TSTP Solution File: SWC077+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC077+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 10:12:34 EST 2010

% Result   : Theorem 4.26s
% Output   : CNFRefutation 4.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   45
%            Number of leaves      :   25
% Syntax   : Number of formulae    :  289 (  21 unt;   0 def)
%            Number of atoms       : 1273 ( 306 equ)
%            Maximal formula atoms :   19 (   4 avg)
%            Number of connectives : 1769 ( 785   ~; 796   |; 124   &)
%                                         (   6 <=>;  58  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   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;   5 con; 0-2 aty)
%            Number of variables   :  458 (   0 sgn 210   !;  29   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] :
      ( ssItem(X1)
     => strictorderedP(cons(X1,nil)) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax68) ).

fof(5,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax84) ).

fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax83) ).

fof(7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax82) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax81) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( frontsegP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax46) ).

fof(12,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax28) ).

fof(13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( frontsegP(X1,X2)
               => frontsegP(app(X1,X3),X2) ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax43) ).

fof(15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax27) ).

fof(16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax26) ).

fof(17,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax21) ).

fof(18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax20) ).

fof(19,axiom,
    ! [X1] :
      ( ssList(X1)
     => frontsegP(X1,nil) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax45) ).

fof(22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( ( frontsegP(X1,X2)
                  & frontsegP(X2,X3) )
               => frontsegP(X1,X3) ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax40) ).

fof(23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax7) ).

fof(24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( frontsegP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & app(X2,X3) = X1 ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax5) ).

fof(30,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( ( frontsegP(X1,X2)
              & frontsegP(X2,X1) )
           => X1 = X2 ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax41) ).

fof(37,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax58) ).

fof(39,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax16) ).

fof(40,axiom,
    ssList(nil),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax17) ).

fof(42,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( ( segmentP(X1,X2)
                  & segmentP(X2,X3) )
               => segmentP(X1,X3) ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax53) ).

fof(44,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,X1) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax55) ).

fof(46,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax57) ).

fof(47,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',ax15) ).

fof(51,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ~ frontsegP(X4,X3)
                    | ~ strictorderedP(X3)
                    | ? [X5] :
                        ( ssList(X5)
                        & neq(X5,nil)
                        & segmentP(X2,X5)
                        & segmentP(X1,X5) )
                    | ? [X6] :
                        ( ssList(X6)
                        & neq(X3,X6)
                        & frontsegP(X4,X6)
                        & segmentP(X6,X3)
                        & strictorderedP(X6) )
                    | ( nil = X2
                      & nil = X1 ) ) ) ) ) ),
    file('/tmp/tmpeS6kvB/sel_SWC077+1.p_1',co1) ).

fof(52,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ frontsegP(X4,X3)
                      | ~ strictorderedP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X5,nil)
                          & segmentP(X2,X5)
                          & segmentP(X1,X5) )
                      | ? [X6] :
                          ( ssList(X6)
                          & neq(X3,X6)
                          & frontsegP(X4,X6)
                          & segmentP(X6,X3)
                          & strictorderedP(X6) )
                      | ( nil = X2
                        & nil = X1 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[51]) ).

fof(55,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ~ frontsegP(X4,X3)
                      | ~ strictorderedP(X3)
                      | ? [X5] :
                          ( ssList(X5)
                          & neq(X5,nil)
                          & segmentP(X2,X5)
                          & segmentP(X1,X5) )
                      | ? [X6] :
                          ( ssList(X6)
                          & neq(X3,X6)
                          & frontsegP(X4,X6)
                          & segmentP(X6,X3)
                          & strictorderedP(X6) )
                      | ( nil = X2
                        & nil = X1 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[52,theory(equality)]) ).

fof(61,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | strictorderedP(cons(X1,nil)) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(62,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | strictorderedP(cons(X2,nil)) ),
    inference(variable_rename,[status(thm)],[61]) ).

cnf(63,plain,
    ( strictorderedP(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[62]) ).

fof(68,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(X1,nil) = X1 ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(69,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[68]) ).

cnf(70,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[69]) ).

fof(71,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(72,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)],[71]) ).

fof(73,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)],[72]) ).

fof(74,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)],[73]) ).

cnf(77,plain,
    ( nil = X2
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(78,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(79,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | app(app(X4,X5),X6) = app(X4,app(X5,X6)) ) ) ),
    inference(variable_rename,[status(thm)],[78]) ).

fof(80,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | app(app(X4,X5),X6) = app(X4,app(X5,X6))
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[79]) ).

cnf(81,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[80]) ).

fof(82,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

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

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

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

fof(90,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ frontsegP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | frontsegP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(91,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ frontsegP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | frontsegP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[90]) ).

fof(92,plain,
    ! [X2] :
      ( ( ~ frontsegP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | frontsegP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[91]) ).

cnf(93,plain,
    ( frontsegP(nil,X1)
    | ~ ssList(X1)
    | nil != X1 ),
    inference(split_conjunct,[status(thm)],[92]) ).

cnf(94,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ frontsegP(nil,X1) ),
    inference(split_conjunct,[status(thm)],[92]) ).

fof(99,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(100,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[99]) ).

