TSTP Solution File: SWC018+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC018+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 10:05:56 EST 2010

% Result   : Theorem 0.22s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   27
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   77 (  18 unt;   0 def)
%            Number of atoms       :  417 ( 137 equ)
%            Maximal formula atoms :   30 (   5 avg)
%            Number of connectives :  542 ( 202   ~; 203   |; 111   &)
%                                         (   3 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :  122 (   0 sgn  77   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,X1) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax42) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax26) ).

fof(12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( frontsegP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax46) ).

fof(17,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax5) ).

fof(24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax15) ).

fof(26,axiom,
    ssList(nil),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',ax17) ).

fof(30,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ! [X5] :
                        ( ssList(X5)
                       => ( app(X3,X5) != X4
                          | ~ equalelemsP(X3)
                          | ? [X6] :
                              ( ssItem(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(cons(X6,nil),X7) = X5
                                  & ? [X8] :
                                      ( ssList(X8)
                                      & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                    | ( nil != X4
                      & nil = X3 )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ? [X9] :
                            ( ssList(X9)
                            & neq(X9,nil)
                            & frontsegP(X2,X9)
                            & frontsegP(X1,X9) ) ) ) ) ) ) ) ),
    file('/tmp/tmpgvEuAH/sel_SWC018+1.p_1',co1) ).

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

fof(32,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ! [X5] :
                          ( ssList(X5)
                         => ( app(X3,X5) != X4
                            | ~ equalelemsP(X3)
                            | ? [X6] :
                                ( ssItem(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(cons(X6,nil),X7) = X5
                                    & ? [X8] :
                                        ( ssList(X8)
                                        & app(X8,cons(X6,nil)) = X3 ) ) ) ) )
                      | ( nil != X4
                        & nil = X3 )
                      | ( ( nil != X2
                          | nil = X1 )
                        & ( ~ neq(X2,nil)
                          | ? [X9] :
                              ( ssList(X9)
                              & neq(X9,nil)
                              & frontsegP(X2,X9)
                              & frontsegP(X1,X9) ) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).

fof(62,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | frontsegP(X1,X1) ),
    inference(fof_nnf,[status(thm)],[8]) ).

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

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

fof(69,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

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

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

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

fof(77,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ frontsegP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | frontsegP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(78,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ frontsegP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | frontsegP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[77]) ).

fof(79,plain,
    ! [X2] :
      ( ( ~ frontsegP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | frontsegP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[78]) ).

cnf(81,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ frontsegP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[79]) ).

fof(102,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ frontsegP(X1,X2)
              | ? [X3] :
                  ( ssList(X3)
                  & app(X2,X3) = X1 ) )
            & ( ! [X3] :
                  ( ~ ssList(X3)
                  | app(X2,X3) != X1 )
              | frontsegP(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(103,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ( ( ~ frontsegP(X4,X5)
              | ? [X6] :
                  ( ssList(X6)
                  & app(X5,X6) = X4 ) )
            & ( ! [X7] :
                  ( ~ ssList(X7)
                  | app(X5,X7) != X4 )
              | frontsegP(X4,X5) ) ) ) ),
    inference(variable_rename,[status(thm)],[102]) ).

fof(104,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ( ( ~ frontsegP(X4,X5)
              | ( ssList(esk3_2(X4,X5))
                & app(X5,esk3_2(X4,X5)) = X4 ) )
            & ( ! [X7] :
                  ( ~ ssList(X7)
                  | app(X5,X7) != X4 )
              | frontsegP(X4,X5) ) ) ) ),
    inference(skolemize,[status(esa)],[103]) ).

fof(105,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ ssList(X7)
          | app(X5,X7) != X4
          | frontsegP(X4,X5) )
        & ( ~ frontsegP(X4,X5)
          | ( ssList(esk3_2(X4,X5))
            & app(X5,esk3_2(X4,X5)) = X4 ) ) )
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[104]) ).

