TSTP Solution File: SWC335+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC335+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.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 11:31:40 EST 2010

% Result   : Theorem 276.89s
% Output   : CNFRefutation 276.89s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :   19
% Syntax   : Number of formulae    :  165 (  19 unt;   0 def)
%            Number of atoms       :  816 ( 180 equ)
%            Maximal formula atoms :   30 (   4 avg)
%            Number of connectives : 1121 ( 470   ~; 472   |; 128   &)
%                                         (   7 <=>;  44  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   3 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  282 (   0 sgn 156   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ssItem(X1)
     => totalorderedP(cons(X1,nil)) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax65) ).

fof(4,axiom,
    totalorderedP(nil),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax66) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax84) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax83) ).

fof(11,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax81) ).

fof(14,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax28) ).

fof(18,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax26) ).

fof(24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax3) ).

fof(25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( ( segmentP(X1,X2)
                  & segmentP(X2,X3) )
               => segmentP(X1,X3) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax53) ).

fof(26,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( segmentP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(app(X3,X2),X4) = X1 ) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax7) ).

fof(38,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( segmentP(nil,X1)
      <=> nil = X1 ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax58) ).

fof(41,axiom,
    ssList(nil),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax17) ).

fof(42,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax36) ).

fof(45,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax38) ).

fof(49,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( segmentP(X1,X2)
                   => segmentP(app(app(X3,X1),X4),X2) ) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax56) ).

fof(50,axiom,
    ! [X1] :
      ( ssList(X1)
     => segmentP(X1,nil) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',ax57) ).

fof(55,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ( cons(X5,nil) != X3
                            | ~ memberP(X4,X5)
                            | ? [X6] :
                                ( ssItem(X6)
                                & X5 != X6
                                & memberP(X4,X6)
                                & leq(X6,X5) ) ) )
                      & ( nil != X4
                        | nil != X3 ) )
                    | ( segmentP(X2,X1)
                      & totalorderedP(X1) ) ) ) ) ) ),
    file('/tmp/tmpOqimKA/sel_SWC335+1.p_5',co1) ).

fof(56,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ! [X5] :
                            ( ssItem(X5)
                           => ( cons(X5,nil) != X3
                              | ~ memberP(X4,X5)
                              | ? [X6] :
                                  ( ssItem(X6)
                                  & X5 != X6
                                  & memberP(X4,X6)
                                  & leq(X6,X5) ) ) )
                        & ( nil != X4
                          | nil != X3 ) )
                      | ( segmentP(X2,X1)
                        & totalorderedP(X1) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[55]) ).

fof(59,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[45,theory(equality)]) ).

fof(60,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ! [X5] :
                            ( ssItem(X5)
                           => ( cons(X5,nil) != X3
                              | ~ memberP(X4,X5)
                              | ? [X6] :
                                  ( ssItem(X6)
                                  & X5 != X6
                                  & memberP(X4,X6)
                                  & leq(X6,X5) ) ) )
                        & ( nil != X4
                          | nil != X3 ) )
                      | ( segmentP(X2,X1)
                        & totalorderedP(X1) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[56,theory(equality)]) ).

fof(61,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | totalorderedP(cons(X1,nil)) ),
    inference(fof_nnf,[status(thm)],[1]) ).

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

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

cnf(77,plain,
    totalorderedP(nil),
    inference(split_conjunct,[status(thm)],[4]) ).

fof(86,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(X1,nil) = X1 ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(87,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[86]) ).

cnf(88,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

fof(89,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)],[9]) ).

fof(90,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)],[89]) ).

fof(91,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)],[90]) ).

fof(92,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)],[91]) ).

cnf(93,plain,
    ( nil = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X1
    | nil != X2 ),
    inference(split_conjunct,[status(thm)],[92]) ).

fof(100,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[11]) ).

fof(101,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[100]) ).

fof(102,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[101]) ).

cnf(103,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[102]) ).

fof(112,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[14]) ).

fof(113,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(nil,X2) = X2 ),
    inference(variable_rename,[status(thm)],[112]) ).

cnf(114,plain,
    ( app(nil,X1) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[113]) ).

fof(126,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[18]) ).

fof(127,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[126]) ).

fof(128,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[127]) ).

cnf(129,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[128]) ).