cnf(101,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[100]) ).

fof(102,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ~ frontsegP(X1,X2)
              | frontsegP(app(X1,X3),X2) ) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

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

fof(104,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ~ frontsegP(X4,X5)
      | frontsegP(app(X4,X6),X5)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[103]) ).

cnf(105,plain,
    ( frontsegP(app(X1,X3),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[104]) ).

fof(109,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)],[15]) ).

fof(110,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)],[109]) ).

fof(111,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)],[110]) ).

cnf(112,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[111]) ).

fof(113,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(114,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[113]) ).

fof(115,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[114]) ).

cnf(116,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(117,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | nil != cons(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[17]) ).

fof(118,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | nil != cons(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[117]) ).

fof(119,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | nil != cons(X4,X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[118]) ).

cnf(120,plain,
    ( ~ ssList(X1)
    | nil != cons(X2,X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[119]) ).

fof(121,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssItem(X3)
              & cons(X3,X2) = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(122,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ? [X5] :
          ( ssList(X5)
          & ? [X6] :
              ( ssItem(X6)
              & cons(X6,X5) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[121]) ).

fof(123,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ( ssList(esk1_1(X4))
        & ssItem(esk2_1(X4))
        & cons(esk2_1(X4),esk1_1(X4)) = X4 ) ),
    inference(skolemize,[status(esa)],[122]) ).

fof(124,plain,
    ! [X4] :
      ( ( ssList(esk1_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( ssItem(esk2_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( cons(esk2_1(X4),esk1_1(X4)) = X4
        | nil = X4
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[123]) ).

cnf(125,plain,
    ( nil = X1
    | cons(esk2_1(X1),esk1_1(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[124]) ).

cnf(126,plain,
    ( nil = X1
    | ssItem(esk2_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[124]) ).

cnf(127,plain,
    ( nil = X1
    | ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[124]) ).

fof(128,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | frontsegP(X1,nil) ),
    inference(fof_nnf,[status(thm)],[19]) ).

fof(129,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | frontsegP(X2,nil) ),
    inference(variable_rename,[status(thm)],[128]) ).

cnf(130,plain,
    ( frontsegP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[129]) ).

fof(143,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ~ frontsegP(X1,X2)
              | ~ frontsegP(X2,X3)
              | frontsegP(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(144,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ~ frontsegP(X4,X5)
              | ~ frontsegP(X5,X6)
              | frontsegP(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[143]) ).

fof(145,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ~ frontsegP(X4,X5)
      | ~ frontsegP(X5,X6)
      | frontsegP(X4,X6)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[144]) ).

cnf(146,plain,
    ( frontsegP(X1,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ frontsegP(X2,X3)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[145]) ).

fof(147,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)],[23]) ).

fof(148,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)],[147]) ).

fof(149,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ( ( ~ segmentP(X5,X6)
              | ( ssList(esk5_2(X5,X6))
                & ssList(esk6_2(X5,X6))
                & app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(app(X9,X6),X10) != X5 ) )
              | segmentP(X5,X6) ) ) ) ),
    inference(skolemize,[status(esa)],[148]) ).

fof(150,plain,
    ! [X5,X6,X9,X10] :
      ( ( ( ~ ssList(X10)
          | app(app(X9,X6),X10) != X5
          | ~ ssList(X9)
          | segmentP(X5,X6) )
        & ( ~ segmentP(X5,X6)
          | ( ssList(esk5_2(X5,X6))
            & ssList(esk6_2(X5,X6))
            & app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5 ) ) )
      | ~ ssList(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[149]) ).

fof(151,plain,
    ! [X5,X6,X9,X10] :
      ( ( ~ ssList(X10)
        | app(app(X9,X6),X10) != X5
        | ~ ssList(X9)
        | segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk5_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( ssList(esk6_2(X5,X6))
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) )
      & ( app(app(esk5_2(X5,X6),X6),esk6_2(X5,X6)) = X5
        | ~ segmentP(X5,X6)
        | ~ ssList(X6)
        | ~ ssList(X5) ) ),
    inference(distribute,[status(thm)],[150]) ).

cnf(155,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[151]) ).

fof(156,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)],[24]) ).

fof(157,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)],[156]) ).

fof(158,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ( ( ~ frontsegP(X4,X5)
              | ( ssList(esk7_2(X4,X5))
                & app(X5,esk7_2(X4,X5)) = X4 ) )
            & ( ! [X7] :
                  ( ~ ssList(X7)
                  | app(X5,X7) != X4 )
              | frontsegP(X4,X5) ) ) ) ),
    inference(skolemize,[status(esa)],[157]) ).

fof(159,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ ssList(X7)
          | app(X5,X7) != X4
          | frontsegP(X4,X5) )
        & ( ~ frontsegP(X4,X5)
          | ( ssList(esk7_2(X4,X5))
            & app(X5,esk7_2(X4,X5)) = X4 ) ) )
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[158]) ).

fof(160,plain,
    ! [X4,X5,X7] :
      ( ( ~ ssList(X7)
        | app(X5,X7) != X4
        | frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( ssList(esk7_2(X4,X5))
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) )
      & ( app(X5,esk7_2(X4,X5)) = X4
        | ~ frontsegP(X4,X5)
        | ~ ssList(X5)
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[159]) ).

