TSTP Solution File: SWC240+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC240+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 11:03:40 EST 2010

% Result   : Theorem 0.38s
% Output   : CNFRefutation 0.38s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   59 (   7 unt;   0 def)
%            Number of atoms       :  376 (  99 equ)
%            Maximal formula atoms :   36 (   6 avg)
%            Number of connectives :  515 ( 198   ~; 188   |; 102   &)
%                                         (   1 <=>;  26  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   8 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :  147 (   0 sgn  72   !;  30   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax81) ).

fof(7,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax28) ).

fof(11,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax20) ).

fof(20,axiom,
    ssList(nil),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax17) ).

fof(25,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( lt(X1,X2)
          <=> ( X1 != X2
              & leq(X1,X2) ) ) ) ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax93) ).

fof(28,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',ax16) ).

fof(30,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | nil = X1
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ! [X8] :
                                    ( ssItem(X8)
                                   => ( ~ memberP(X6,X8)
                                      | ~ memberP(X7,X8)
                                      | ~ lt(X5,X8)
                                      | leq(X5,X8) ) ) ) ) )
                    | ! [X9] :
                        ( ssItem(X9)
                       => ? [X10] :
                            ( ssItem(X10)
                            & X9 != X10
                            & memberP(X3,X10) ) ) ) ) ) ) ),
    file('/tmp/tmpo8PqqB/sel_SWC240+1.p_1',co1) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) )
                      | ! [X9] :
                          ( ssItem(X9)
                         => ? [X10] :
                              ( ssItem(X10)
                              & X9 != X10
                              & memberP(X3,X10) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[30]) ).

fof(35,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) )
                      | ! [X9] :
                          ( ssItem(X9)
                         => ? [X10] :
                              ( ssItem(X10)
                              & X9 != X10
                              & memberP(X3,X10) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).

fof(50,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(51,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[50]) ).

fof(52,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[51]) ).

cnf(53,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(62,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(63,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[62]) ).

cnf(64,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[63]) ).

fof(77,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssItem(X3)
              & cons(X3,X2) = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(78,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ? [X5] :
          ( ssList(X5)
          & ? [X6] :
              ( ssItem(X6)
              & cons(X6,X5) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[77]) ).

fof(79,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ( ssList(esk1_1(X4))
        & ssItem(esk2_1(X4))
        & cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
    inference(skolemize,[status(esa)],[78]) ).

fof(80,plain,
    ! [X4] :
      ( ( ssList(esk1_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( ssItem(esk2_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( cons(esk2_1(X4),esk1_1(X4)) = X4
        | nil = X4
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[79]) ).

cnf(81,plain,
    ( nil = X1
    | cons(esk2_1(X1),esk1_1(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

cnf(82,plain,
    ( nil = X1
    | ssItem(esk2_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

cnf(83,plain,
    ( nil = X1
    | ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[80]) ).

cnf(121,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(143,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ( ( ~ lt(X1,X2)
              | ( X1 != X2
                & leq(X1,X2) ) )
            & ( X1 = X2
              | ~ leq(X1,X2)
              | lt(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(144,plain,
    ! [X3] :
      ( ~ ssItem(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ( ( ~ lt(X3,X4)
              | ( X3 != X4
                & leq(X3,X4) ) )
            & ( X3 = X4
              | ~ leq(X3,X4)
              | lt(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[143]) ).

fof(145,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ( ( ~ lt(X3,X4)
          | ( X3 != X4
            & leq(X3,X4) ) )
        & ( X3 = X4
          | ~ leq(X3,X4)
          | lt(X3,X4) ) )
      | ~ ssItem(X3) ),
    inference(shift_quantors,[status(thm)],[144]) ).

fof(146,plain,
    ! [X3,X4] :
      ( ( X3 != X4
        | ~ lt(X3,X4)
        | ~ ssItem(X4)
        | ~ ssItem(X3) )
      & ( leq(X3,X4)
        | ~ lt(X3,X4)
        | ~ ssItem(X4)
        | ~ ssItem(X3) )
      & ( X3 = X4
        | ~ leq(X3,X4)
        | lt(X3,X4)
        | ~ ssItem(X4)
        | ~ ssItem(X3) ) ),
    inference(distribute,[status(thm)],[145]) ).

cnf(148,plain,
    ( leq(X1,X2)
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ lt(X1,X2) ),
    inference(split_conjunct,[status(thm)],[146]) ).

fof(160,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(161,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[160]) ).

fof(162,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[161]) ).

cnf(163,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[162]) ).

fof(167,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & nil != X1
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X1
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & memberP(X6,X8)
                                  & memberP(X7,X8)
                                  & lt(X5,X8)
                                  & ~ leq(X5,X8) ) ) ) )
                  & ? [X9] :
                      ( ssItem(X9)
                      & ! [X10] :
                          ( ~ ssItem(X10)
                          | X9 = X10
                          | ~ memberP(X3,X10) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(168,negated_conjecture,
    ? [X11] :
      ( ssList(X11)
      & ? [X12] :
          ( ssList(X12)
          & ? [X13] :
              ( ssList(X13)
              & ? [X14] :
                  ( ssList(X14)
                  & X12 = X14
                  & X11 = X13
                  & nil != X11
                  & ! [X15] :
                      ( ~ ssItem(X15)
                      | ! [X16] :
                          ( ~ ssList(X16)
                          | ! [X17] :
                              ( ~ ssList(X17)
                              | app(app(X16,cons(X15,nil)),X17) != X11
                              | ? [X18] :
                                  ( ssItem(X18)
                                  & memberP(X16,X18)
                                  & memberP(X17,X18)
                                  & lt(X15,X18)
                                  & ~ leq(X15,X18) ) ) ) )
                  & ? [X19] :
                      ( ssItem(X19)
                      & ! [X20] :
                          ( ~ ssItem(X20)
                          | X19 = X20
                          | ~ memberP(X13,X20) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[167]) ).

