TSTP Solution File: SWC015+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC015+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 10:05:34 EST 2010

% Result   : Theorem 88.84s
% Output   : CNFRefutation 88.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   49
%            Number of leaves      :   20
% Syntax   : Number of formulae    :  240 (  15 unt;   0 def)
%            Number of atoms       : 1003 ( 405 equ)
%            Maximal formula atoms :   34 (   4 avg)
%            Number of connectives : 1308 ( 545   ~; 623   |;  87   &)
%                                         (   2 <=>;  51  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :  359 (   0 sgn 167   !;  20   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil != X1
           => tl(app(X1,X2)) = app(tl(X1),X2) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax86) ).

fof(3,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax84) ).

fof(4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax83) ).

fof(5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax82) ).

fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax81) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax28) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => tl(cons(X2,X1)) = X1 ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax25) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssList(tl(X1)) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax24) ).

fof(11,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax27) ).

fof(12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax26) ).

fof(13,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => nil != cons(X2,X1) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax21) ).

fof(15,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => hd(cons(X2,X1)) = X2 ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax23) ).

fof(16,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => ssItem(hd(X1)) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax22) ).

fof(22,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil != X1
       => cons(hd(X1),tl(X1)) = X1 ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax78) ).

fof(23,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X3,X2) = app(X1,X2)
               => X3 = X1 ) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax79) ).

fof(24,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( neq(X1,X2)
          <=> X1 != X2 ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax15) ).

fof(25,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax16) ).

fof(26,axiom,
    ssList(nil),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax17) ).

fof(27,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) != X1 ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',ax18) ).

fof(29,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ? [X5] :
                            ( ssList(X5)
                            & X4 != X5
                            & ? [X6] :
                                ( ssList(X6)
                                & tl(X4) = X6
                                & app(X3,X6) = X5
                                & neq(nil,X4) ) )
                        | ? [X7] :
                            ( ssItem(X7)
                            & ? [X8] :
                                ( ssList(X8)
                                & cons(X7,nil) = X1
                                & app(cons(X7,nil),X8) = X2 ) ) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpsLcjbr/sel_SWC015+1.p_2',co1) ).

fof(30,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X4 != X5
                              & ? [X6] :
                                  ( ssList(X6)
                                  & tl(X4) = X6
                                  & app(X3,X6) = X5
                                  & neq(nil,X4) ) )
                          | ? [X7] :
                              ( ssItem(X7)
                              & ? [X8] :
                                  ( ssList(X8)
                                  & cons(X7,nil) = X1
                                  & app(cons(X7,nil),X8) = X2 ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[29]) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssList(X5)
                              & X4 != X5
                              & ? [X6] :
                                  ( ssList(X6)
                                  & tl(X4) = X6
                                  & app(X3,X6) = X5
                                  & neq(nil,X4) ) )
                          | ? [X7] :
                              ( ssItem(X7)
                              & ? [X8] :
                                  ( ssList(X8)
                                  & cons(X7,nil) = X1
                                  & app(cons(X7,nil),X8) = X2 ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[30,theory(equality)]) ).

fof(32,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | nil = X1
          | tl(app(X1,X2)) = app(tl(X1),X2) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(33,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | nil = X3
          | tl(app(X3,X4)) = app(tl(X3),X4) ) ),
    inference(variable_rename,[status(thm)],[32]) ).

fof(34,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | nil = X3
      | tl(app(X3,X4)) = app(tl(X3),X4)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[33]) ).

cnf(35,plain,
    ( tl(app(X1,X2)) = app(tl(X1),X2)
    | nil = X1
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(40,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(X1,nil) = X1 ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(41,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[40]) ).

cnf(42,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(43,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)],[4]) ).

fof(44,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)],[43]) ).

fof(45,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)],[44]) ).

fof(46,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)],[45]) ).

cnf(47,plain,
    ( nil = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X1
    | nil != X2 ),
    inference(split_conjunct,[status(thm)],[46]) ).

cnf(48,plain,
    ( nil = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(50,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)],[5]) ).

fof(51,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)],[50]) ).

fof(52,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)],[51]) ).

cnf(53,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[52]) ).

fof(54,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(55,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[54]) ).

fof(56,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[55]) ).

cnf(57,plain,
    ( cons(X2,X1) = app(cons(X2,nil),X1)
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[56]) ).

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

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

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

fof(65,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | tl(cons(X2,X1)) = X1 ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(66,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | tl(cons(X4,X3)) = X3 ) ),
    inference(variable_rename,[status(thm)],[65]) ).

fof(67,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | tl(cons(X4,X3)) = X3
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[66]) ).

cnf(68,plain,
    ( tl(cons(X2,X1)) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[67]) ).