cnf(161,plain,
    ( app(X2,esk7_2(X1,X2)) = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[160]) ).

cnf(162,plain,
    ( ssList(esk7_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ frontsegP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[160]) ).

cnf(163,plain,
    ( frontsegP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X2,X3) != X1
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[160]) ).

fof(188,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ~ frontsegP(X1,X2)
          | ~ frontsegP(X2,X1)
          | X1 = X2 ) ),
    inference(fof_nnf,[status(thm)],[30]) ).

fof(189,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ~ frontsegP(X3,X4)
          | ~ frontsegP(X4,X3)
          | X3 = X4 ) ),
    inference(variable_rename,[status(thm)],[188]) ).

fof(190,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ~ frontsegP(X3,X4)
      | ~ frontsegP(X4,X3)
      | X3 = X4
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[189]) ).

cnf(191,plain,
    ( X1 = X2
    | ~ ssList(X1)
    | ~ frontsegP(X2,X1)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[190]) ).

fof(222,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ segmentP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | segmentP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(223,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ segmentP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | segmentP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[222]) ).

fof(224,plain,
    ! [X2] :
      ( ( ~ segmentP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | segmentP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[223]) ).

cnf(225,plain,
    ( segmentP(nil,X1)
    | ~ ssList(X1)
    | nil != X1 ),
    inference(split_conjunct,[status(thm)],[224]) ).

fof(231,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(232,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[231]) ).

fof(233,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[232]) ).

cnf(234,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[233]) ).

cnf(235,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[40]) ).

fof(249,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X2,X3)
              | segmentP(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(250,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ~ segmentP(X4,X5)
              | ~ segmentP(X5,X6)
              | segmentP(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[249]) ).

fof(251,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ~ segmentP(X4,X5)
      | ~ segmentP(X5,X6)
      | segmentP(X4,X6)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[250]) ).

cnf(252,plain,
    ( segmentP(X1,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X2,X3)
    | ~ segmentP(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[251]) ).

fof(257,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | segmentP(X1,X1) ),
    inference(fof_nnf,[status(thm)],[44]) ).

fof(258,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | segmentP(X2,X2) ),
    inference(variable_rename,[status(thm)],[257]) ).

cnf(259,plain,
    ( segmentP(X1,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[258]) ).

fof(264,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | segmentP(X1,nil) ),
    inference(fof_nnf,[status(thm)],[46]) ).

fof(265,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | segmentP(X2,nil) ),
    inference(variable_rename,[status(thm)],[264]) ).

cnf(266,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[265]) ).

fof(267,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[47]) ).

fof(268,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[267]) ).

fof(269,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[268]) ).

fof(270,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)],[269]) ).

cnf(271,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[270]) ).

fof(286,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & frontsegP(X4,X3)
                  & strictorderedP(X3)
                  & ! [X5] :
                      ( ~ ssList(X5)
                      | ~ neq(X5,nil)
                      | ~ segmentP(X2,X5)
                      | ~ segmentP(X1,X5) )
                  & ! [X6] :
                      ( ~ ssList(X6)
                      | ~ neq(X3,X6)
                      | ~ frontsegP(X4,X6)
                      | ~ segmentP(X6,X3)
                      | ~ strictorderedP(X6) )
                  & ( nil != X2
                    | nil != X1 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[55]) ).

fof(287,negated_conjecture,
    ? [X7] :
      ( ssList(X7)
      & ? [X8] :
          ( ssList(X8)
          & ? [X9] :
              ( ssList(X9)
              & ? [X10] :
                  ( ssList(X10)
                  & X8 = X10
                  & X7 = X9
                  & frontsegP(X10,X9)
                  & strictorderedP(X9)
                  & ! [X11] :
                      ( ~ ssList(X11)
                      | ~ neq(X11,nil)
                      | ~ segmentP(X8,X11)
                      | ~ segmentP(X7,X11) )
                  & ! [X12] :
                      ( ~ ssList(X12)
                      | ~ neq(X9,X12)
                      | ~ frontsegP(X10,X12)
                      | ~ segmentP(X12,X9)
                      | ~ strictorderedP(X12) )
                  & ( nil != X8
                    | nil != X7 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[286]) ).

fof(288,negated_conjecture,
    ( ssList(esk14_0)
    & ssList(esk15_0)
    & ssList(esk16_0)
    & ssList(esk17_0)
    & esk15_0 = esk17_0
    & esk14_0 = esk16_0
    & frontsegP(esk17_0,esk16_0)
    & strictorderedP(esk16_0)
    & ! [X11] :
        ( ~ ssList(X11)
        | ~ neq(X11,nil)
        | ~ segmentP(esk15_0,X11)
        | ~ segmentP(esk14_0,X11) )
    & ! [X12] :
        ( ~ ssList(X12)
        | ~ neq(esk16_0,X12)
        | ~ frontsegP(esk17_0,X12)
        | ~ segmentP(X12,esk16_0)
        | ~ strictorderedP(X12) )
    & ( nil != esk15_0
      | nil != esk14_0 ) ),
    inference(skolemize,[status(esa)],[287]) ).