fof(169,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & nil != esk7_0
    & ! [X15] :
        ( ~ ssItem(X15)
        | ! [X16] :
            ( ~ ssList(X16)
            | ! [X17] :
                ( ~ ssList(X17)
                | app(app(X16,cons(X15,nil)),X17) != esk7_0
                | ( ssItem(esk11_3(X15,X16,X17))
                  & memberP(X16,esk11_3(X15,X16,X17))
                  & memberP(X17,esk11_3(X15,X16,X17))
                  & lt(X15,esk11_3(X15,X16,X17))
                  & ~ leq(X15,esk11_3(X15,X16,X17)) ) ) ) )
    & ssItem(esk12_0)
    & ! [X20] :
        ( ~ ssItem(X20)
        | esk12_0 = X20
        | ~ memberP(esk9_0,X20) ) ),
    inference(skolemize,[status(esa)],[168]) ).

fof(170,negated_conjecture,
    ! [X15,X16,X17,X20] :
      ( ( ~ ssItem(X20)
        | esk12_0 = X20
        | ~ memberP(esk9_0,X20) )
      & ssItem(esk12_0)
      & ( ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ( ssItem(esk11_3(X15,X16,X17))
          & memberP(X16,esk11_3(X15,X16,X17))
          & memberP(X17,esk11_3(X15,X16,X17))
          & lt(X15,esk11_3(X15,X16,X17))
          & ~ leq(X15,esk11_3(X15,X16,X17)) )
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & nil != esk7_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[169]) ).

fof(171,negated_conjecture,
    ! [X15,X16,X17,X20] :
      ( ( ~ ssItem(X20)
        | esk12_0 = X20
        | ~ memberP(esk9_0,X20) )
      & ssItem(esk12_0)
      & ( ssItem(esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( memberP(X16,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( memberP(X17,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( lt(X15,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( ~ leq(X15,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & nil != esk7_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[170]) ).

cnf(172,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(176,negated_conjecture,
    nil != esk7_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(179,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk7_0
    | ~ ssList(X3)
    | ~ leq(X1,esk11_3(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(180,negated_conjecture,
    ( lt(X1,esk11_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk7_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(183,negated_conjecture,
    ( ssItem(esk11_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk7_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(278,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != esk7_0
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ ssList(X1)
    | ~ lt(X2,esk11_3(X2,X1,X3))
    | ~ ssItem(esk11_3(X2,X1,X3)) ),
    inference(spm,[status(thm)],[179,148,theory(equality)]) ).

cnf(3050,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != esk7_0
    | ~ lt(X2,esk11_3(X2,X1,X3))
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[278,183]) ).

cnf(3051,negated_conjecture,
    ( app(app(X1,cons(X2,nil)),X3) != esk7_0
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[3050,180]) ).

cnf(3053,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(nil)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[3051,64,theory(equality)]) ).

cnf(3065,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false
    | ~ ssList(cons(X1,nil)) ),
    inference(rw,[status(thm)],[3053,121,theory(equality)]) ).

cnf(3066,negated_conjecture,
    ( app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(cons(X1,nil)) ),
    inference(cn,[status(thm)],[3065,theory(equality)]) ).

cnf(3207,negated_conjecture,
    ( cons(X1,X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[3066,53,theory(equality)]) ).

cnf(3269,negated_conjecture,
    ( cons(X1,X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[3207,163,theory(equality)]) ).

cnf(3270,negated_conjecture,
    ( cons(X1,X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false ),
    inference(rw,[status(thm)],[3269,121,theory(equality)]) ).

cnf(3271,negated_conjecture,
    ( cons(X1,X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[3270,theory(equality)]) ).

cnf(3272,negated_conjecture,
    ( nil = X1
    | X1 != esk7_0
    | ~ ssItem(esk2_1(X1))
    | ~ ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[3271,81,theory(equality)]) ).

cnf(3279,negated_conjecture,
    ( nil = X1
    | X1 != esk7_0
    | ~ ssItem(esk2_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[3272,83]) ).

cnf(3280,negated_conjecture,
    ( nil = X1
    | X1 != esk7_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[3279,82]) ).

cnf(3281,negated_conjecture,
    nil = esk7_0,
    inference(spm,[status(thm)],[3280,172,theory(equality)]) ).

cnf(3289,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[3281,176,theory(equality)]) ).

cnf(3290,negated_conjecture,
    $false,
    3289,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC240+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpo8PqqB/sel_SWC240+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC240+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC240+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC240+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
% 
%------------------------------------------------------------------------------