TSTP Solution File: SWC029+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC029+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 10:07:04 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   33
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   87 (  16 unt;   0 def)
%            Number of atoms       :  344 ( 159 equ)
%            Maximal formula atoms :   24 (   3 avg)
%            Number of connectives :  406 ( 149   ~; 162   |;  72   &)
%                                         (   2 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   7 con; 0-2 aty)
%            Number of variables   :   72 (   0 sgn  51   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax83) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax15) ).

fof(11,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax16) ).

fof(12,axiom,
    ssList(nil),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax17) ).

fof(14,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax28) ).

fof(17,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',ax21) ).

fof(19,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( nil != X3
                      & nil = X4 )
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ( app(cons(X5,nil),X6) != X4
                                | app(X6,cons(X5,nil)) != X3 ) ) )
                      & neq(X4,nil) )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( nil != X1
                        | nil = X2 ) ) ) ) ) ) ),
    file('/tmp/tmpe4roiI/sel_SWC029+1.p_1',co1) ).

fof(20,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( nil != X3
                        & nil = X4 )
                      | ( ! [X5] :
                            ( ssItem(X5)
                           => ! [X6] :
                                ( ssList(X6)
                               => ( app(cons(X5,nil),X6) != X4
                                  | app(X6,cons(X5,nil)) != X3 ) ) )
                        & neq(X4,nil) )
                      | ( ( nil != X2
                          | nil = X1 )
                        & ( nil != X1
                          | nil = X2 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[19]) ).

fof(41,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( nil != app(X1,X2)
              | ( nil = X2
                & nil = X1 ) )
            & ( nil != X2
              | nil != X1
              | nil = app(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(42,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( nil != app(X3,X4)
              | ( nil = X4
                & nil = X3 ) )
            & ( nil != X4
              | nil != X3
              | nil = app(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[41]) ).

fof(43,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( nil != app(X3,X4)
          | ( nil = X4
            & nil = X3 ) )
        & ( nil != X4
          | nil != X3
          | nil = app(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[42]) ).

fof(44,plain,
    ! [X3,X4] :
      ( ( nil = X4
        | nil != app(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) )
      & ( nil = X3
        | nil != app(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) )
      & ( nil != X4
        | nil != X3
        | nil = app(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) ) ),
    inference(distribute,[status(thm)],[43]) ).

cnf(46,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[44]) ).

fof(63,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(64,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[63]) ).

fof(65,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[64]) ).

fof(66,plain,
    ! [X3,X4] :
      ( ( ~ neq(X3,X4)
        | X3 != X4
        | ~ ssList(X4)
        | ~ ssList(X3) )
      & ( X3 = X4
        | neq(X3,X4)
        | ~ ssList(X4)
        | ~ ssList(X3) ) ),
    inference(distribute,[status(thm)],[65]) ).

cnf(67,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[66]) ).

fof(69,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(70,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[69]) ).

fof(71,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[70]) ).

cnf(72,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(73,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[12]) ).

fof(80,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(81,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[80]) ).

cnf(82,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[81]) ).

fof(91,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | nil != cons(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(92,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | nil != cons(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[91]) ).

fof(93,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | nil != cons(X4,X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[92]) ).

cnf(94,plain,
    ( ~ ssList(X1)
    | nil != cons(X2,X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[93]) ).

fof(101,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( nil = X3
                    | nil != X4 )
                  & ( ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & app(cons(X5,nil),X6) = X4
                            & app(X6,cons(X5,nil)) = X3 ) )
                    | ~ neq(X4,nil) )
                  & ( ( nil = X2
                      & nil != X1 )
                    | ( nil = X1
                      & nil != X2 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(102,negated_conjecture,
    ? [X7] :
      ( ssList(X7)
      & ? [X8] :
          ( ssList(X8)
          & ? [X9] :
              ( ssList(X9)
              & ? [X10] :
                  ( ssList(X10)
                  & X8 = X10
                  & X7 = X9
                  & ( nil = X9
                    | nil != X10 )
                  & ( ? [X11] :
                        ( ssItem(X11)
                        & ? [X12] :
                            ( ssList(X12)
                            & app(cons(X11,nil),X12) = X10
                            & app(X12,cons(X11,nil)) = X9 ) )
                    | ~ neq(X10,nil) )
                  & ( ( nil = X8
                      & nil != X7 )
                    | ( nil = X7
                      & nil != X8 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[101]) ).

fof(103,negated_conjecture,
    ( ssList(esk5_0)
    & ssList(esk6_0)
    & ssList(esk7_0)
    & ssList(esk8_0)
    & esk6_0 = esk8_0
    & esk5_0 = esk7_0
    & ( nil = esk7_0
      | nil != esk8_0 )
    & ( ( ssItem(esk9_0)
        & ssList(esk10_0)
        & app(cons(esk9_0,nil),esk10_0) = esk8_0
        & app(esk10_0,cons(esk9_0,nil)) = esk7_0 )
      | ~ neq(esk8_0,nil) )
    & ( ( nil = esk6_0
        & nil != esk5_0 )
      | ( nil = esk5_0
        & nil != esk6_0 ) ) ),
    inference(skolemize,[status(esa)],[102]) ).