fof(289,negated_conjecture,
    ! [X11,X12] :
      ( ( ~ ssList(X12)
        | ~ neq(esk16_0,X12)
        | ~ frontsegP(esk17_0,X12)
        | ~ segmentP(X12,esk16_0)
        | ~ strictorderedP(X12) )
      & ( ~ ssList(X11)
        | ~ neq(X11,nil)
        | ~ segmentP(esk15_0,X11)
        | ~ segmentP(esk14_0,X11) )
      & esk15_0 = esk17_0
      & esk14_0 = esk16_0
      & frontsegP(esk17_0,esk16_0)
      & strictorderedP(esk16_0)
      & ( nil != esk15_0
        | nil != esk14_0 )
      & ssList(esk17_0)
      & ssList(esk16_0)
      & ssList(esk15_0)
      & ssList(esk14_0) ),
    inference(shift_quantors,[status(thm)],[288]) ).

cnf(290,negated_conjecture,
    ssList(esk14_0),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(291,negated_conjecture,
    ssList(esk15_0),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(294,negated_conjecture,
    ( nil != esk14_0
    | nil != esk15_0 ),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(296,negated_conjecture,
    frontsegP(esk17_0,esk16_0),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(297,negated_conjecture,
    esk14_0 = esk16_0,
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(298,negated_conjecture,
    esk15_0 = esk17_0,
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(299,negated_conjecture,
    ( ~ segmentP(esk14_0,X1)
    | ~ segmentP(esk15_0,X1)
    | ~ neq(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(300,negated_conjecture,
    ( ~ strictorderedP(X1)
    | ~ segmentP(X1,esk16_0)
    | ~ frontsegP(esk17_0,X1)
    | ~ neq(esk16_0,X1)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[289]) ).

cnf(301,negated_conjecture,
    ssList(esk16_0),
    inference(rw,[status(thm)],[290,297,theory(equality)]) ).

cnf(302,negated_conjecture,
    ssList(esk17_0),
    inference(rw,[status(thm)],[291,298,theory(equality)]) ).

cnf(303,negated_conjecture,
    ( esk16_0 != nil
    | esk15_0 != nil ),
    inference(rw,[status(thm)],[294,297,theory(equality)]) ).

cnf(304,negated_conjecture,
    ( esk16_0 != nil
    | esk17_0 != nil ),
    inference(rw,[status(thm)],[303,298,theory(equality)]) ).

cnf(321,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(esk16_0,X1)
    | ~ segmentP(esk15_0,X1) ),
    inference(rw,[status(thm)],[299,297,theory(equality)]) ).

cnf(322,negated_conjecture,
    ( ~ ssList(X1)
    | ~ neq(X1,nil)
    | ~ segmentP(esk16_0,X1)
    | ~ segmentP(esk17_0,X1) ),
    inference(rw,[status(thm)],[321,298,theory(equality)]) ).

cnf(323,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ segmentP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[322,271,theory(equality)]) ).

cnf(325,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ segmentP(esk17_0,X1)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[323,235,theory(equality)]) ).

cnf(326,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ segmentP(esk17_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[325,theory(equality)]) ).

cnf(350,negated_conjecture,
    ( esk16_0 = X1
    | ~ segmentP(X1,esk16_0)
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1)
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[300,271,theory(equality)]) ).

cnf(353,negated_conjecture,
    ( frontsegP(X1,esk16_0)
    | ~ frontsegP(X1,esk17_0)
    | ~ ssList(esk16_0)
    | ~ ssList(esk17_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[146,296,theory(equality)]) ).

cnf(363,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | ~ ssList(nil)
    | ~ ssList(X1)
    | nil != X2 ),
    inference(spm,[status(thm)],[252,225,theory(equality)]) ).

cnf(366,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | $false
    | ~ ssList(X1)
    | nil != X2 ),
    inference(rw,[status(thm)],[363,235,theory(equality)]) ).

cnf(367,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | nil != X2 ),
    inference(cn,[status(thm)],[366,theory(equality)]) ).

cnf(368,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X1,X2)) ),
    inference(er,[status(thm)],[163,theory(equality)]) ).

cnf(380,plain,
    ( X1 = app(X2,X3)
    | ~ frontsegP(X1,app(X2,X3))
    | ~ ssList(app(X2,X3))
    | ~ ssList(X1)
    | ~ frontsegP(X2,X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[191,105,theory(equality)]) ).

cnf(398,plain,
    ( nil = esk7_2(X1,X2)
    | X1 != nil
    | ~ ssList(esk7_2(X1,X2))
    | ~ ssList(X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[77,161,theory(equality)]) ).

cnf(448,plain,
    ( frontsegP(X1,cons(X2,nil))
    | cons(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(cons(X2,nil))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[163,85,theory(equality)]) ).

cnf(458,plain,
    ( segmentP(X1,X2)
    | app(X3,X2) != X1
    | ~ ssList(nil)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X3,X2)) ),
    inference(spm,[status(thm)],[155,70,theory(equality)]) ).

cnf(459,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[155,101,theory(equality)]) ).

cnf(467,plain,
    ( segmentP(X1,X2)
    | app(X3,X2) != X1
    | $false
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X3,X2)) ),
    inference(rw,[status(thm)],[458,235,theory(equality)]) ).