fof(153,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ( ( ~ memberP(X1,X2)
              | ? [X3] :
                  ( ssList(X3)
                  & ? [X4] :
                      ( ssList(X4)
                      & app(X3,cons(X2,X4)) = X1 ) ) )
            & ( ! [X3] :
                  ( ~ ssList(X3)
                  | ! [X4] :
                      ( ~ ssList(X4)
                      | app(X3,cons(X2,X4)) != X1 ) )
              | memberP(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(154,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssItem(X6)
          | ( ( ~ memberP(X5,X6)
              | ? [X7] :
                  ( ssList(X7)
                  & ? [X8] :
                      ( ssList(X8)
                      & app(X7,cons(X6,X8)) = X5 ) ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(X9,cons(X6,X10)) != X5 ) )
              | memberP(X5,X6) ) ) ) ),
    inference(variable_rename,[status(thm)],[153]) ).

fof(155,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssItem(X6)
          | ( ( ~ memberP(X5,X6)
              | ( ssList(esk5_2(X5,X6))
                & ssList(esk6_2(X5,X6))
                & app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(X9,cons(X6,X10)) != X5 ) )
              | memberP(X5,X6) ) ) ) ),
    inference(skolemize,[status(esa)],[154]) ).

fof(156,plain,
    ! [X5,X6,X9,X10] :
      ( ( ( ~ ssList(X10)
          | app(X9,cons(X6,X10)) != X5
          | ~ ssList(X9)
          | memberP(X5,X6) )
        & ( ~ memberP(X5,X6)
          | ( ssList(esk5_2(X5,X6))
            & ssList(esk6_2(X5,X6))
            & app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5 ) ) )
      | ~ ssItem(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[155]) ).

fof(157,plain,
    ! [X5,X6,X9,X10] :
      ( ( ~ ssList(X10)
        | app(X9,cons(X6,X10)) != X5
        | ~ ssList(X9)
        | memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( ssList(esk5_2(X5,X6))
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( ssList(esk6_2(X5,X6))
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( app(esk5_2(X5,X6),cons(X6,esk6_2(X5,X6))) = X5
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) ) ),
    inference(distribute,[status(thm)],[156]) ).

cnf(158,plain,
    ( app(esk5_2(X1,X2),cons(X2,esk6_2(X1,X2))) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(159,plain,
    ( ssList(esk6_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(160,plain,
    ( ssList(esk5_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[157]) ).

fof(162,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ~ segmentP(X1,X2)
              | ~ segmentP(X2,X3)
              | segmentP(X1,X3) ) ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(163,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ~ segmentP(X4,X5)
              | ~ segmentP(X5,X6)
              | segmentP(X4,X6) ) ) ),
    inference(variable_rename,[status(thm)],[162]) ).

fof(164,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ~ segmentP(X4,X5)
      | ~ segmentP(X5,X6)
      | segmentP(X4,X6)
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[163]) ).

cnf(165,plain,
    ( segmentP(X1,X3)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ segmentP(X2,X3)
    | ~ segmentP(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[164]) ).

fof(166,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)],[26]) ).

fof(167,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)],[166]) ).

fof(168,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)],[167]) ).

fof(169,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)],[168]) ).

fof(170,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)],[169]) ).

cnf(174,plain,
    ( segmentP(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | app(app(X3,X2),X4) != X1
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[170]) ).

fof(226,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ( ( ~ segmentP(nil,X1)
          | nil = X1 )
        & ( nil != X1
          | segmentP(nil,X1) ) ) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(227,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | ( ( ~ segmentP(nil,X2)
          | nil = X2 )
        & ( nil != X2
          | segmentP(nil,X2) ) ) ),
    inference(variable_rename,[status(thm)],[226]) ).

fof(228,plain,
    ! [X2] :
      ( ( ~ segmentP(nil,X2)
        | nil = X2
        | ~ ssList(X2) )
      & ( nil != X2
        | segmentP(nil,X2)
        | ~ ssList(X2) ) ),
    inference(distribute,[status(thm)],[227]) ).

cnf(229,plain,
    ( segmentP(nil,X1)
    | ~ ssList(X1)
    | nil != X1 ),
    inference(split_conjunct,[status(thm)],[228]) ).