fof(106,plain,
    ! [X4,X5,X7] :
      ( ( ~ ssList(X7)
        | app(X5,X7) != X4
        | frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( ssList(esk3_2(X4,X5))
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( app(X5,esk3_2(X4,X5)) = X4
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[105]) ).

cnf(109,plain,
    ( frontsegP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X2,X3) != X1
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[106]) ).

fof(140,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(141,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[140]) ).

fof(142,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[141]) ).

fof(143,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)],[142]) ).

cnf(144,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[143]) ).

cnf(145,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | X1 != X2
    | ~ neq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[143]) ).

cnf(150,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(167,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ? [X5] :
                      ( ssList(X5)
                      & app(X3,X5) = X4
                      & equalelemsP(X3)
                      & ! [X6] :
                          ( ~ ssItem(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(cons(X6,nil),X7) != X5
                              | ! [X8] :
                                  ( ~ ssList(X8)
                                  | app(X8,cons(X6,nil)) != X3 ) ) ) )
                  & ( nil = X4
                    | nil != X3 )
                  & ( ( nil = X2
                      & nil != X1 )
                    | ( neq(X2,nil)
                      & ! [X9] :
                          ( ~ ssList(X9)
                          | ~ neq(X9,nil)
                          | ~ frontsegP(X2,X9)
                          | ~ frontsegP(X1,X9) ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(168,negated_conjecture,
    ? [X10] :
      ( ssList(X10)
      & ? [X11] :
          ( ssList(X11)
          & ? [X12] :
              ( ssList(X12)
              & ? [X13] :
                  ( ssList(X13)
                  & X11 = X13
                  & X10 = X12
                  & ? [X14] :
                      ( ssList(X14)
                      & app(X12,X14) = X13
                      & equalelemsP(X12)
                      & ! [X15] :
                          ( ~ ssItem(X15)
                          | ! [X16] :
                              ( ~ ssList(X16)
                              | app(cons(X15,nil),X16) != X14
                              | ! [X17] :
                                  ( ~ ssList(X17)
                                  | app(X17,cons(X15,nil)) != X12 ) ) ) )
                  & ( nil = X13
                    | nil != X12 )
                  & ( ( nil = X11
                      & nil != X10 )
                    | ( neq(X11,nil)
                      & ! [X18] :
                          ( ~ ssList(X18)
                          | ~ neq(X18,nil)
                          | ~ frontsegP(X11,X18)
                          | ~ frontsegP(X10,X18) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[167]) ).

fof(169,negated_conjecture,
    ( ssList(esk10_0)
    & ssList(esk11_0)
    & ssList(esk12_0)
    & ssList(esk13_0)
    & esk11_0 = esk13_0
    & esk10_0 = esk12_0
    & ssList(esk14_0)
    & app(esk12_0,esk14_0) = esk13_0
    & equalelemsP(esk12_0)
    & ! [X15] :
        ( ~ ssItem(X15)
        | ! [X16] :
            ( ~ ssList(X16)
            | app(cons(X15,nil),X16) != esk14_0
            | ! [X17] :
                ( ~ ssList(X17)
                | app(X17,cons(X15,nil)) != esk12_0 ) ) )
    & ( nil = esk13_0
      | nil != esk12_0 )
    & ( ( nil = esk11_0
        & nil != esk10_0 )
      | ( neq(esk11_0,nil)
        & ! [X18] :
            ( ~ ssList(X18)
            | ~ neq(X18,nil)
            | ~ frontsegP(esk11_0,X18)
            | ~ frontsegP(esk10_0,X18) ) ) ) ),
    inference(skolemize,[status(esa)],[168]) ).