cnf(468,plain,
    ( segmentP(X1,X2)
    | app(X3,X2) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(app(X3,X2)) ),
    inference(cn,[status(thm)],[467,theory(equality)]) ).

cnf(469,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[459,235,theory(equality)]) ).

cnf(470,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[469,theory(equality)]) ).

cnf(501,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[70,81,theory(equality)]) ).

cnf(503,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[81,101,theory(equality)]) ).

cnf(525,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[501,235,theory(equality)]) ).

cnf(526,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[525,theory(equality)]) ).

cnf(529,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[503,235,theory(equality)]) ).

cnf(530,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[529,theory(equality)]) ).

cnf(564,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssList(app(X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[234,112,theory(equality)]) ).

cnf(565,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssList(app(X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[120,112,theory(equality)]) ).

cnf(635,negated_conjecture,
    ( esk17_0 = nil
    | ~ segmentP(esk16_0,esk17_0)
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[326,259,theory(equality)]) ).

cnf(636,negated_conjecture,
    ( esk17_0 = nil
    | ~ segmentP(esk16_0,esk17_0)
    | $false ),
    inference(rw,[status(thm)],[635,302,theory(equality)]) ).

cnf(637,negated_conjecture,
    ( esk17_0 = nil
    | ~ segmentP(esk16_0,esk17_0) ),
    inference(cn,[status(thm)],[636,theory(equality)]) ).

cnf(638,negated_conjecture,
    ( esk16_0 = X1
    | ~ segmentP(X1,esk16_0)
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1)
    | $false ),
    inference(rw,[status(thm)],[350,301,theory(equality)]) ).

cnf(639,negated_conjecture,
    ( esk16_0 = X1
    | ~ segmentP(X1,esk16_0)
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1) ),
    inference(cn,[status(thm)],[638,theory(equality)]) ).

cnf(664,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[565,116]) ).

cnf(675,negated_conjecture,
    ( frontsegP(X1,esk16_0)
    | ~ frontsegP(X1,esk17_0)
    | $false
    | ~ ssList(esk17_0)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[353,301,theory(equality)]) ).

cnf(676,negated_conjecture,
    ( frontsegP(X1,esk16_0)
    | ~ frontsegP(X1,esk17_0)
    | $false
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[675,302,theory(equality)]) ).

cnf(677,negated_conjecture,
    ( frontsegP(X1,esk16_0)
    | ~ frontsegP(X1,esk17_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[676,theory(equality)]) ).

cnf(679,negated_conjecture,
    ( frontsegP(nil,esk16_0)
    | ~ ssList(nil)
    | nil != esk17_0
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[677,93,theory(equality)]) ).

cnf(684,negated_conjecture,
    ( frontsegP(nil,esk16_0)
    | $false
    | nil != esk17_0
    | ~ ssList(esk17_0) ),
    inference(rw,[status(thm)],[679,235,theory(equality)]) ).

cnf(685,negated_conjecture,
    ( frontsegP(nil,esk16_0)
    | $false
    | nil != esk17_0
    | $false ),
    inference(rw,[status(thm)],[684,302,theory(equality)]) ).

cnf(686,negated_conjecture,
    ( frontsegP(nil,esk16_0)
    | nil != esk17_0 ),
    inference(cn,[status(thm)],[685,theory(equality)]) ).

cnf(689,negated_conjecture,
    ( nil = esk16_0
    | ~ ssList(esk16_0)
    | esk17_0 != nil ),
    inference(spm,[status(thm)],[94,686,theory(equality)]) ).

cnf(692,negated_conjecture,
    ( nil = esk16_0
    | $false
    | esk17_0 != nil ),
    inference(rw,[status(thm)],[689,301,theory(equality)]) ).

cnf(693,negated_conjecture,
    ( nil = esk16_0
    | esk17_0 != nil ),
    inference(cn,[status(thm)],[692,theory(equality)]) ).

cnf(700,negated_conjecture,
    esk17_0 != nil,
    inference(csr,[status(thm)],[693,304]) ).

cnf(730,plain,
    ( segmentP(X1,X2)
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[367,266]) ).

cnf(736,negated_conjecture,
    ( esk16_0 = X1
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1)
    | nil != esk16_0
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[639,730,theory(equality)]) ).

cnf(744,negated_conjecture,
    ( esk16_0 = X1
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1)
    | nil != esk16_0
    | $false ),
    inference(rw,[status(thm)],[736,301,theory(equality)]) ).

cnf(745,negated_conjecture,
    ( esk16_0 = X1
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(X1)
    | ~ strictorderedP(X1)
    | nil != esk16_0 ),
    inference(cn,[status(thm)],[744,theory(equality)]) ).

cnf(747,negated_conjecture,
    ( esk16_0 = cons(X1,nil)
    | esk16_0 != nil
    | ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[745,63,theory(equality)]) ).

cnf(773,plain,
    ( frontsegP(app(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[368,116]) ).

cnf(781,plain,
    ( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
    | ~ ssList(X3)
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[773,81,theory(equality)]) ).