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

fof(70,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | ssList(tl(X2)) ),
    inference(variable_rename,[status(thm)],[69]) ).

cnf(71,plain,
    ( ssList(tl(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(72,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)],[11]) ).

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

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

cnf(75,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[74]) ).

fof(76,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(77,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[76]) ).

fof(78,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[77]) ).

cnf(79,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[78]) ).

fof(80,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | nil != cons(X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[13]) ).

fof(81,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | nil != cons(X4,X3) ) ),
    inference(variable_rename,[status(thm)],[80]) ).

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

cnf(83,plain,
    ( ~ ssList(X1)
    | nil != cons(X2,X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[82]) ).

fof(91,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | hd(cons(X2,X1)) = X2 ) ),
    inference(fof_nnf,[status(thm)],[15]) ).

fof(92,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | hd(cons(X4,X3)) = X4 ) ),
    inference(variable_rename,[status(thm)],[91]) ).

fof(93,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | hd(cons(X4,X3)) = X4
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[92]) ).

cnf(94,plain,
    ( hd(cons(X2,X1)) = X2
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[93]) ).

fof(95,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ssItem(hd(X1)) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(96,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | ssItem(hd(X2)) ),
    inference(variable_rename,[status(thm)],[95]) ).

cnf(97,plain,
    ( ssItem(hd(X1))
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[96]) ).

fof(125,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | cons(hd(X1),tl(X1)) = X1 ),
    inference(fof_nnf,[status(thm)],[22]) ).

fof(126,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | nil = X2
      | cons(hd(X2),tl(X2)) = X2 ),
    inference(variable_rename,[status(thm)],[125]) ).

cnf(127,plain,
    ( cons(hd(X1),tl(X1)) = X1
    | nil = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[126]) ).

fof(128,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | app(X3,X2) != app(X1,X2)
              | X3 = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(129,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | app(X6,X5) != app(X4,X5)
              | X6 = X4 ) ) ),
    inference(variable_rename,[status(thm)],[128]) ).

fof(130,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | app(X6,X5) != app(X4,X5)
      | X6 = X4
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[129]) ).

cnf(131,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X3,X2) != app(X1,X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[130]) ).

fof(132,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ( ( ~ neq(X1,X2)
              | X1 != X2 )
            & ( X1 = X2
              | neq(X1,X2) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(133,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ( ( ~ neq(X3,X4)
              | X3 != X4 )
            & ( X3 = X4
              | neq(X3,X4) ) ) ) ),
    inference(variable_rename,[status(thm)],[132]) ).

fof(134,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ( ( ~ neq(X3,X4)
          | X3 != X4 )
        & ( X3 = X4
          | neq(X3,X4) ) )
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[133]) ).

fof(135,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)],[134]) ).

cnf(136,plain,
    ( neq(X1,X2)
    | X1 = X2
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

cnf(137,plain,
    ( ~ ssList(X1)
    | ~ ssList(X2)
    | X1 != X2
    | ~ neq(X1,X2) ),
    inference(split_conjunct,[status(thm)],[135]) ).

fof(138,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[25]) ).

fof(139,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[138]) ).

fof(140,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[139]) ).

cnf(141,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[140]) ).

cnf(142,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[26]) ).

fof(143,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) != X1 ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(144,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) != X3 ) ),
    inference(variable_rename,[status(thm)],[143]) ).

fof(145,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) != X3
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[144]) ).

cnf(146,plain,
    ( ~ ssList(X1)
    | cons(X2,X1) != X1
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[145]) ).

fof(153,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & ! [X5] :
                          ( ~ ssList(X5)
                          | X4 = X5
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | tl(X4) != X6
                              | app(X3,X6) != X5
                              | ~ neq(nil,X4) ) )
                      & ! [X7] :
                          ( ~ ssItem(X7)
                          | ! [X8] :
                              ( ~ ssList(X8)
                              | cons(X7,nil) != X1
                              | app(cons(X7,nil),X8) != X2 ) ) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(154,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & ( ( neq(X10,nil)
                      & ! [X13] :
                          ( ~ ssList(X13)
                          | X12 = X13
                          | ! [X14] :
                              ( ~ ssList(X14)
                              | tl(X12) != X14
                              | app(X11,X14) != X13
                              | ~ neq(nil,X12) ) )
                      & ! [X15] :
                          ( ~ ssItem(X15)
                          | ! [X16] :
                              ( ~ ssList(X16)
                              | cons(X15,nil) != X9
                              | app(cons(X15,nil),X16) != X10 ) ) )
                    | ( neq(X10,nil)
                      & ~ neq(X12,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[153]) ).