cnf(239,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(240,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ( ( ~ memberP(app(X2,X3),X1)
                  | memberP(X2,X1)
                  | memberP(X3,X1) )
                & ( ( ~ memberP(X2,X1)
                    & ~ memberP(X3,X1) )
                  | memberP(app(X2,X3),X1) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[42]) ).

fof(241,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ( ( ~ memberP(app(X5,X6),X4)
                  | memberP(X5,X4)
                  | memberP(X6,X4) )
                & ( ( ~ memberP(X5,X4)
                    & ~ memberP(X6,X4) )
                  | memberP(app(X5,X6),X4) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[240]) ).

fof(242,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ( ( ~ memberP(app(X5,X6),X4)
          | memberP(X5,X4)
          | memberP(X6,X4) )
        & ( ( ~ memberP(X5,X4)
            & ~ memberP(X6,X4) )
          | memberP(app(X5,X6),X4) ) )
      | ~ ssList(X5)
      | ~ ssItem(X4) ),
    inference(shift_quantors,[status(thm)],[241]) ).

fof(243,plain,
    ! [X4,X5,X6] :
      ( ( ~ memberP(app(X5,X6),X4)
        | memberP(X5,X4)
        | memberP(X6,X4)
        | ~ ssList(X6)
        | ~ ssList(X5)
        | ~ ssItem(X4) )
      & ( ~ memberP(X5,X4)
        | memberP(app(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssList(X5)
        | ~ ssItem(X4) )
      & ( ~ memberP(X6,X4)
        | memberP(app(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssList(X5)
        | ~ ssItem(X4) ) ),
    inference(distribute,[status(thm)],[242]) ).

cnf(244,plain,
    ( memberP(app(X2,X3),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ memberP(X3,X1) ),
    inference(split_conjunct,[status(thm)],[243]) ).

fof(273,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ memberP(nil,X1) ),
    inference(fof_nnf,[status(thm)],[59]) ).

fof(274,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[273]) ).

cnf(275,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[274]) ).

fof(293,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ! [X4] :
                  ( ~ ssList(X4)
                  | ~ segmentP(X1,X2)
                  | segmentP(app(app(X3,X1),X4),X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[49]) ).

fof(294,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssList(X6)
          | ! [X7] :
              ( ~ ssList(X7)
              | ! [X8] :
                  ( ~ ssList(X8)
                  | ~ segmentP(X5,X6)
                  | segmentP(app(app(X7,X5),X8),X6) ) ) ) ),
    inference(variable_rename,[status(thm)],[293]) ).

fof(295,plain,
    ! [X5,X6,X7,X8] :
      ( ~ ssList(X8)
      | ~ segmentP(X5,X6)
      | segmentP(app(app(X7,X5),X8),X6)
      | ~ ssList(X7)
      | ~ ssList(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[294]) ).

cnf(296,plain,
    ( segmentP(app(app(X3,X1),X4),X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ segmentP(X1,X2)
    | ~ ssList(X4) ),
    inference(split_conjunct,[status(thm)],[295]) ).

fof(297,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | segmentP(X1,nil) ),
    inference(fof_nnf,[status(thm)],[50]) ).

fof(298,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | segmentP(X2,nil) ),
    inference(variable_rename,[status(thm)],[297]) ).

cnf(299,plain,
    ( segmentP(X1,nil)
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[298]) ).

fof(317,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ? [X5] :
                        ( ssItem(X5)
                        & cons(X5,nil) = X3
                        & memberP(X4,X5)
                        & ! [X6] :
                            ( ~ ssItem(X6)
                            | X5 = X6
                            | ~ memberP(X4,X6)
                            | ~ leq(X6,X5) ) )
                    | ( nil = X4
                      & nil = X3 ) )
                  & ( ~ segmentP(X2,X1)
                    | ~ totalorderedP(X1) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[60]) ).

fof(318,negated_conjecture,
    ? [X7] :
      ( ssList(X7)
      & ? [X8] :
          ( ssList(X8)
          & ? [X9] :
              ( ssList(X9)
              & ? [X10] :
                  ( ssList(X10)
                  & X8 = X10
                  & X7 = X9
                  & ( ? [X11] :
                        ( ssItem(X11)
                        & cons(X11,nil) = X9
                        & memberP(X10,X11)
                        & ! [X12] :
                            ( ~ ssItem(X12)
                            | X11 = X12
                            | ~ memberP(X10,X12)
                            | ~ leq(X12,X11) ) )
                    | ( nil = X10
                      & nil = X9 ) )
                  & ( ~ segmentP(X8,X7)
                    | ~ totalorderedP(X7) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[317]) ).