cnf(843,plain,
    ( X1 = app(X2,X3)
    | ~ frontsegP(X1,app(X2,X3))
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[380,116]) ).

cnf(849,plain,
    ( X1 = X3
    | ~ frontsegP(X1,X3)
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(esk7_2(X3,X2))
    | ~ ssList(X2)
    | ~ frontsegP(X3,X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[843,161,theory(equality)]) ).

cnf(1139,plain,
    ( esk7_2(X1,X2) = nil
    | X1 != nil
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[398,162]) ).

cnf(1141,plain,
    ( app(X1,nil) = X2
    | ~ frontsegP(X2,X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | X2 != nil ),
    inference(spm,[status(thm)],[161,1139,theory(equality)]) ).

cnf(1266,plain,
    ( app(nil,nil) = X1
    | X1 != nil
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[1141,130,theory(equality)]) ).

cnf(1277,plain,
    ( app(nil,nil) = X1
    | X1 != nil
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1266,235,theory(equality)]) ).

cnf(1278,plain,
    ( app(nil,nil) = X1
    | X1 != nil
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1277,theory(equality)]) ).

cnf(1516,plain,
    app(nil,nil) = nil,
    inference(spm,[status(thm)],[1278,235,theory(equality)]) ).

cnf(1542,plain,
    ( app(nil,X1) = app(nil,app(nil,X1))
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[81,1516,theory(equality)]) ).

cnf(1543,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssList(nil)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[112,1516,theory(equality)]) ).

cnf(1571,plain,
    ( app(nil,X1) = app(nil,app(nil,X1))
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[1542,235,theory(equality)]) ).

cnf(1572,plain,
    ( app(nil,X1) = app(nil,app(nil,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1571,theory(equality)]) ).

cnf(1573,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[1543,235,theory(equality)]) ).

cnf(1574,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[1573,theory(equality)]) ).

cnf(1817,plain,
    ( cons(X1,nil) != nil
    | ~ ssList(nil)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[664,1574,theory(equality)]) ).

cnf(1858,plain,
    ( cons(X1,nil) != nil
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[1817,235,theory(equality)]) ).

cnf(1859,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[1858,theory(equality)]) ).

cnf(2165,plain,
    ( frontsegP(X1,cons(esk2_1(X2),nil))
    | nil = X2
    | X2 != X1
    | ~ ssList(cons(esk2_1(X2),nil))
    | ~ ssList(esk1_1(X2))
    | ~ ssList(X1)
    | ~ ssItem(esk2_1(X2))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[448,125,theory(equality)]) ).

cnf(2169,plain,
    ( frontsegP(X1,cons(esk2_1(X1),nil))
    | nil = X1
    | ~ ssList(cons(esk2_1(X1),nil))
    | ~ ssList(esk1_1(X1))
    | ~ ssList(X1)
    | ~ ssItem(esk2_1(X1)) ),
    inference(er,[status(thm)],[2165,theory(equality)]) ).

cnf(3106,plain,
    ( segmentP(X1,X2)
    | app(X3,X2) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[468,116]) ).

cnf(3192,plain,
    ( segmentP(X1,X2)
    | X3 != X1
    | ~ ssList(esk7_2(X3,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ frontsegP(X3,X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[470,161,theory(equality)]) ).

cnf(3213,plain,
    ( segmentP(X1,X2)
    | ~ ssList(esk7_2(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ frontsegP(X1,X2) ),
    inference(er,[status(thm)],[3192,theory(equality)]) ).

cnf(4761,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[526,116]) ).

cnf(4817,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[530,4761,theory(equality)]) ).

cnf(4873,plain,
    ( app(nil,X1) = app(X1,nil)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[4817,235,theory(equality)]) ).

cnf(4874,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[4873,theory(equality)]) ).

cnf(5168,plain,
    ( frontsegP(X1,X2)
    | app(nil,X2) != X1
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[163,4874,theory(equality)]) ).

cnf(5229,plain,
    ( app(nil,app(X1,nil)) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[1572,4874,theory(equality)]) ).

cnf(5250,plain,
    ( segmentP(X1,X2)
    | app(X2,nil) != X1
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[3106,4874,theory(equality)]) ).

cnf(5324,plain,
    ( frontsegP(X1,X2)
    | app(nil,X2) != X1
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[5168,235,theory(equality)]) ).

cnf(5325,plain,
    ( frontsegP(X1,X2)
    | app(nil,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[5324,theory(equality)]) ).

cnf(5477,plain,
    ( segmentP(X1,X2)
    | app(X2,nil) != X1
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[5250,235,theory(equality)]) ).

cnf(5478,plain,
    ( segmentP(X1,X2)
    | app(X2,nil) != X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[5477,theory(equality)]) ).

cnf(10830,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[564,116]) ).

cnf(10838,plain,
    ( ssList(cons(X1,nil))
    | ~ ssList(nil)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[10830,1574,theory(equality)]) ).

cnf(10860,plain,
    ( ssList(cons(X1,nil))
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[10838,235,theory(equality)]) ).

cnf(10861,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[10860,theory(equality)]) ).

cnf(12478,negated_conjecture,
    ( esk17_0 = nil
    | app(esk17_0,nil) != esk16_0
    | ~ ssList(esk17_0)
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[637,5478,theory(equality)]) ).