fof(104,negated_conjecture,
    ( ssList(esk5_0)
    & ssList(esk6_0)
    & ssList(esk7_0)
    & ssList(esk8_0)
    & esk6_0 = esk8_0
    & esk5_0 = esk7_0
    & ( nil = esk7_0
      | nil != esk8_0 )
    & ( ssItem(esk9_0)
      | ~ neq(esk8_0,nil) )
    & ( ssList(esk10_0)
      | ~ neq(esk8_0,nil) )
    & ( app(cons(esk9_0,nil),esk10_0) = esk8_0
      | ~ neq(esk8_0,nil) )
    & ( app(esk10_0,cons(esk9_0,nil)) = esk7_0
      | ~ neq(esk8_0,nil) )
    & ( nil = esk5_0
      | nil = esk6_0 )
    & ( nil != esk6_0
      | nil = esk6_0 )
    & ( nil = esk5_0
      | nil != esk5_0 )
    & ( nil != esk6_0
      | nil != esk5_0 ) ),
    inference(distribute,[status(thm)],[103]) ).

cnf(105,negated_conjecture,
    ( nil != esk5_0
    | nil != esk6_0 ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(108,negated_conjecture,
    ( nil = esk6_0
    | nil = esk5_0 ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(109,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = esk7_0
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(111,negated_conjecture,
    ( ssList(esk10_0)
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(112,negated_conjecture,
    ( ssItem(esk9_0)
    | ~ neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(113,negated_conjecture,
    ( nil = esk7_0
    | nil != esk8_0 ),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(114,negated_conjecture,
    esk5_0 = esk7_0,
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(115,negated_conjecture,
    esk6_0 = esk8_0,
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(118,negated_conjecture,
    ssList(esk6_0),
    inference(split_conjunct,[status(thm)],[104]) ).

cnf(122,negated_conjecture,
    ssList(esk8_0),
    inference(rw,[status(thm)],[118,115,theory(equality)]) ).

cnf(123,negated_conjecture,
    ( esk5_0 = nil
    | esk8_0 = nil ),
    inference(rw,[status(thm)],[108,115,theory(equality)]) ).

cnf(126,negated_conjecture,
    ( esk5_0 = nil
    | esk8_0 != nil ),
    inference(rw,[status(thm)],[113,114,theory(equality)]) ).

cnf(127,negated_conjecture,
    esk5_0 = nil,
    inference(csr,[status(thm)],[126,123]) ).

cnf(133,negated_conjecture,
    ( $false
    | esk6_0 != nil ),
    inference(rw,[status(thm)],[105,127,theory(equality)]) ).

cnf(134,negated_conjecture,
    ( $false
    | esk8_0 != nil ),
    inference(rw,[status(thm)],[133,115,theory(equality)]) ).

cnf(135,negated_conjecture,
    esk8_0 != nil,
    inference(cn,[status(thm)],[134,theory(equality)]) ).

cnf(142,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | ~ neq(esk8_0,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[109,114,theory(equality)]),127,theory(equality)]) ).

cnf(151,negated_conjecture,
    ( ssItem(esk9_0)
    | esk8_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk8_0) ),
    inference(spm,[status(thm)],[112,67,theory(equality)]) ).

cnf(152,negated_conjecture,
    ( ssList(esk10_0)
    | esk8_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk8_0) ),
    inference(spm,[status(thm)],[111,67,theory(equality)]) ).

cnf(153,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | esk8_0 = nil
    | ~ ssList(nil)
    | ~ ssList(esk8_0) ),
    inference(spm,[status(thm)],[142,67,theory(equality)]) ).

cnf(155,negated_conjecture,
    ( ssItem(esk9_0)
    | esk8_0 = nil
    | $false
    | ~ ssList(esk8_0) ),
    inference(rw,[status(thm)],[151,73,theory(equality)]) ).

cnf(156,negated_conjecture,
    ( ssItem(esk9_0)
    | esk8_0 = nil
    | ~ ssList(esk8_0) ),
    inference(cn,[status(thm)],[155,theory(equality)]) ).

cnf(157,negated_conjecture,
    ( ssItem(esk9_0)
    | ~ ssList(esk8_0) ),
    inference(sr,[status(thm)],[156,135,theory(equality)]) ).

cnf(158,negated_conjecture,
    ( ssList(esk10_0)
    | esk8_0 = nil
    | $false
    | ~ ssList(esk8_0) ),
    inference(rw,[status(thm)],[152,73,theory(equality)]) ).