fof(319,negated_conjecture,
    ( ssList(esk21_0)
    & ssList(esk22_0)
    & ssList(esk23_0)
    & ssList(esk24_0)
    & esk22_0 = esk24_0
    & esk21_0 = esk23_0
    & ( ( ssItem(esk25_0)
        & cons(esk25_0,nil) = esk23_0
        & memberP(esk24_0,esk25_0)
        & ! [X12] :
            ( ~ ssItem(X12)
            | esk25_0 = X12
            | ~ memberP(esk24_0,X12)
            | ~ leq(X12,esk25_0) ) )
      | ( nil = esk24_0
        & nil = esk23_0 ) )
    & ( ~ segmentP(esk22_0,esk21_0)
      | ~ totalorderedP(esk21_0) ) ),
    inference(skolemize,[status(esa)],[318]) ).

fof(320,negated_conjecture,
    ! [X12] :
      ( ( ( ( ~ ssItem(X12)
            | esk25_0 = X12
            | ~ memberP(esk24_0,X12)
            | ~ leq(X12,esk25_0) )
          & cons(esk25_0,nil) = esk23_0
          & memberP(esk24_0,esk25_0)
          & ssItem(esk25_0) )
        | ( nil = esk24_0
          & nil = esk23_0 ) )
      & esk22_0 = esk24_0
      & esk21_0 = esk23_0
      & ( ~ segmentP(esk22_0,esk21_0)
        | ~ totalorderedP(esk21_0) )
      & ssList(esk24_0)
      & ssList(esk23_0)
      & ssList(esk22_0)
      & ssList(esk21_0) ),
    inference(shift_quantors,[status(thm)],[319]) ).

fof(321,negated_conjecture,
    ! [X12] :
      ( ( nil = esk24_0
        | ~ ssItem(X12)
        | esk25_0 = X12
        | ~ memberP(esk24_0,X12)
        | ~ leq(X12,esk25_0) )
      & ( nil = esk23_0
        | ~ ssItem(X12)
        | esk25_0 = X12
        | ~ memberP(esk24_0,X12)
        | ~ leq(X12,esk25_0) )
      & ( nil = esk24_0
        | cons(esk25_0,nil) = esk23_0 )
      & ( nil = esk23_0
        | cons(esk25_0,nil) = esk23_0 )
      & ( nil = esk24_0
        | memberP(esk24_0,esk25_0) )
      & ( nil = esk23_0
        | memberP(esk24_0,esk25_0) )
      & ( nil = esk24_0
        | ssItem(esk25_0) )
      & ( nil = esk23_0
        | ssItem(esk25_0) )
      & esk22_0 = esk24_0
      & esk21_0 = esk23_0
      & ( ~ segmentP(esk22_0,esk21_0)
        | ~ totalorderedP(esk21_0) )
      & ssList(esk24_0)
      & ssList(esk23_0)
      & ssList(esk22_0)
      & ssList(esk21_0) ),
    inference(distribute,[status(thm)],[320]) ).

cnf(322,negated_conjecture,
    ssList(esk21_0),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(325,negated_conjecture,
    ssList(esk24_0),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(326,negated_conjecture,
    ( ~ totalorderedP(esk21_0)
    | ~ segmentP(esk22_0,esk21_0) ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(327,negated_conjecture,
    esk21_0 = esk23_0,
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(328,negated_conjecture,
    esk22_0 = esk24_0,
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(329,negated_conjecture,
    ( ssItem(esk25_0)
    | nil = esk23_0 ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(330,negated_conjecture,
    ( ssItem(esk25_0)
    | nil = esk24_0 ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(331,negated_conjecture,
    ( memberP(esk24_0,esk25_0)
    | nil = esk23_0 ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(332,negated_conjecture,
    ( memberP(esk24_0,esk25_0)
    | nil = esk24_0 ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(334,negated_conjecture,
    ( cons(esk25_0,nil) = esk23_0
    | nil = esk24_0 ),
    inference(split_conjunct,[status(thm)],[321]) ).

