TSTP Solution File: SWC109+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC109+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art07.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 10:18:02 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   85 (  16 unt;   0 def)
%            Number of atoms       :  496 ( 169 equ)
%            Maximal formula atoms :   52 (   5 avg)
%            Number of connectives :  648 ( 237   ~; 254   |; 132   &)
%                                         (   3 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   8 con; 0-2 aty)
%            Number of variables   :  119 (   0 sgn  75   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',ax21) ).

fof(15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',ax7) ).

fof(22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',ax58) ).

fof(25,axiom,
    ssList(nil),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',ax17) ).

fof(35,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',ax15) ).

fof(39,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ~ ssList(X4)
                  | X2 != X4
                  | X1 != X3
                  | ( ! [X5] :
                        ( ssItem(X5)
                       => ! [X6] :
                            ( ssList(X6)
                           => ! [X7] :
                                ( ~ ssList(X7)
                                | cons(X5,nil) != X3
                                | app(app(X6,X3),X7) != X4
                                | ? [X8] :
                                    ( ssItem(X8)
                                    & memberP(X6,X8)
                                    & lt(X5,X8) )
                                | ? [X9] :
                                    ( ssItem(X9)
                                    & memberP(X7,X9)
                                    & lt(X9,X5) ) ) ) )
                    & ( nil != X4
                      | nil != X3 ) )
                  | ( ( nil != X2
                      | nil = X1 )
                    & ( ~ neq(X2,nil)
                      | ( neq(X1,nil)
                        & segmentP(X2,X1) ) ) ) ) ) ) ),
    file('/tmp/tmpsKEmof/sel_SWC109+1.p_1',co1) ).

fof(40,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X2 != X4
                    | X1 != X3
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ~ ssList(X7)
                                  | cons(X5,nil) != X3
                                  | app(app(X6,X3),X7) != X4
                                  | ? [X8] :
                                      ( ssItem(X8)
                                      & memberP(X6,X8)
                                      & lt(X5,X8) )
                                  | ? [X9] :
                                      ( ssItem(X9)
                                      & memberP(X7,X9)
                                      & lt(X9,X5) ) ) ) )
                      & ( nil != X4
                        | nil != X3 ) )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ( neq(X1,nil)
                          & segmentP(X2,X1) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[39]) ).

fof(44,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ~ ssList(X4)
                    | X2 != X4
                    | X1 != X3
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ~ ssList(X7)
                                  | cons(X5,nil) != X3
                                  | app(app(X6,X3),X7) != X4
                                  | ? [X8] :
                                      ( ssItem(X8)
                                      & memberP(X6,X8)
                                      & lt(X5,X8) )
                                  | ? [X9] :
                                      ( ssItem(X9)
                                      & memberP(X7,X9)
                                      & lt(X9,X5) ) ) ) )
                      & ( nil != X4
                        | nil != X3 ) )
                    | ( ( nil != X2
                        | nil = X1 )
                      & ( ~ neq(X2,nil)
                        | ( neq(X1,nil)
                          & segmentP(X2,X1) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[40,theory(equality)]) ).

fof(82,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | nil != cons(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

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

fof(84,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | nil != cons(X4,X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[83]) ).

cnf(85,plain,
    ( ~ ssList(X1)
    | nil != cons(X2,X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[84]) ).

fof(111,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ segmentP(X1,X2)
              | ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & app(app(X3,X2),X4) = X1 ) ) )
            & ( ! [X3] :
                  ( ~ ssList(X3)
                  | ! [X4] :
                      ( ~ ssList(X4)
                      | app(app(X3,X2),X4) != X1 ) )
              | segmentP(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(112,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ( ( ~ segmentP(X5,X6)
              | ? [X7] :
                  ( ssList(X7)
                  & ? [X8] :
                      ( ssList(X8)
                      & app(app(X7,X6),X8) = X5 ) ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(app(X9,X6),X10) != X5 ) )
              | segmentP(X5,X6) ) ) ) ),
    inference(variable_rename,[status(thm)],[111]) ).

fof(113,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ( ( ~ segmentP(X5,X6)
              | ( ssList(esk7_2(X5,X6))
                & ssList(esk8_2(X5,X6))
                & app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(app(X9,X6),X10) != X5 ) )
              | segmentP(X5,X6) ) ) ) ),
    inference(skolemize,[status(esa)],[112]) ).

fof(114,plain,
    ! [X5,X6,X9,X10] :
      ( ( ( ~ ssList(X10)
          | app(app(X9,X6),X10) != X5
          | ~ ssList(X9)
          | segmentP(X5,X6) )
        & ( ~ segmentP(X5,X6)
          | ( ssList(esk7_2(X5,X6))
            & ssList(esk8_2(X5,X6))
            & app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5 ) ) )
      | ~ ssList(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[113]) ).