fof(155,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ( ( neq(esk8_0,nil)
        & ! [X13] :
            ( ~ ssList(X13)
            | esk10_0 = X13
            | ! [X14] :
                ( ~ ssList(X14)
                | tl(esk10_0) != X14
                | app(esk9_0,X14) != X13
                | ~ neq(nil,esk10_0) ) )
        & ! [X15] :
            ( ~ ssItem(X15)
            | ! [X16] :
                ( ~ ssList(X16)
                | cons(X15,nil) != esk7_0
                | app(cons(X15,nil),X16) != esk8_0 ) ) )
      | ( neq(esk8_0,nil)
        & ~ neq(esk10_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[154]) ).

fof(156,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ( ( ( ~ ssList(X16)
            | cons(X15,nil) != esk7_0
            | app(cons(X15,nil),X16) != esk8_0
            | ~ ssItem(X15) )
          & ( ~ ssList(X14)
            | tl(esk10_0) != X14
            | app(esk9_0,X14) != X13
            | ~ neq(nil,esk10_0)
            | ~ ssList(X13)
            | esk10_0 = X13 )
          & neq(esk8_0,nil) )
        | ( neq(esk8_0,nil)
          & ~ neq(esk10_0,nil) ) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[155]) ).

fof(157,negated_conjecture,
    ! [X13,X14,X15,X16] :
      ( ( neq(esk8_0,nil)
        | ~ ssList(X16)
        | cons(X15,nil) != esk7_0
        | app(cons(X15,nil),X16) != esk8_0
        | ~ ssItem(X15) )
      & ( ~ neq(esk10_0,nil)
        | ~ ssList(X16)
        | cons(X15,nil) != esk7_0
        | app(cons(X15,nil),X16) != esk8_0
        | ~ ssItem(X15) )
      & ( neq(esk8_0,nil)
        | ~ ssList(X14)
        | tl(esk10_0) != X14
        | app(esk9_0,X14) != X13
        | ~ neq(nil,esk10_0)
        | ~ ssList(X13)
        | esk10_0 = X13 )
      & ( ~ neq(esk10_0,nil)
        | ~ ssList(X14)
        | tl(esk10_0) != X14
        | app(esk9_0,X14) != X13
        | ~ neq(nil,esk10_0)
        | ~ ssList(X13)
        | esk10_0 = X13 )
      & ( neq(esk8_0,nil)
        | neq(esk8_0,nil) )
      & ( ~ neq(esk10_0,nil)
        | neq(esk8_0,nil) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[156]) ).

cnf(158,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(159,negated_conjecture,
    ssList(esk8_0),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(162,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(163,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(165,negated_conjecture,
    ( neq(esk8_0,nil)
    | neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(166,negated_conjecture,
    ( esk10_0 = X1
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | app(esk9_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(168,negated_conjecture,
    ( ~ ssItem(X1)
    | app(cons(X1,nil),X2) != esk8_0
    | cons(X1,nil) != esk7_0
    | ~ ssList(X2)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[157]) ).

cnf(172,negated_conjecture,
    ssList(esk10_0),
    inference(rw,[status(thm)],[159,163,theory(equality)]) ).

cnf(173,negated_conjecture,
    neq(esk10_0,nil),
    inference(rw,[status(thm)],[165,163,theory(equality)]) ).

cnf(186,plain,
    ( ~ neq(X1,X1)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[137,theory(equality)]) ).

cnf(199,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | nil = cons(X1,X2)
    | ~ ssList(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[127,94,theory(equality)]) ).

cnf(200,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[47,theory(equality)]) ).

cnf(201,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[200,142,theory(equality)]) ).

cnf(202,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[201,theory(equality)]) ).

cnf(231,plain,
    ( cons(X1,nil) = X2
    | cons(X1,X3) != app(X2,X3)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[131,57,theory(equality)]) ).

cnf(242,plain,
    ( nil = app(X1,X2)
    | ssList(app(tl(X1),X2))
    | nil = X1
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[71,35,theory(equality)]) ).

cnf(244,plain,
    ( tl(cons(X1,X2)) = app(tl(cons(X1,nil)),X2)
    | nil = cons(X1,nil)
    | ~ ssList(X2)
    | ~ ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[35,57,theory(equality)]) ).

cnf(269,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[42,53,theory(equality)]) ).

cnf(271,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[53,64,theory(equality)]) ).