cnf(337,negated_conjecture,
    ssList(esk23_0),
    inference(rw,[status(thm)],[322,327,theory(equality)]) ).

cnf(339,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | ~ segmentP(esk22_0,esk21_0) ),
    inference(rw,[status(thm)],[326,327,theory(equality)]) ).

cnf(340,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | ~ segmentP(esk24_0,esk23_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[339,328,theory(equality)]),327,theory(equality)]) ).

cnf(342,negated_conjecture,
    ( totalorderedP(esk23_0)
    | esk24_0 = nil
    | ~ ssItem(esk25_0) ),
    inference(spm,[status(thm)],[63,334,theory(equality)]) ).

cnf(441,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | ~ ssList(nil)
    | ~ ssList(X1)
    | nil != X2 ),
    inference(spm,[status(thm)],[165,229,theory(equality)]) ).

cnf(444,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | $false
    | ~ ssList(X1)
    | nil != X2 ),
    inference(rw,[status(thm)],[441,239,theory(equality)]) ).

cnf(445,plain,
    ( segmentP(X1,X2)
    | ~ segmentP(X1,nil)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | nil != X2 ),
    inference(cn,[status(thm)],[444,theory(equality)]) ).

cnf(470,plain,
    ( memberP(nil,X3)
    | ~ memberP(X2,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3)
    | nil != X2
    | nil != X1 ),
    inference(spm,[status(thm)],[244,93,theory(equality)]) ).

cnf(616,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[174,114,theory(equality)]) ).

cnf(624,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[616,239,theory(equality)]) ).

cnf(625,plain,
    ( segmentP(X1,X2)
    | app(X2,X3) != X1
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[624,theory(equality)]) ).

cnf(691,plain,
    ( segmentP(app(X1,X3),X4)
    | ~ segmentP(cons(X2,esk6_2(X1,X2)),X4)
    | ~ ssList(X3)
    | ~ ssList(esk5_2(X1,X2))
    | ~ ssList(X4)
    | ~ ssList(cons(X2,esk6_2(X1,X2)))
    | ~ memberP(X1,X2)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[296,158,theory(equality)]) ).

cnf(871,negated_conjecture,
    ( esk24_0 = nil
    | totalorderedP(esk23_0) ),
    inference(csr,[status(thm)],[342,330]) ).

cnf(1414,plain,
    ( segmentP(X1,X2)
    | nil != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[445,299]) ).

cnf(1415,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | nil != esk23_0
    | ~ ssList(esk23_0)
    | ~ ssList(esk24_0) ),
    inference(spm,[status(thm)],[340,1414,theory(equality)]) ).

cnf(1419,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | nil != esk23_0
    | $false
    | ~ ssList(esk24_0) ),
    inference(rw,[status(thm)],[1415,337,theory(equality)]) ).

cnf(1420,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | nil != esk23_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[1419,325,theory(equality)]) ).

cnf(1421,negated_conjecture,
    ( ~ totalorderedP(esk23_0)
    | nil != esk23_0 ),
    inference(cn,[status(thm)],[1420,theory(equality)]) ).

cnf(2118,plain,
    ( nil != X2
    | nil != X1
    | ~ memberP(X2,X3)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(X3) ),
    inference(csr,[status(thm)],[470,275]) ).

fof(2119,plain,
    ( ~ epred3_0
  <=> ! [X3,X2] :
        ( ~ ssItem(X3)
        | ~ ssList(X2)
        | ~ memberP(X2,X3)
        | nil != X2 ) ),
    introduced(definition),
    [split] ).

cnf(2120,plain,
    ( epred3_0
    | ~ ssItem(X3)
    | ~ ssList(X2)
    | ~ memberP(X2,X3)
    | nil != X2 ),
    inference(split_equiv,[status(thm)],[2119]) ).

fof(2121,plain,
    ( ~ epred4_0
  <=> ! [X1] :
        ( ~ ssList(X1)
        | nil != X1 ) ),
    introduced(definition),
    [split] ).

cnf(2122,plain,
    ( epred4_0
    | ~ ssList(X1)
    | nil != X1 ),
    inference(split_equiv,[status(thm)],[2121]) ).

cnf(2123,plain,
    ( ~ epred4_0
    | ~ epred3_0 ),
    inference(apply_def,[status(esa)],[inference(apply_def,[status(esa)],[2118,2119,theory(equality)]),2121,theory(equality)]),
    [split] ).