fof(115,plain,
    ! [X5,X6,X9,X10] :
      ( ( ~ ssList(X10)
        | app(app(X9,X6),X10) != X5
        | ~ ssList(X9)
        | segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk7_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk8_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( app(app(esk7_2(X5,X6),X6),esk8_2(X5,X6)) = X5
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) ) ),
    inference(distribute,[status(thm)],[114]) ).

cnf(119,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(142,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ segmentP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | segmentP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(143,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ segmentP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | segmentP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[142]) ).

fof(144,plain,
    ! [X2] :
      ( ( ~ segmentP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | segmentP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[143]) ).

cnf(146,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ segmentP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(155,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[25]) ).

fof(201,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(202,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[201]) ).

fof(203,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[202]) ).

fof(204,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)],[203]) ).

cnf(205,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[204]) ).

cnf(206,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | X1 != X2
    | ~ neq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[204]) ).

fof(220,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & cons(X5,nil) = X3
                                & app(app(X6,X3),X7) = X4
                                & ! [X8] :
                                    ( ~ ssItem(X8)
                                    | ~ memberP(X6,X8)
                                    | ~ lt(X5,X8) )
                                & ! [X9] :
                                    ( ~ ssItem(X9)
                                    | ~ memberP(X7,X9)
                                    | ~ lt(X9,X5) ) ) ) )
                    | ( nil = X4
                      & nil = X3 ) )
                  & ( ( nil = X2
                      & nil != X1 )
                    | ( neq(X2,nil)
                      & ( ~ neq(X1,nil)
                        | ~ segmentP(X2,X1) ) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[44]) ).

fof(221,negated_conjecture,
    ? [X10] :
      ( ssList(X10)
      & ? [X11] :
          ( ssList(X11)
          & ? [X12] :
              ( ssList(X12)
              & ? [X13] :
                  ( ssList(X13)
                  & X11 = X13
                  & X10 = X12
                  & ( ? [X14] :
                        ( ssItem(X14)
                        & ? [X15] :
                            ( ssList(X15)
                            & ? [X16] :
                                ( ssList(X16)
                                & cons(X14,nil) = X12
                                & app(app(X15,X12),X16) = X13
                                & ! [X17] :
                                    ( ~ ssItem(X17)
                                    | ~ memberP(X15,X17)
                                    | ~ lt(X14,X17) )
                                & ! [X18] :
                                    ( ~ ssItem(X18)
                                    | ~ memberP(X16,X18)
                                    | ~ lt(X18,X14) ) ) ) )
                    | ( nil = X13
                      & nil = X12 ) )
                  & ( ( nil = X11
                      & nil != X10 )
                    | ( neq(X11,nil)
                      & ( ~ neq(X10,nil)
                        | ~ segmentP(X11,X10) ) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[220]) ).

fof(222,negated_conjecture,
    ( ssList(esk9_0)
    & ssList(esk10_0)
    & ssList(esk11_0)
    & ssList(esk12_0)
    & esk10_0 = esk12_0
    & esk9_0 = esk11_0
    & ( ( ssItem(esk13_0)
        & ssList(esk14_0)
        & ssList(esk15_0)
        & cons(esk13_0,nil) = esk11_0
        & app(app(esk14_0,esk11_0),esk15_0) = esk12_0
        & ! [X17] :
            ( ~ ssItem(X17)
            | ~ memberP(esk14_0,X17)
            | ~ lt(esk13_0,X17) )
        & ! [X18] :
            ( ~ ssItem(X18)
            | ~ memberP(esk15_0,X18)
            | ~ lt(X18,esk13_0) ) )
      | ( nil = esk12_0
        & nil = esk11_0 ) )
    & ( ( nil = esk10_0
        & nil != esk9_0 )
      | ( neq(esk10_0,nil)
        & ( ~ neq(esk9_0,nil)
          | ~ segmentP(esk10_0,esk9_0) ) ) ) ),
    inference(skolemize,[status(esa)],[221]) ).

fof(223,negated_conjecture,
    ! [X17,X18] :
      ( ( ( ( ~ ssItem(X18)
            | ~ memberP(esk15_0,X18)
            | ~ lt(X18,esk13_0) )
          & ( ~ ssItem(X17)
            | ~ memberP(esk14_0,X17)
            | ~ lt(esk13_0,X17) )
          & ssList(esk15_0)
          & cons(esk13_0,nil) = esk11_0
          & app(app(esk14_0,esk11_0),esk15_0) = esk12_0
          & ssList(esk14_0)
          & ssItem(esk13_0) )
        | ( nil = esk12_0
          & nil = esk11_0 ) )
      & ssList(esk12_0)
      & esk10_0 = esk12_0
      & esk9_0 = esk11_0
      & ( ( nil = esk10_0
          & nil != esk9_0 )
        | ( neq(esk10_0,nil)
          & ( ~ neq(esk9_0,nil)
            | ~ segmentP(esk10_0,esk9_0) ) ) )
      & ssList(esk11_0)
      & ssList(esk10_0)
      & ssList(esk9_0) ),
    inference(shift_quantors,[status(thm)],[222]) ).

