TSTP Solution File: SWC327+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC327+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art02.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 11:29:01 EST 2010

% Result   : Theorem 0.34s
% Output   : CNFRefutation 0.34s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :    7
% Syntax   : Number of formulae    :  131 (  18 unt;   0 def)
%            Number of atoms       :  660 ( 294 equ)
%            Maximal formula atoms :   66 (   5 avg)
%            Number of connectives :  862 ( 333   ~; 373   |; 120   &)
%                                         (   1 <=>;  35  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :  183 (   0 sgn  90   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax26) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax83) ).

fof(13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax16) ).

fof(14,axiom,
    ssList(nil),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax17) ).

fof(16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax27) ).

fof(18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',ax21) ).

fof(20,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 )
                    | ( ? [X9] :
                          ( ssList(X9)
                          & app(X1,X9) = X2
                          & ! [X10] :
                              ( ssItem(X10)
                             => ! [X11] :
                                  ( ssList(X11)
                                 => ( app(cons(X10,nil),X11) != X9
                                    | ! [X12] :
                                        ( ssList(X12)
                                       => app(X12,cons(X10,nil)) != X1 ) ) ) )
                          & equalelemsP(X1) )
                      & ( nil != X1
                        | nil = X2 ) ) ) ) ) ) ),
    file('/tmp/tmp6-0fPb/sel_SWC327+1.p_1',co1) ).

fof(21,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 )
                      | ( ? [X9] :
                            ( ssList(X9)
                            & app(X1,X9) = X2
                            & ! [X10] :
                                ( ssItem(X10)
                               => ! [X11] :
                                    ( ssList(X11)
                                   => ( app(cons(X10,nil),X11) != X9
                                      | ! [X12] :
                                          ( ssList(X12)
                                         => app(X12,cons(X10,nil)) != X1 ) ) ) )
                            & equalelemsP(X1) )
                        & ( nil != X1
                          | nil = X2 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[20]) ).

fof(22,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 )
                      | ( ? [X9] :
                            ( ssList(X9)
                            & app(X1,X9) = X2
                            & ! [X10] :
                                ( ssItem(X10)
                               => ! [X11] :
                                    ( ssList(X11)
                                   => ( app(cons(X10,nil),X11) != X9
                                      | ! [X12] :
                                          ( ssList(X12)
                                         => app(X12,cons(X10,nil)) != X1 ) ) ) )
                            & equalelemsP(X1) )
                        & ( nil != X1
                          | nil = X2 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[21,theory(equality)]) ).

fof(29,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(30,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[29]) ).

fof(31,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[30]) ).

cnf(32,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[31]) ).

fof(47,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)],[8]) ).

fof(48,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)],[47]) ).

fof(49,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)],[48]) ).

fof(50,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)],[49]) ).

cnf(51,plain,
    ( nil = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X1
    | nil != X2 ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(81,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(82,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[81]) ).

fof(83,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[82]) ).

cnf(84,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[83]) ).

cnf(85,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[14]) ).

fof(89,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssItem(X3)
              | cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(90,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssItem(X6)
              | cons(X6,app(X5,X4)) = app(cons(X6,X5),X4) ) ) ),
    inference(variable_rename,[status(thm)],[89]) ).

fof(91,plain,
    ! [X4,X5,X6] :
      ( ~ ssItem(X6)
      | cons(X6,app(X5,X4)) = app(cons(X6,X5),X4)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[90]) ).

cnf(92,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[91]) ).

fof(97,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | nil != cons(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(98,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | nil != cons(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[97]) ).

fof(99,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | nil != cons(X4,X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[98]) ).

cnf(100,plain,
    ( ~ ssList(X1)
    | nil != cons(X2,X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[99]) ).

