inference(rw,[status(thm)],[1936,767,theory(equality)]) ).

cnf(1938,negated_conjecture,
    ( vd1123 = X1
    | ~ rpoint(X1)
    | ~ ron(vd1127,esk4_2(vd1123,X1)) ),
    inference(cn,[status(thm)],[1937,theory(equality)]) ).

cnf(1939,negated_conjecture,
    ( vd1123 = vd1127
    | ~ rpoint(vd1127)
    | ~ rpoint(vd1123) ),
    inference(spm,[status(thm)],[1938,841,theory(equality)]) ).

cnf(1940,negated_conjecture,
    ( vd1123 = vd1127
    | $false
    | ~ rpoint(vd1123) ),
    inference(rw,[status(thm)],[1939,769,theory(equality)]) ).

cnf(1941,negated_conjecture,
    ( vd1123 = vd1127
    | $false
    | $false ),
    inference(rw,[status(thm)],[1940,767,theory(equality)]) ).

cnf(1942,negated_conjecture,
    vd1123 = vd1127,
    inference(cn,[status(thm)],[1941,theory(equality)]) ).

cnf(1943,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1942,768,theory(equality)]) ).

cnf(1944,negated_conjecture,
    $false,
    1943,
    [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/GEO/GEO284+1.p
% --creating new selector for []
% -running prover on /tmp/tmprztlLg/sel_GEO284+1.p_1 with time limit 29
% -prover status Theorem
% Problem GEO284+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/GEO/GEO284+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/GEO/GEO284+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
% 
%------------------------------------------------------------------------------