fof(170,negated_conjecture,
    ! [X15,X16,X17,X18] :
      ( ( ( ( ~ ssList(X18)
            | ~ neq(X18,nil)
            | ~ frontsegP(esk11_0,X18)
            | ~ frontsegP(esk10_0,X18) )
          & neq(esk11_0,nil) )
        | ( nil = esk11_0
          & nil != esk10_0 ) )
      & ( ~ ssList(X17)
        | app(X17,cons(X15,nil)) != esk12_0
        | ~ ssList(X16)
        | app(cons(X15,nil),X16) != esk14_0
        | ~ ssItem(X15) )
      & app(esk12_0,esk14_0) = esk13_0
      & equalelemsP(esk12_0)
      & ssList(esk14_0)
      & esk11_0 = esk13_0
      & esk10_0 = esk12_0
      & ( nil = esk13_0
        | nil != esk12_0 )
      & ssList(esk13_0)
      & ssList(esk12_0)
      & ssList(esk11_0)
      & ssList(esk10_0) ),
    inference(shift_quantors,[status(thm)],[169]) ).

fof(171,negated_conjecture,
    ! [X15,X16,X17,X18] :
      ( ( nil = esk11_0
        | ~ ssList(X18)
        | ~ neq(X18,nil)
        | ~ frontsegP(esk11_0,X18)
        | ~ frontsegP(esk10_0,X18) )
      & ( nil != esk10_0
        | ~ ssList(X18)
        | ~ neq(X18,nil)
        | ~ frontsegP(esk11_0,X18)
        | ~ frontsegP(esk10_0,X18) )
      & ( nil = esk11_0
        | neq(esk11_0,nil) )
      & ( nil != esk10_0
        | neq(esk11_0,nil) )
      & ( ~ ssList(X17)
        | app(X17,cons(X15,nil)) != esk12_0
        | ~ ssList(X16)
        | app(cons(X15,nil),X16) != esk14_0
        | ~ ssItem(X15) )
      & app(esk12_0,esk14_0) = esk13_0
      & equalelemsP(esk12_0)
      & ssList(esk14_0)
      & esk11_0 = esk13_0
      & esk10_0 = esk12_0
      & ( nil = esk13_0
        | nil != esk12_0 )
      & ssList(esk13_0)
      & ssList(esk12_0)
      & ssList(esk11_0)
      & ssList(esk10_0) ),
    inference(distribute,[status(thm)],[170]) ).

cnf(172,negated_conjecture,
    ssList(esk10_0),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(176,negated_conjecture,
    ( nil = esk13_0
    | nil != esk12_0 ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(177,negated_conjecture,
    esk10_0 = esk12_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(178,negated_conjecture,
    esk11_0 = esk13_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(179,negated_conjecture,
    ssList(esk14_0),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(181,negated_conjecture,
    app(esk12_0,esk14_0) = esk13_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(183,negated_conjecture,
    ( neq(esk11_0,nil)
    | nil != esk10_0 ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(186,negated_conjecture,
    ( nil = esk11_0
    | ~ frontsegP(esk10_0,X1)
    | ~ frontsegP(esk11_0,X1)
    | ~ neq(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(192,negated_conjecture,
    ( esk11_0 = nil
    | esk12_0 != nil ),
    inference(rw,[status(thm)],[176,178,theory(equality)]) ).

cnf(193,negated_conjecture,
    ( esk11_0 = nil
    | esk10_0 != nil ),
    inference(rw,[status(thm)],[192,177,theory(equality)]) ).

cnf(194,negated_conjecture,
    app(esk10_0,esk14_0) = esk13_0,
    inference(rw,[status(thm)],[181,177,theory(equality)]) ).

cnf(195,negated_conjecture,
    app(esk10_0,esk14_0) = esk11_0,
    inference(rw,[status(thm)],[194,178,theory(equality)]) ).

cnf(212,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[145,theory(equality)]) ).

cnf(227,negated_conjecture,
    ( esk11_0 = nil
    | X1 = nil
    | ~ frontsegP(esk10_0,X1)
    | ~ frontsegP(esk11_0,X1)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[186,144,theory(equality)]) ).

cnf(231,negated_conjecture,
    ( esk11_0 = nil
    | X1 = nil
    | ~ frontsegP(esk10_0,X1)
    | ~ frontsegP(esk11_0,X1)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[227,150,theory(equality)]) ).