fof(107,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 )
                  & ( ! [X9] :
                        ( ~ ssList(X9)
                        | app(X1,X9) != X2
                        | ? [X10] :
                            ( ssItem(X10)
                            & ? [X11] :
                                ( ssList(X11)
                                & app(cons(X10,nil),X11) = X9
                                & ? [X12] :
                                    ( ssList(X12)
                                    & app(X12,cons(X10,nil)) = X1 ) ) )
                        | ~ equalelemsP(X1) )
                    | ( nil = X1
                      & nil != X2 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(108,negated_conjecture,
    ? [X13] :
      ( ssList(X13)
      & ? [X14] :
          ( ssList(X14)
          & ? [X15] :
              ( ssList(X15)
              & ? [X16] :
                  ( ssList(X16)
                  & X14 = X16
                  & X13 = X15
                  & ? [X17] :
                      ( ssList(X17)
                      & app(X15,X17) = X16
                      & equalelemsP(X15)
                      & ! [X18] :
                          ( ~ ssItem(X18)
                          | ! [X19] :
                              ( ~ ssList(X19)
                              | app(cons(X18,nil),X19) != X17
                              | ! [X20] :
                                  ( ~ ssList(X20)
                                  | app(X20,cons(X18,nil)) != X15 ) ) ) )
                  & ( nil = X16
                    | nil != X15 )
                  & ( ! [X21] :
                        ( ~ ssList(X21)
                        | app(X13,X21) != X14
                        | ? [X22] :
                            ( ssItem(X22)
                            & ? [X23] :
                                ( ssList(X23)
                                & app(cons(X22,nil),X23) = X21
                                & ? [X24] :
                                    ( ssList(X24)
                                    & app(X24,cons(X22,nil)) = X13 ) ) )
                        | ~ equalelemsP(X13) )
                    | ( nil = X13
                      & nil != X14 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[107]) ).

fof(109,negated_conjecture,
    ( ssList(esk9_0)
    & ssList(esk10_0)
    & ssList(esk11_0)
    & ssList(esk12_0)
    & esk10_0 = esk12_0
    & esk9_0 = esk11_0
    & ssList(esk13_0)
    & app(esk11_0,esk13_0) = esk12_0
    & equalelemsP(esk11_0)
    & ! [X18] :
        ( ~ ssItem(X18)
        | ! [X19] :
            ( ~ ssList(X19)
            | app(cons(X18,nil),X19) != esk13_0
            | ! [X20] :
                ( ~ ssList(X20)
                | app(X20,cons(X18,nil)) != esk11_0 ) ) )
    & ( nil = esk12_0
      | nil != esk11_0 )
    & ( ! [X21] :
          ( ~ ssList(X21)
          | app(esk9_0,X21) != esk10_0
          | ( ssItem(esk14_1(X21))
            & ssList(esk15_1(X21))
            & app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
            & ssList(esk16_1(X21))
            & app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0 )
          | ~ equalelemsP(esk9_0) )
      | ( nil = esk9_0
        & nil != esk10_0 ) ) ),
    inference(skolemize,[status(esa)],[108]) ).

fof(110,negated_conjecture,
    ! [X18,X19,X20,X21] :
      ( ( ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ( ssItem(esk14_1(X21))
          & ssList(esk15_1(X21))
          & app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
          & ssList(esk16_1(X21))
          & app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0 )
        | ~ equalelemsP(esk9_0)
        | ( nil = esk9_0
          & nil != esk10_0 ) )
      & ( ~ ssList(X20)
        | app(X20,cons(X18,nil)) != esk11_0
        | ~ ssList(X19)
        | app(cons(X18,nil),X19) != esk13_0
        | ~ ssItem(X18) )
      & app(esk11_0,esk13_0) = esk12_0
      & equalelemsP(esk11_0)
      & ssList(esk13_0)
      & esk10_0 = esk12_0
      & esk9_0 = esk11_0
      & ( nil = esk12_0
        | nil != esk11_0 )
      & ssList(esk12_0)
      & ssList(esk11_0)
      & ssList(esk10_0)
      & ssList(esk9_0) ),
    inference(shift_quantors,[status(thm)],[109]) ).

fof(111,negated_conjecture,
    ! [X18,X19,X20,X21] :
      ( ( nil = esk9_0
        | ssItem(esk14_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil != esk10_0
        | ssItem(esk14_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil = esk9_0
        | ssList(esk15_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil != esk10_0
        | ssList(esk15_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil = esk9_0
        | app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil != esk10_0
        | app(cons(esk14_1(X21),nil),esk15_1(X21)) = X21
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil = esk9_0
        | ssList(esk16_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil != esk10_0
        | ssList(esk16_1(X21))
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil = esk9_0
        | app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( nil != esk10_0
        | app(esk16_1(X21),cons(esk14_1(X21),nil)) = esk9_0
        | ~ ssList(X21)
        | app(esk9_0,X21) != esk10_0
        | ~ equalelemsP(esk9_0) )
      & ( ~ ssList(X20)
        | app(X20,cons(X18,nil)) != esk11_0
        | ~ ssList(X19)
        | app(cons(X18,nil),X19) != esk13_0
        | ~ ssItem(X18) )
      & app(esk11_0,esk13_0) = esk12_0
      & equalelemsP(esk11_0)
      & ssList(esk13_0)
      & esk10_0 = esk12_0
      & esk9_0 = esk11_0
      & ( nil = esk12_0
        | nil != esk11_0 )
      & ssList(esk12_0)
      & ssList(esk11_0)
      & ssList(esk10_0)
      & ssList(esk9_0) ),
    inference(distribute,[status(thm)],[110]) ).