cnf(284,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[269,142,theory(equality)]) ).

cnf(285,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[284,theory(equality)]) ).

cnf(288,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[271,142,theory(equality)]) ).

cnf(289,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[288,theory(equality)]) ).

cnf(292,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssItem(X1)
    | ~ ssList(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[141,75,theory(equality)]) ).

cnf(294,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssItem(X1)
    | ~ ssList(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[83,75,theory(equality)]) ).

cnf(295,plain,
    ( app(cons(X1,X2),X3) != app(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[146,75,theory(equality)]) ).

cnf(307,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[166,162,theory(equality)]) ).

cnf(308,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0)
    | $false ),
    inference(rw,[status(thm)],[307,173,theory(equality)]) ).

cnf(309,negated_conjecture,
    ( esk10_0 = X1
    | tl(esk10_0) != X2
    | app(esk7_0,X2) != X1
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ neq(nil,esk10_0) ),
    inference(cn,[status(thm)],[308,theory(equality)]) ).

cnf(310,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(esk7_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(esk10_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[309,136,theory(equality)]) ).

cnf(312,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(esk7_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(esk10_0)
    | $false ),
    inference(rw,[status(thm)],[310,142,theory(equality)]) ).

cnf(313,negated_conjecture,
    ( esk10_0 = X1
    | nil = esk10_0
    | app(esk7_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(esk10_0) ),
    inference(cn,[status(thm)],[312,theory(equality)]) ).

cnf(314,negated_conjecture,
    ( cons(X1,nil) != esk7_0
    | app(cons(X1,nil),X2) != esk10_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[168,163,theory(equality)]) ).

cnf(315,negated_conjecture,
    ( cons(X1,nil) != esk7_0
    | app(cons(X1,nil),X2) != esk10_0
    | ~ ssList(X2)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[314,173,theory(equality)]) ).

cnf(316,negated_conjecture,
    ( cons(X1,nil) != esk7_0
    | app(cons(X1,nil),X2) != esk10_0
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[315,theory(equality)]) ).

cnf(330,plain,
    ( app(nil,nil) = nil
    | ~ ssList(nil) ),
    inference(er,[status(thm)],[202,theory(equality)]) ).

cnf(331,plain,
    ( app(nil,nil) = nil
    | $false ),
    inference(rw,[status(thm)],[330,142,theory(equality)]) ).

cnf(332,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[331,theory(equality)]) ).

cnf(339,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[75,332,theory(equality)]) ).

cnf(353,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[339,142,theory(equality)]) ).

cnf(354,plain,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[353,theory(equality)]) ).

cnf(425,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | cons(X1,X2) = nil
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[199,141]) ).

cnf(426,plain,
    ( cons(X1,tl(cons(X1,X2))) = cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[425,83]) ).

cnf(518,plain,
    ( app(cons(X1,X2),X3) != nil
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[294,79]) ).

cnf(526,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[518,354,theory(equality)]) ).

cnf(531,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[526,142,theory(equality)]) ).

cnf(532,plain,
    ( cons(X1,nil) != nil
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[531,theory(equality)]) ).

cnf(580,plain,
    ( app(cons(X1,X2),X3) != app(X2,X3)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[295,79]) ).

cnf(583,plain,
    ( cons(X1,X2) != app(nil,X2)
    | ~ ssItem(X1)
    | ~ ssList(nil)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[580,57,theory(equality)]) ).

cnf(591,plain,
    ( cons(X1,X2) != app(nil,X2)
    | ~ ssItem(X1)
    | $false
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[583,142,theory(equality)]) ).

cnf(592,plain,
    ( cons(X1,X2) != app(nil,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[591,theory(equality)]) ).

cnf(621,plain,
    ( cons(X1,X2) != app(nil,tl(cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(tl(cons(X1,X2)))
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[592,426,theory(equality)]) ).

cnf(795,plain,
    ( cons(hd(X1),nil) = X2
    | nil = X1
    | X1 != app(X2,tl(X1))
    | ~ ssItem(hd(X1))
    | ~ ssList(cons(hd(X1),nil))
    | ~ ssList(X2)
    | ~ ssList(tl(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[231,127,theory(equality)]) ).

cnf(888,plain,
    ( app(X1,X2) = nil
    | nil = X1
    | ssList(app(tl(X1),X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[242,79]) ).

cnf(889,plain,
    ( nil = X1
    | ssList(app(tl(X1),X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[888,48]) ).

cnf(993,plain,
    ( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(cons(X1,nil))
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[244,532]) ).