cnf(232,negated_conjecture,
    ( esk11_0 = nil
    | X1 = nil
    | ~ frontsegP(esk10_0,X1)
    | ~ frontsegP(esk11_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[231,theory(equality)]) ).

cnf(243,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X1,X2)) ),
    inference(er,[status(thm)],[109,theory(equality)]) ).

cnf(469,negated_conjecture,
    ( esk11_0 = nil
    | esk10_0 = nil
    | ~ frontsegP(esk11_0,esk10_0)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[232,64,theory(equality)]) ).

cnf(470,negated_conjecture,
    ( esk11_0 = nil
    | esk10_0 = nil
    | ~ frontsegP(esk11_0,esk10_0)
    | $false ),
    inference(rw,[status(thm)],[469,172,theory(equality)]) ).

cnf(471,negated_conjecture,
    ( esk11_0 = nil
    | esk10_0 = nil
    | ~ frontsegP(esk11_0,esk10_0) ),
    inference(cn,[status(thm)],[470,theory(equality)]) ).

cnf(480,negated_conjecture,
    ( esk11_0 = nil
    | ~ frontsegP(esk11_0,esk10_0) ),
    inference(csr,[status(thm)],[471,193]) ).

cnf(605,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[243,72]) ).

cnf(606,negated_conjecture,
    ( frontsegP(esk11_0,esk10_0)
    | ~ ssList(esk14_0)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[605,195,theory(equality)]) ).

cnf(618,negated_conjecture,
    ( frontsegP(esk11_0,esk10_0)
    | ~ ssList(esk14_0)
    | $false ),
    inference(rw,[status(thm)],[606,172,theory(equality)]) ).

cnf(619,negated_conjecture,
    ( frontsegP(esk11_0,esk10_0)
    | ~ ssList(esk14_0) ),
    inference(cn,[status(thm)],[618,theory(equality)]) ).

cnf(642,negated_conjecture,
    frontsegP(esk11_0,esk10_0),
    inference(spm,[status(thm)],[619,179,theory(equality)]) ).

cnf(649,negated_conjecture,
    ( esk11_0 = nil
    | $false ),
    inference(rw,[status(thm)],[480,642,theory(equality)]) ).

cnf(650,negated_conjecture,
    esk11_0 = nil,
    inference(cn,[status(thm)],[649,theory(equality)]) ).

cnf(666,negated_conjecture,
    frontsegP(nil,esk10_0),
    inference(rw,[status(thm)],[642,650,theory(equality)]) ).

cnf(681,negated_conjecture,
    ( neq(nil,nil)
    | esk10_0 != nil ),
    inference(rw,[status(thm)],[183,650,theory(equality)]) ).

cnf(685,negated_conjecture,
    ( nil = esk10_0
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[81,666,theory(equality)]) ).

cnf(691,negated_conjecture,
    ( nil = esk10_0
    | $false ),
    inference(rw,[status(thm)],[685,172,theory(equality)]) ).

cnf(692,negated_conjecture,
    nil = esk10_0,
    inference(cn,[status(thm)],[691,theory(equality)]) ).

cnf(727,negated_conjecture,
    ( neq(nil,nil)
    | $false ),
    inference(rw,[status(thm)],[681,692,theory(equality)]) ).

cnf(728,negated_conjecture,
    neq(nil,nil),
    inference(cn,[status(thm)],[727,theory(equality)]) ).

cnf(729,negated_conjecture,
    ~ ssList(nil),
    inference(spm,[status(thm)],[212,728,theory(equality)]) ).

cnf(731,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[729,150,theory(equality)]) ).

cnf(732,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[731,theory(equality)]) ).

cnf(733,negated_conjecture,
    $false,
    732,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC018+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpgvEuAH/sel_SWC018+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC018+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC018+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC018+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
% 
%------------------------------------------------------------------------------