cnf(116,negated_conjecture,
    ( nil = esk12_0
    | nil != esk11_0 ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(117,negated_conjecture,
    esk9_0 = esk11_0,
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(118,negated_conjecture,
    esk10_0 = esk12_0,
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(119,negated_conjecture,
    ssList(esk13_0),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(120,negated_conjecture,
    equalelemsP(esk11_0),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(121,negated_conjecture,
    app(esk11_0,esk13_0) = esk12_0,
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(122,negated_conjecture,
    ( ~ ssItem(X1)
    | app(cons(X1,nil),X2) != esk13_0
    | ~ ssList(X2)
    | app(X3,cons(X1,nil)) != esk11_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(124,negated_conjecture,
    ( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
    | nil = esk9_0
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(126,negated_conjecture,
    ( ssList(esk16_1(X1))
    | nil = esk9_0
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(127,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | nil != esk10_0 ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(128,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | nil = esk9_0
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(129,negated_conjecture,
    ( ssList(esk15_1(X1))
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | nil != esk10_0 ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(130,negated_conjecture,
    ( ssList(esk15_1(X1))
    | nil = esk9_0
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(131,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | nil != esk10_0 ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(132,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | nil = esk9_0
    | ~ equalelemsP(esk9_0)
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[111]) ).

cnf(135,negated_conjecture,
    equalelemsP(esk9_0),
    inference(rw,[status(thm)],[120,117,theory(equality)]) ).

cnf(138,negated_conjecture,
    ( esk10_0 = nil
    | esk11_0 != nil ),
    inference(rw,[status(thm)],[116,118,theory(equality)]) ).

cnf(139,negated_conjecture,
    ( esk10_0 = nil
    | esk9_0 != nil ),
    inference(rw,[status(thm)],[138,117,theory(equality)]) ).

cnf(140,negated_conjecture,
    app(esk9_0,esk13_0) = esk12_0,
    inference(rw,[status(thm)],[121,117,theory(equality)]) ).

cnf(141,negated_conjecture,
    app(esk9_0,esk13_0) = esk10_0,
    inference(rw,[status(thm)],[140,118,theory(equality)]) ).

cnf(167,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[51,theory(equality)]) ).

cnf(168,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[167,85,theory(equality)]) ).

cnf(169,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[168,theory(equality)]) ).

cnf(247,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssList(app(X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[100,92,theory(equality)]) ).

cnf(261,negated_conjecture,
    ( app(X3,cons(X1,nil)) != esk9_0
    | app(cons(X1,nil),X2) != esk13_0
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[122,117,theory(equality)]) ).

cnf(286,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[127,135,theory(equality)]) ).

cnf(287,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[286,theory(equality)]) ).

cnf(288,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | esk9_0 = nil
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[128,135,theory(equality)]) ).

cnf(289,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | esk9_0 = nil
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[288,theory(equality)]) ).

cnf(292,negated_conjecture,
    ( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
    | esk9_0 = nil
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[124,135,theory(equality)]) ).

cnf(293,negated_conjecture,
    ( app(esk16_1(X1),cons(esk14_1(X1),nil)) = esk9_0
    | esk9_0 = nil
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[292,theory(equality)]) ).

cnf(296,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[129,135,theory(equality)]) ).

cnf(297,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[296,theory(equality)]) ).

cnf(298,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[131,135,theory(equality)]) ).

cnf(299,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(esk9_0,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[298,theory(equality)]) ).

cnf(300,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk16_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[126,135,theory(equality)]) ).

cnf(301,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk16_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[300,theory(equality)]) ).

cnf(302,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk15_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[130,135,theory(equality)]) ).

cnf(303,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk15_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[302,theory(equality)]) ).

cnf(304,negated_conjecture,
    ( esk9_0 = nil
    | ssItem(esk14_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[132,135,theory(equality)]) ).