fof(224,negated_conjecture,
    ! [X17,X18] :
      ( ( nil = esk12_0
        | ~ ssItem(X18)
        | ~ memberP(esk15_0,X18)
        | ~ lt(X18,esk13_0) )
      & ( nil = esk11_0
        | ~ ssItem(X18)
        | ~ memberP(esk15_0,X18)
        | ~ lt(X18,esk13_0) )
      & ( nil = esk12_0
        | ~ ssItem(X17)
        | ~ memberP(esk14_0,X17)
        | ~ lt(esk13_0,X17) )
      & ( nil = esk11_0
        | ~ ssItem(X17)
        | ~ memberP(esk14_0,X17)
        | ~ lt(esk13_0,X17) )
      & ( nil = esk12_0
        | ssList(esk15_0) )
      & ( nil = esk11_0
        | ssList(esk15_0) )
      & ( nil = esk12_0
        | cons(esk13_0,nil) = esk11_0 )
      & ( nil = esk11_0
        | cons(esk13_0,nil) = esk11_0 )
      & ( nil = esk12_0
        | app(app(esk14_0,esk11_0),esk15_0) = esk12_0 )
      & ( nil = esk11_0
        | app(app(esk14_0,esk11_0),esk15_0) = esk12_0 )
      & ( nil = esk12_0
        | ssList(esk14_0) )
      & ( nil = esk11_0
        | ssList(esk14_0) )
      & ( nil = esk12_0
        | ssItem(esk13_0) )
      & ( nil = esk11_0
        | ssItem(esk13_0) )
      & ssList(esk12_0)
      & esk10_0 = esk12_0
      & esk9_0 = esk11_0
      & ( neq(esk10_0,nil)
        | nil = esk10_0 )
      & ( ~ neq(esk9_0,nil)
        | ~ segmentP(esk10_0,esk9_0)
        | nil = esk10_0 )
      & ( neq(esk10_0,nil)
        | nil != esk9_0 )
      & ( ~ neq(esk9_0,nil)
        | ~ segmentP(esk10_0,esk9_0)
        | nil != esk9_0 )
      & ssList(esk11_0)
      & ssList(esk10_0)
      & ssList(esk9_0) ),
    inference(distribute,[status(thm)],[223]) ).

cnf(225,negated_conjecture,
    ssList(esk9_0),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(226,negated_conjecture,
    ssList(esk10_0),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(229,negated_conjecture,
    ( neq(esk10_0,nil)
    | nil != esk9_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(230,negated_conjecture,
    ( nil = esk10_0
    | ~ segmentP(esk10_0,esk9_0)
    | ~ neq(esk9_0,nil) ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(232,negated_conjecture,
    esk9_0 = esk11_0,
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(233,negated_conjecture,
    esk10_0 = esk12_0,
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(236,negated_conjecture,
    ( ssItem(esk13_0)
    | nil = esk12_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(237,negated_conjecture,
    ( ssList(esk14_0)
    | nil = esk11_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(239,negated_conjecture,
    ( app(app(esk14_0,esk11_0),esk15_0) = esk12_0
    | nil = esk11_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(242,negated_conjecture,
    ( cons(esk13_0,nil) = esk11_0
    | nil = esk12_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(243,negated_conjecture,
    ( ssList(esk15_0)
    | nil = esk11_0 ),
    inference(split_conjunct,[status(thm)],[224]) ).

cnf(249,negated_conjecture,
    ssList(esk11_0),
    inference(rw,[status(thm)],[225,232,theory(equality)]) ).

cnf(250,negated_conjecture,
    ssList(esk12_0),
    inference(rw,[status(thm)],[226,233,theory(equality)]) ).

cnf(253,negated_conjecture,
    ( neq(esk12_0,nil)
    | esk9_0 != nil ),
    inference(rw,[status(thm)],[229,233,theory(equality)]) ).

cnf(254,negated_conjecture,
    ( neq(esk12_0,nil)
    | esk11_0 != nil ),
    inference(rw,[status(thm)],[253,232,theory(equality)]) ).

cnf(255,negated_conjecture,
    ( esk12_0 = nil
    | ~ segmentP(esk10_0,esk9_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[230,233,theory(equality)]) ).

cnf(256,negated_conjecture,
    ( esk12_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | ~ neq(esk9_0,nil) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[255,233,theory(equality)]),232,theory(equality)]) ).

cnf(257,negated_conjecture,
    ( esk12_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | ~ neq(esk11_0,nil) ),
    inference(rw,[status(thm)],[256,232,theory(equality)]) ).