cnf(2124,plain,
    epred4_0,
    inference(spm,[status(thm)],[2122,239,theory(equality)]) ).

cnf(2145,plain,
    ( $false
    | ~ epred3_0 ),
    inference(rw,[status(thm)],[2123,2124,theory(equality)]) ).

cnf(2146,plain,
    ~ epred3_0,
    inference(cn,[status(thm)],[2145,theory(equality)]) ).

cnf(2164,plain,
    ( ~ ssItem(X3)
    | ~ ssList(X2)
    | ~ memberP(X2,X3)
    | nil != X2 ),
    inference(sr,[status(thm)],[2120,2146,theory(equality)]) ).

cnf(2165,negated_conjecture,
    ( esk23_0 = nil
    | nil != esk24_0
    | ~ ssList(esk24_0)
    | ~ ssItem(esk25_0) ),
    inference(spm,[status(thm)],[2164,331,theory(equality)]) ).

cnf(2177,negated_conjecture,
    ( esk23_0 = nil
    | nil != esk24_0
    | $false
    | ~ ssItem(esk25_0) ),
    inference(rw,[status(thm)],[2165,325,theory(equality)]) ).

cnf(2178,negated_conjecture,
    ( esk23_0 = nil
    | nil != esk24_0
    | ~ ssItem(esk25_0) ),
    inference(cn,[status(thm)],[2177,theory(equality)]) ).

cnf(2189,negated_conjecture,
    ( esk23_0 = nil
    | esk24_0 != nil ),
    inference(csr,[status(thm)],[2178,329]) ).

cnf(2202,negated_conjecture,
    ( ~ totalorderedP(nil)
    | esk24_0 != nil ),
    inference(spm,[status(thm)],[1421,2189,theory(equality)]) ).

cnf(2215,negated_conjecture,
    ( $false
    | esk24_0 != nil ),
    inference(rw,[status(thm)],[2202,77,theory(equality)]) ).

cnf(2216,negated_conjecture,
    esk24_0 != nil,
    inference(cn,[status(thm)],[2215,theory(equality)]) ).

cnf(2217,negated_conjecture,
    ssItem(esk25_0),
    inference(sr,[status(thm)],[330,2216,theory(equality)]) ).

cnf(2218,negated_conjecture,
    memberP(esk24_0,esk25_0),
    inference(sr,[status(thm)],[332,2216,theory(equality)]) ).

cnf(2219,negated_conjecture,
    cons(esk25_0,nil) = esk23_0,
    inference(sr,[status(thm)],[334,2216,theory(equality)]) ).

cnf(2220,negated_conjecture,
    totalorderedP(esk23_0),
    inference(sr,[status(thm)],[871,2216,theory(equality)]) ).

cnf(2233,negated_conjecture,
    ( ~ segmentP(esk24_0,esk23_0)
    | $false ),
    inference(rw,[status(thm)],[340,2220,theory(equality)]) ).

cnf(2234,negated_conjecture,
    ~ segmentP(esk24_0,esk23_0),
    inference(cn,[status(thm)],[2233,theory(equality)]) ).

cnf(2260,negated_conjecture,
    ( app(esk23_0,X1) = cons(esk25_0,X1)
    | ~ ssList(X1)
    | ~ ssItem(esk25_0) ),
    inference(spm,[status(thm)],[103,2219,theory(equality)]) ).

cnf(2320,negated_conjecture,
    ( app(esk23_0,X1) = cons(esk25_0,X1)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[2260,2217,theory(equality)]) ).

cnf(2321,negated_conjecture,
    ( app(esk23_0,X1) = cons(esk25_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2320,theory(equality)]) ).

cnf(2633,negated_conjecture,
    ( ssList(cons(esk25_0,X1))
    | ~ ssList(X1)
    | ~ ssList(esk23_0) ),
    inference(spm,[status(thm)],[129,2321,theory(equality)]) ).

cnf(2658,negated_conjecture,
    ( ssList(cons(esk25_0,X1))
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[2633,337,theory(equality)]) ).

cnf(2659,negated_conjecture,
    ( ssList(cons(esk25_0,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2658,theory(equality)]) ).