cnf(305,negated_conjecture,
    ( esk9_0 = nil
    | ssItem(esk14_1(X1))
    | app(esk9_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[304,theory(equality)]) ).

cnf(308,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[247,32]) ).

cnf(318,plain,
    ( app(nil,nil) = nil
    | ~ ssList(nil) ),
    inference(er,[status(thm)],[169,theory(equality)]) ).

cnf(319,plain,
    ( app(nil,nil) = nil
    | $false ),
    inference(rw,[status(thm)],[318,85,theory(equality)]) ).

cnf(320,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[319,theory(equality)]) ).

cnf(360,negated_conjecture,
    ( app(cons(esk14_1(esk13_0),nil),esk15_1(esk13_0)) = esk13_0
    | esk9_0 = nil
    | ~ ssList(esk13_0) ),
    inference(spm,[status(thm)],[289,141,theory(equality)]) ).

cnf(394,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk16_1(esk13_0))
    | ~ ssList(esk13_0) ),
    inference(spm,[status(thm)],[301,141,theory(equality)]) ).

cnf(399,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk16_1(esk13_0)) ),
    inference(spm,[status(thm)],[394,119,theory(equality)]) ).

cnf(400,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk15_1(esk13_0))
    | ~ ssList(esk13_0) ),
    inference(spm,[status(thm)],[303,141,theory(equality)]) ).

cnf(405,negated_conjecture,
    ( app(esk16_1(esk13_0),cons(esk14_1(esk13_0),nil)) = esk9_0
    | esk9_0 = nil
    | ~ ssList(esk13_0) ),
    inference(spm,[status(thm)],[293,141,theory(equality)]) ).

cnf(420,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk15_1(esk13_0)) ),
    inference(spm,[status(thm)],[400,119,theory(equality)]) ).

cnf(421,negated_conjecture,
    ( esk9_0 = nil
    | ssItem(esk14_1(esk13_0))
    | ~ ssList(esk13_0) ),
    inference(spm,[status(thm)],[305,141,theory(equality)]) ).

cnf(440,negated_conjecture,
    ( esk9_0 = nil
    | ssItem(esk14_1(esk13_0)) ),
    inference(spm,[status(thm)],[421,119,theory(equality)]) ).

cnf(506,negated_conjecture,
    ( app(cons(esk14_1(esk13_0),nil),esk15_1(esk13_0)) = esk13_0
    | esk9_0 = nil ),
    inference(spm,[status(thm)],[360,119,theory(equality)]) ).

cnf(579,negated_conjecture,
    ( ssList(esk13_0)
    | esk9_0 = nil
    | ~ ssList(esk15_1(esk13_0))
    | ~ ssList(cons(esk14_1(esk13_0),nil)) ),
    inference(spm,[status(thm)],[32,506,theory(equality)]) ).

cnf(623,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk13_0)
    | ~ ssList(cons(esk14_1(esk13_0),nil)) ),
    inference(csr,[status(thm)],[579,420]) ).

cnf(624,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk13_0)
    | ~ ssList(nil)
    | ~ ssItem(esk14_1(esk13_0)) ),
    inference(spm,[status(thm)],[623,84,theory(equality)]) ).

cnf(625,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk13_0)
    | $false
    | ~ ssItem(esk14_1(esk13_0)) ),
    inference(rw,[status(thm)],[624,85,theory(equality)]) ).

cnf(626,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk13_0)
    | ~ ssItem(esk14_1(esk13_0)) ),
    inference(cn,[status(thm)],[625,theory(equality)]) ).

cnf(627,negated_conjecture,
    ( esk9_0 = nil
    | ssList(esk13_0) ),
    inference(csr,[status(thm)],[626,440]) ).

cnf(682,negated_conjecture,
    ( app(esk16_1(esk13_0),cons(esk14_1(esk13_0),nil)) = esk9_0
    | esk9_0 = nil ),
    inference(csr,[status(thm)],[405,627]) ).

cnf(692,negated_conjecture,
    ( esk9_0 = nil
    | app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
    | ~ ssList(esk16_1(esk13_0))
    | ~ ssList(X1)
    | ~ ssItem(esk14_1(esk13_0)) ),
    inference(spm,[status(thm)],[261,682,theory(equality)]) ).

cnf(1862,negated_conjecture,
    ( esk9_0 = nil
    | app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
    | ~ ssList(esk16_1(esk13_0))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[692,440]) ).