cnf(267,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | ~ ssList(nil)
    | ~ ssList(esk11_0) ),
    inference(spm,[status(thm)],[257,205,theory(equality)]) ).

cnf(268,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | $false
    | ~ ssList(esk11_0) ),
    inference(rw,[status(thm)],[267,155,theory(equality)]) ).

cnf(269,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | ~ ssList(esk11_0) ),
    inference(cn,[status(thm)],[268,theory(equality)]) ).

cnf(277,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 != nil
    | ~ ssItem(esk13_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[85,242,theory(equality)]) ).

cnf(280,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 != nil
    | ~ ssItem(esk13_0)
    | $false ),
    inference(rw,[status(thm)],[277,155,theory(equality)]) ).

cnf(281,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 != nil
    | ~ ssItem(esk13_0) ),
    inference(cn,[status(thm)],[280,theory(equality)]) ).

cnf(308,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[206,theory(equality)]) ).

cnf(621,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 != nil ),
    inference(csr,[status(thm)],[281,236]) ).

cnf(623,negated_conjecture,
    ( neq(nil,nil)
    | esk11_0 != nil ),
    inference(spm,[status(thm)],[254,621,theory(equality)]) ).

cnf(625,negated_conjecture,
    ( ~ ssList(nil)
    | esk11_0 != nil ),
    inference(spm,[status(thm)],[308,623,theory(equality)]) ).

cnf(627,negated_conjecture,
    ( $false
    | esk11_0 != nil ),
    inference(rw,[status(thm)],[625,155,theory(equality)]) ).

cnf(628,negated_conjecture,
    esk11_0 != nil,
    inference(cn,[status(thm)],[627,theory(equality)]) ).

cnf(629,negated_conjecture,
    ssList(esk14_0),
    inference(sr,[status(thm)],[237,628,theory(equality)]) ).

cnf(630,negated_conjecture,
    ssList(esk15_0),
    inference(sr,[status(thm)],[243,628,theory(equality)]) ).

cnf(633,negated_conjecture,
    app(app(esk14_0,esk11_0),esk15_0) = esk12_0,
    inference(sr,[status(thm)],[239,628,theory(equality)]) ).

cnf(698,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | esk12_0 != X1
    | ~ ssList(esk15_0)
    | ~ ssList(esk14_0)
    | ~ ssList(esk11_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[119,633,theory(equality)]) ).

cnf(738,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | esk12_0 != X1
    | $false
    | ~ ssList(esk14_0)
    | ~ ssList(esk11_0)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[698,630,theory(equality)]) ).

cnf(739,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | esk12_0 != X1
    | $false
    | $false
    | ~ ssList(esk11_0)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[738,629,theory(equality)]) ).

cnf(740,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | esk12_0 != X1
    | $false
    | $false
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[739,249,theory(equality)]) ).

cnf(741,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | esk12_0 != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[740,theory(equality)]) ).

cnf(759,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 = nil
    | ~ segmentP(esk12_0,esk11_0)
    | $false ),
    inference(rw,[status(thm)],[269,249,theory(equality)]) ).

cnf(760,negated_conjecture,
    ( esk12_0 = nil
    | esk11_0 = nil
    | ~ segmentP(esk12_0,esk11_0) ),
    inference(cn,[status(thm)],[759,theory(equality)]) ).

cnf(761,negated_conjecture,
    ( esk12_0 = nil
    | ~ segmentP(esk12_0,esk11_0) ),
    inference(sr,[status(thm)],[760,628,theory(equality)]) ).

cnf(762,negated_conjecture,
    ( esk12_0 = nil
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[761,741,theory(equality)]) ).

cnf(763,negated_conjecture,
    ( esk12_0 = nil
    | $false ),
    inference(rw,[status(thm)],[762,250,theory(equality)]) ).

cnf(764,negated_conjecture,
    esk12_0 = nil,
    inference(cn,[status(thm)],[763,theory(equality)]) ).

cnf(773,negated_conjecture,
    ( segmentP(X1,esk11_0)
    | nil != X1
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[741,764,theory(equality)]) ).

cnf(781,negated_conjecture,
    ( nil = esk11_0
    | ~ ssList(esk11_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[146,773,theory(equality)]) ).

cnf(784,negated_conjecture,
    ( nil = esk11_0
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[781,249,theory(equality)]) ).

cnf(785,negated_conjecture,
    ( nil = esk11_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[784,155,theory(equality)]) ).

cnf(786,negated_conjecture,
    nil = esk11_0,
    inference(cn,[status(thm)],[785,theory(equality)]) ).

cnf(787,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[786,628,theory(equality)]) ).

cnf(788,negated_conjecture,
    $false,
    787,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC109+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpsKEmof/sel_SWC109+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC109+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC109+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC109+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
% 
%------------------------------------------------------------------------------