cnf(159,negated_conjecture,
    ( ssList(esk10_0)
    | esk8_0 = nil
    | ~ ssList(esk8_0) ),
    inference(cn,[status(thm)],[158,theory(equality)]) ).

cnf(160,negated_conjecture,
    ( ssList(esk10_0)
    | ~ ssList(esk8_0) ),
    inference(sr,[status(thm)],[159,135,theory(equality)]) ).

cnf(161,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | esk8_0 = nil
    | $false
    | ~ ssList(esk8_0) ),
    inference(rw,[status(thm)],[153,73,theory(equality)]) ).

cnf(162,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | esk8_0 = nil
    | ~ ssList(esk8_0) ),
    inference(cn,[status(thm)],[161,theory(equality)]) ).

cnf(163,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | ~ ssList(esk8_0) ),
    inference(sr,[status(thm)],[162,135,theory(equality)]) ).

cnf(255,negated_conjecture,
    ( ssItem(esk9_0)
    | $false ),
    inference(rw,[status(thm)],[157,122,theory(equality)]) ).

cnf(256,negated_conjecture,
    ssItem(esk9_0),
    inference(cn,[status(thm)],[255,theory(equality)]) ).

cnf(258,negated_conjecture,
    ( ssList(esk10_0)
    | $false ),
    inference(rw,[status(thm)],[160,122,theory(equality)]) ).

cnf(259,negated_conjecture,
    ssList(esk10_0),
    inference(cn,[status(thm)],[258,theory(equality)]) ).

cnf(265,negated_conjecture,
    ( app(esk10_0,cons(esk9_0,nil)) = nil
    | $false ),
    inference(rw,[status(thm)],[163,122,theory(equality)]) ).

cnf(266,negated_conjecture,
    app(esk10_0,cons(esk9_0,nil)) = nil,
    inference(cn,[status(thm)],[265,theory(equality)]) ).

cnf(269,negated_conjecture,
    ( nil = esk10_0
    | ~ ssList(cons(esk9_0,nil))
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[46,266,theory(equality)]) ).

cnf(283,negated_conjecture,
    ( nil = esk10_0
    | ~ ssList(cons(esk9_0,nil))
    | $false ),
    inference(rw,[status(thm)],[269,259,theory(equality)]) ).

cnf(284,negated_conjecture,
    ( nil = esk10_0
    | ~ ssList(cons(esk9_0,nil)) ),
    inference(cn,[status(thm)],[283,theory(equality)]) ).

cnf(297,negated_conjecture,
    ( esk10_0 = nil
    | ~ ssList(nil)
    | ~ ssItem(esk9_0) ),
    inference(spm,[status(thm)],[284,72,theory(equality)]) ).

cnf(298,negated_conjecture,
    ( esk10_0 = nil
    | $false
    | ~ ssItem(esk9_0) ),
    inference(rw,[status(thm)],[297,73,theory(equality)]) ).

cnf(299,negated_conjecture,
    ( esk10_0 = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[298,256,theory(equality)]) ).

cnf(300,negated_conjecture,
    esk10_0 = nil,
    inference(cn,[status(thm)],[299,theory(equality)]) ).

cnf(301,negated_conjecture,
    app(nil,cons(esk9_0,nil)) = nil,
    inference(rw,[status(thm)],[266,300,theory(equality)]) ).

cnf(306,negated_conjecture,
    ( nil = cons(esk9_0,nil)
    | ~ ssList(cons(esk9_0,nil)) ),
    inference(spm,[status(thm)],[82,301,theory(equality)]) ).

cnf(332,negated_conjecture,
    ( cons(esk9_0,nil) = nil
    | ~ ssList(nil)
    | ~ ssItem(esk9_0) ),
    inference(spm,[status(thm)],[306,72,theory(equality)]) ).

cnf(333,negated_conjecture,
    ( cons(esk9_0,nil) = nil
    | $false
    | ~ ssItem(esk9_0) ),
    inference(rw,[status(thm)],[332,73,theory(equality)]) ).

cnf(334,negated_conjecture,
    ( cons(esk9_0,nil) = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[333,256,theory(equality)]) ).

cnf(335,negated_conjecture,
    cons(esk9_0,nil) = nil,
    inference(cn,[status(thm)],[334,theory(equality)]) ).

cnf(337,negated_conjecture,
    ( ~ ssList(nil)
    | ~ ssItem(esk9_0) ),
    inference(spm,[status(thm)],[94,335,theory(equality)]) ).

cnf(352,negated_conjecture,
    ( $false
    | ~ ssItem(esk9_0) ),
    inference(rw,[status(thm)],[337,73,theory(equality)]) ).

cnf(353,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[352,256,theory(equality)]) ).

cnf(354,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[353,theory(equality)]) ).

cnf(355,negated_conjecture,
    $false,
    354,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC029+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpe4roiI/sel_SWC029+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC029+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC029+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC029+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
% 
%------------------------------------------------------------------------------