cnf(7488,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | cons(esk25_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(esk23_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[625,2321,theory(equality)]) ).

cnf(7511,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | cons(esk25_0,X2) != X1
    | ~ ssList(X2)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[7488,337,theory(equality)]) ).

cnf(7512,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | cons(esk25_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[7511,theory(equality)]) ).

cnf(7688,negated_conjecture,
    ( segmentP(cons(esk25_0,X1),esk23_0)
    | ~ ssList(X1)
    | ~ ssList(cons(esk25_0,X1)) ),
    inference(er,[status(thm)],[7512,theory(equality)]) ).

cnf(7749,negated_conjecture,
    ( segmentP(cons(esk25_0,X1),esk23_0)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[7688,2659]) ).

cnf(12235,plain,
    ( segmentP(app(X1,X3),X4)
    | ~ segmentP(cons(X2,esk6_2(X1,X2)),X4)
    | ~ memberP(X1,X2)
    | ~ ssList(cons(X2,esk6_2(X1,X2)))
    | ~ ssList(X4)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[691,160]) ).

cnf(12243,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(cons(esk25_0,esk6_2(X1,esk25_0)))
    | ~ ssList(X2)
    | ~ ssList(esk23_0)
    | ~ ssList(X1)
    | ~ ssItem(esk25_0)
    | ~ ssList(esk6_2(X1,esk25_0)) ),
    inference(spm,[status(thm)],[12235,7749,theory(equality)]) ).

cnf(12256,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(cons(esk25_0,esk6_2(X1,esk25_0)))
    | ~ ssList(X2)
    | $false
    | ~ ssList(X1)
    | ~ ssItem(esk25_0)
    | ~ ssList(esk6_2(X1,esk25_0)) ),
    inference(rw,[status(thm)],[12243,337,theory(equality)]) ).

cnf(12257,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(cons(esk25_0,esk6_2(X1,esk25_0)))
    | ~ ssList(X2)
    | $false
    | ~ ssList(X1)
    | $false
    | ~ ssList(esk6_2(X1,esk25_0)) ),
    inference(rw,[status(thm)],[12256,2217,theory(equality)]) ).

cnf(12258,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(cons(esk25_0,esk6_2(X1,esk25_0)))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(esk6_2(X1,esk25_0)) ),
    inference(cn,[status(thm)],[12257,theory(equality)]) ).

cnf(638646,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(esk6_2(X1,esk25_0))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[12258,2659]) ).

cnf(638647,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssItem(esk25_0) ),
    inference(spm,[status(thm)],[638646,159,theory(equality)]) ).

cnf(638648,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[638647,2217,theory(equality)]) ).

cnf(638649,negated_conjecture,
    ( segmentP(app(X1,X2),esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[638648,theory(equality)]) ).

cnf(638662,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[638649,88,theory(equality)]) ).

cnf(638885,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | ~ memberP(X1,esk25_0)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[638662,239,theory(equality)]) ).

cnf(638886,negated_conjecture,
    ( segmentP(X1,esk23_0)
    | ~ memberP(X1,esk25_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[638885,theory(equality)]) ).

cnf(639701,negated_conjecture,
    ( ~ memberP(esk24_0,esk25_0)
    | ~ ssList(esk24_0) ),
    inference(spm,[status(thm)],[2234,638886,theory(equality)]) ).

cnf(639809,negated_conjecture,
    ( $false
    | ~ ssList(esk24_0) ),
    inference(rw,[status(thm)],[639701,2218,theory(equality)]) ).

cnf(639810,negated_conjecture,
    ( $false
    | $false ),
    inference(rw,[status(thm)],[639809,325,theory(equality)]) ).

cnf(639811,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[639810,theory(equality)]) ).

cnf(639812,negated_conjecture,
    $false,
    639811,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC335+1.p
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOqimKA/sel_SWC335+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpOqimKA/sel_SWC335+1.p_2 with time limit 80
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOqimKA/sel_SWC335+1.p_3 with time limit 75
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpOqimKA/sel_SWC335+1.p_4 with time limit 55
% -prover status ResourceOut
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpOqimKA/sel_SWC335+1.p_5 with time limit 54
% -prover status Theorem
% Problem SWC335+1.p solved in phase 4.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC335+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC335+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
% 
%------------------------------------------------------------------------------