cnf(12499,negated_conjecture,
    ( esk17_0 = nil
    | app(esk17_0,nil) != esk16_0
    | $false
    | ~ ssList(esk16_0) ),
    inference(rw,[status(thm)],[12478,302,theory(equality)]) ).

cnf(12500,negated_conjecture,
    ( esk17_0 = nil
    | app(esk17_0,nil) != esk16_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[12499,301,theory(equality)]) ).

cnf(12501,negated_conjecture,
    ( esk17_0 = nil
    | app(esk17_0,nil) != esk16_0 ),
    inference(cn,[status(thm)],[12500,theory(equality)]) ).

cnf(12502,negated_conjecture,
    app(esk17_0,nil) != esk16_0,
    inference(sr,[status(thm)],[12501,700,theory(equality)]) ).

cnf(12541,negated_conjecture,
    ( esk17_0 != esk16_0
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[12502,70,theory(equality)]) ).

cnf(12546,negated_conjecture,
    ( esk17_0 != esk16_0
    | $false ),
    inference(rw,[status(thm)],[12541,302,theory(equality)]) ).

cnf(12547,negated_conjecture,
    esk17_0 != esk16_0,
    inference(cn,[status(thm)],[12546,theory(equality)]) ).

cnf(17304,plain,
    ( frontsegP(app(X1,app(X2,X3)),app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[781,116]) ).

cnf(17396,plain,
    ( frontsegP(app(X1,nil),app(nil,X1))
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[17304,5229,theory(equality)]) ).

cnf(17496,plain,
    ( frontsegP(app(X1,nil),app(nil,X1))
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[17396,235,theory(equality)]) ).

cnf(17497,plain,
    ( frontsegP(app(X1,nil),app(nil,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[17496,theory(equality)]) ).

cnf(18269,plain,
    ( frontsegP(X1,app(nil,X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[17497,70,theory(equality)]) ).

cnf(18860,plain,
    ( X1 = X3
    | ~ frontsegP(X3,X2)
    | ~ frontsegP(X1,X3)
    | ~ frontsegP(X2,X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[849,162]) ).

cnf(18861,negated_conjecture,
    ( esk17_0 = esk16_0
    | ~ frontsegP(X1,esk17_0)
    | ~ frontsegP(esk16_0,X1)
    | ~ ssList(esk17_0)
    | ~ ssList(X1)
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[18860,296,theory(equality)]) ).

cnf(18908,negated_conjecture,
    ( esk17_0 = esk16_0
    | ~ frontsegP(X1,esk17_0)
    | ~ frontsegP(esk16_0,X1)
    | $false
    | ~ ssList(X1)
    | ~ ssList(esk16_0) ),
    inference(rw,[status(thm)],[18861,302,theory(equality)]) ).

cnf(18909,negated_conjecture,
    ( esk17_0 = esk16_0
    | ~ frontsegP(X1,esk17_0)
    | ~ frontsegP(esk16_0,X1)
    | $false
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[18908,301,theory(equality)]) ).

cnf(18910,negated_conjecture,
    ( esk17_0 = esk16_0
    | ~ frontsegP(X1,esk17_0)
    | ~ frontsegP(esk16_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[18909,theory(equality)]) ).

cnf(18911,negated_conjecture,
    ( ~ frontsegP(X1,esk17_0)
    | ~ frontsegP(esk16_0,X1)
    | ~ ssList(X1) ),
    inference(sr,[status(thm)],[18910,12547,theory(equality)]) ).

cnf(18981,negated_conjecture,
    ( ~ frontsegP(esk16_0,X1)
    | ~ ssList(X1)
    | app(nil,esk17_0) != X1
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[18911,5325,theory(equality)]) ).

cnf(19012,negated_conjecture,
    ( ~ frontsegP(esk16_0,X1)
    | ~ ssList(X1)
    | app(nil,esk17_0) != X1
    | $false ),
    inference(rw,[status(thm)],[18981,302,theory(equality)]) ).

cnf(19013,negated_conjecture,
    ( ~ frontsegP(esk16_0,X1)
    | ~ ssList(X1)
    | app(nil,esk17_0) != X1 ),
    inference(cn,[status(thm)],[19012,theory(equality)]) ).

cnf(19358,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | ~ ssList(app(nil,esk16_0))
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[19013,18269,theory(equality)]) ).

cnf(19387,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | ~ ssList(app(nil,esk16_0))
    | $false ),
    inference(rw,[status(thm)],[19358,301,theory(equality)]) ).

cnf(19388,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | ~ ssList(app(nil,esk16_0)) ),
    inference(cn,[status(thm)],[19387,theory(equality)]) ).

cnf(22034,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | ~ ssList(esk16_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[19388,116,theory(equality)]) ).

cnf(22040,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[22034,301,theory(equality)]) ).

cnf(22041,negated_conjecture,
    ( app(nil,esk17_0) != app(nil,esk16_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[22040,235,theory(equality)]) ).

cnf(22042,negated_conjecture,
    app(nil,esk17_0) != app(nil,esk16_0),
    inference(cn,[status(thm)],[22041,theory(equality)]) ).