cnf(1863,negated_conjecture,
    ( esk9_0 = nil
    | app(cons(esk14_1(esk13_0),nil),X1) != esk13_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[1862,399]) ).

cnf(1866,negated_conjecture,
    ( esk9_0 = nil
    | ~ ssList(esk15_1(esk13_0)) ),
    inference(spm,[status(thm)],[1863,506,theory(equality)]) ).

cnf(1874,negated_conjecture,
    esk9_0 = nil,
    inference(csr,[status(thm)],[1866,420]) ).

cnf(1934,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(nil,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[299,1874,theory(equality)]) ).

cnf(1938,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(nil,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[297,1874,theory(equality)]) ).

cnf(1939,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(nil,X1) != esk10_0
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[287,1874,theory(equality)]) ).

cnf(1942,negated_conjecture,
    ( esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[139,1874,theory(equality)]) ).

cnf(1943,negated_conjecture,
    esk10_0 = nil,
    inference(cn,[status(thm)],[1942,theory(equality)]) ).

cnf(1991,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(nil,X1) != nil
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1934,1943,theory(equality)]) ).

cnf(1992,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(nil,X1) != nil
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1991,1943,theory(equality)]) ).

cnf(1993,negated_conjecture,
    ( ssItem(esk14_1(X1))
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1992,theory(equality)]) ).

cnf(1994,negated_conjecture,
    ( ssItem(esk14_1(nil))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[1993,320,theory(equality)]) ).

cnf(2001,negated_conjecture,
    ( ssItem(esk14_1(nil))
    | $false ),
    inference(rw,[status(thm)],[1994,85,theory(equality)]) ).

cnf(2002,negated_conjecture,
    ssItem(esk14_1(nil)),
    inference(cn,[status(thm)],[2001,theory(equality)]) ).

cnf(2053,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(nil,X1) != nil
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1938,1943,theory(equality)]) ).

cnf(2054,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(nil,X1) != nil
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2053,1943,theory(equality)]) ).

cnf(2055,negated_conjecture,
    ( ssList(esk15_1(X1))
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2054,theory(equality)]) ).

cnf(2056,negated_conjecture,
    ( ssList(esk15_1(nil))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[2055,320,theory(equality)]) ).

cnf(2063,negated_conjecture,
    ( ssList(esk15_1(nil))
    | $false ),
    inference(rw,[status(thm)],[2056,85,theory(equality)]) ).

cnf(2064,negated_conjecture,
    ssList(esk15_1(nil)),
    inference(cn,[status(thm)],[2063,theory(equality)]) ).

cnf(2172,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(nil,X1) != nil
    | esk10_0 != nil
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1939,1943,theory(equality)]) ).

cnf(2173,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(nil,X1) != nil
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2172,1943,theory(equality)]) ).

cnf(2174,negated_conjecture,
    ( app(cons(esk14_1(X1),nil),esk15_1(X1)) = X1
    | app(nil,X1) != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2173,theory(equality)]) ).

cnf(2175,negated_conjecture,
    ( app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[2174,320,theory(equality)]) ).

cnf(2183,negated_conjecture,
    ( app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil
    | $false ),
    inference(rw,[status(thm)],[2175,85,theory(equality)]) ).

cnf(2184,negated_conjecture,
    app(cons(esk14_1(nil),nil),esk15_1(nil)) = nil,
    inference(cn,[status(thm)],[2183,theory(equality)]) ).

cnf(2201,negated_conjecture,
    ( ~ ssList(nil)
    | ~ ssList(esk15_1(nil))
    | ~ ssItem(esk14_1(nil)) ),
    inference(spm,[status(thm)],[308,2184,theory(equality)]) ).

cnf(2239,negated_conjecture,
    ( $false
    | ~ ssList(esk15_1(nil))
    | ~ ssItem(esk14_1(nil)) ),
    inference(rw,[status(thm)],[2201,85,theory(equality)]) ).

cnf(2240,negated_conjecture,
    ( $false
    | $false
    | ~ ssItem(esk14_1(nil)) ),
    inference(rw,[status(thm)],[2239,2064,theory(equality)]) ).

cnf(2241,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[2240,2002,theory(equality)]) ).

cnf(2242,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[2241,theory(equality)]) ).

cnf(2243,negated_conjecture,
    $false,
    2242,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC327+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmp6-0fPb/sel_SWC327+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC327+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC327+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC327+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
% 
%------------------------------------------------------------------------------