cnf(22051,negated_conjecture,
    ( esk17_0 != app(nil,esk16_0)
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[22042,101,theory(equality)]) ).

cnf(22055,negated_conjecture,
    ( esk17_0 != app(nil,esk16_0)
    | $false ),
    inference(rw,[status(thm)],[22051,302,theory(equality)]) ).

cnf(22056,negated_conjecture,
    esk17_0 != app(nil,esk16_0),
    inference(cn,[status(thm)],[22055,theory(equality)]) ).

cnf(51088,plain,
    ( nil = X1
    | frontsegP(X1,cons(esk2_1(X1),nil))
    | ~ ssList(cons(esk2_1(X1),nil))
    | ~ ssList(esk1_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[2169,126]) ).

cnf(51089,plain,
    ( nil = X1
    | frontsegP(X1,cons(esk2_1(X1),nil))
    | ~ ssList(cons(esk2_1(X1),nil))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[51088,127]) ).

cnf(78322,plain,
    ( segmentP(X1,X2)
    | ~ frontsegP(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[3213,162]) ).

cnf(78327,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ ssList(X1)
    | ~ frontsegP(esk17_0,X1)
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[326,78322,theory(equality)]) ).

cnf(78371,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ ssList(X1)
    | ~ frontsegP(esk17_0,X1)
    | $false ),
    inference(rw,[status(thm)],[78327,302,theory(equality)]) ).

cnf(78372,negated_conjecture,
    ( X1 = nil
    | ~ segmentP(esk16_0,X1)
    | ~ ssList(X1)
    | ~ frontsegP(esk17_0,X1) ),
    inference(cn,[status(thm)],[78371,theory(equality)]) ).

cnf(78648,negated_conjecture,
    ( esk16_0 = nil
    | ~ frontsegP(esk17_0,esk16_0)
    | ~ ssList(esk16_0) ),
    inference(spm,[status(thm)],[78372,259,theory(equality)]) ).

cnf(78675,negated_conjecture,
    ( esk16_0 = nil
    | $false
    | ~ ssList(esk16_0) ),
    inference(rw,[status(thm)],[78648,296,theory(equality)]) ).

cnf(78676,negated_conjecture,
    ( esk16_0 = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[78675,301,theory(equality)]) ).

cnf(78677,negated_conjecture,
    esk16_0 = nil,
    inference(cn,[status(thm)],[78676,theory(equality)]) ).

cnf(78750,negated_conjecture,
    nil != esk17_0,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[22056,78677,theory(equality)]),1516,theory(equality)]) ).

cnf(79435,negated_conjecture,
    ( cons(X1,nil) = nil
    | esk16_0 != nil
    | ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[747,78677,theory(equality)]) ).

cnf(79436,negated_conjecture,
    ( cons(X1,nil) = nil
    | $false
    | ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[79435,78677,theory(equality)]) ).

cnf(79437,negated_conjecture,
    ( cons(X1,nil) = nil
    | ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[79436,theory(equality)]) ).

cnf(80659,negated_conjecture,
    ( cons(X1,nil) = nil
    | ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[79437,10861]) ).

cnf(80660,negated_conjecture,
    ( ~ frontsegP(esk17_0,cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[80659,1859]) ).

cnf(80670,negated_conjecture,
    ( nil = esk17_0
    | ~ ssItem(esk2_1(esk17_0))
    | ~ ssList(cons(esk2_1(esk17_0),nil))
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[80660,51089,theory(equality)]) ).

cnf(80683,negated_conjecture,
    ( nil = esk17_0
    | ~ ssItem(esk2_1(esk17_0))
    | ~ ssList(cons(esk2_1(esk17_0),nil))
    | $false ),
    inference(rw,[status(thm)],[80670,302,theory(equality)]) ).

cnf(80684,negated_conjecture,
    ( nil = esk17_0
    | ~ ssItem(esk2_1(esk17_0))
    | ~ ssList(cons(esk2_1(esk17_0),nil)) ),
    inference(cn,[status(thm)],[80683,theory(equality)]) ).

cnf(80685,negated_conjecture,
    ( ~ ssItem(esk2_1(esk17_0))
    | ~ ssList(cons(esk2_1(esk17_0),nil)) ),
    inference(sr,[status(thm)],[80684,78750,theory(equality)]) ).

cnf(80745,negated_conjecture,
    ~ ssItem(esk2_1(esk17_0)),
    inference(csr,[status(thm)],[80685,10861]) ).

cnf(80746,negated_conjecture,
    ( nil = esk17_0
    | ~ ssList(esk17_0) ),
    inference(spm,[status(thm)],[80745,126,theory(equality)]) ).

cnf(80748,negated_conjecture,
    ( nil = esk17_0
    | $false ),
    inference(rw,[status(thm)],[80746,302,theory(equality)]) ).

cnf(80749,negated_conjecture,
    nil = esk17_0,
    inference(cn,[status(thm)],[80748,theory(equality)]) ).

cnf(80750,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[80749,78750,theory(equality)]) ).

cnf(80751,negated_conjecture,
    $false,
    80750,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC077+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpeS6kvB/sel_SWC077+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC077+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC077+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC077+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
% 
%------------------------------------------------------------------------------