cnf(994,plain,
    ( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[993,141,theory(equality)]) ).

cnf(996,plain,
    ( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false ),
    inference(rw,[status(thm)],[994,142,theory(equality)]) ).

cnf(997,plain,
    ( app(tl(cons(X1,nil)),X2) = tl(cons(X1,X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[996,theory(equality)]) ).

cnf(1000,plain,
    ( ssList(tl(cons(X1,X2)))
    | ~ ssList(X2)
    | ~ ssList(tl(cons(X1,nil)))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[79,997,theory(equality)]) ).

cnf(1099,plain,
    ( ssList(tl(cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(nil)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[1000,68,theory(equality)]) ).

cnf(1102,plain,
    ( ssList(tl(cons(X1,X2)))
    | ~ ssItem(X1)
    | $false
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[1099,142,theory(equality)]) ).

cnf(1103,plain,
    ( ssList(tl(cons(X1,X2)))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[1102,theory(equality)]) ).

cnf(1964,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[285,79]) ).

cnf(1990,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[289,1964,theory(equality)]) ).

cnf(2026,plain,
    ( app(nil,X1) = app(X1,nil)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1990,142,theory(equality)]) ).

cnf(2027,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2026,theory(equality)]) ).

cnf(2083,plain,
    ( tl(app(nil,X1)) = app(tl(X1),nil)
    | nil = X1
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[35,2027,theory(equality)]) ).

cnf(2180,plain,
    ( tl(app(nil,X1)) = app(tl(X1),nil)
    | nil = X1
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2083,142,theory(equality)]) ).

cnf(2181,plain,
    ( tl(app(nil,X1)) = app(tl(X1),nil)
    | nil = X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2180,theory(equality)]) ).

cnf(3808,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[292,79]) ).

cnf(3816,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[3808,354,theory(equality)]) ).

cnf(3837,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[3816,142,theory(equality)]) ).

cnf(3838,plain,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[3837,theory(equality)]) ).

cnf(4703,negated_conjecture,
    ( esk10_0 = X1
    | esk10_0 = nil
    | app(esk7_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[313,172,theory(equality)]) ).

cnf(4704,negated_conjecture,
    ( esk10_0 = X1
    | esk10_0 = nil
    | app(esk7_0,X2) != X1
    | tl(esk10_0) != X2
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[4703,theory(equality)]) ).

cnf(4705,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(esk7_0,tl(esk10_0)) != X1
    | ~ ssList(tl(esk10_0))
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[4704,theory(equality)]) ).

cnf(5863,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(esk7_0,tl(esk10_0)) != X1
    | ~ ssList(X1)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[4705,71,theory(equality)]) ).

cnf(5864,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(esk7_0,tl(esk10_0)) != X1
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[5863,172,theory(equality)]) ).

cnf(5865,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = X1
    | app(esk7_0,tl(esk10_0)) != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[5864,theory(equality)]) ).

cnf(5866,negated_conjecture,
    ( esk10_0 = nil
    | esk10_0 = app(esk7_0,tl(esk10_0))
    | ~ ssList(app(esk7_0,tl(esk10_0))) ),
    inference(er,[status(thm)],[5865,theory(equality)]) ).

cnf(6039,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0))
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[5866,79,theory(equality)]) ).

cnf(6040,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[6039,158,theory(equality)]) ).

cnf(6041,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0)) ),
    inference(cn,[status(thm)],[6040,theory(equality)]) ).

cnf(6042,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[6041,71,theory(equality)]) ).

cnf(6043,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[6042,172,theory(equality)]) ).

cnf(6044,negated_conjecture,
    ( app(esk7_0,tl(esk10_0)) = esk10_0
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[6043,theory(equality)]) ).

cnf(6058,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0))
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[289,6044,theory(equality)]) ).

cnf(6101,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[6058,158,theory(equality)]) ).

cnf(6102,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(tl(esk10_0)) ),
    inference(cn,[status(thm)],[6101,theory(equality)]) ).

cnf(6131,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[6102,71,theory(equality)]) ).

cnf(6132,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[6131,172,theory(equality)]) ).

cnf(6133,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[6132,theory(equality)]) ).

cnf(6174,negated_conjecture,
    ( tl(esk10_0) = app(tl(esk10_0),nil)
    | nil = esk10_0
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[2181,6133,theory(equality)]) ).

cnf(6261,negated_conjecture,
    ( tl(esk10_0) = app(tl(esk10_0),nil)
    | nil = esk10_0
    | $false ),
    inference(rw,[status(thm)],[6174,172,theory(equality)]) ).

cnf(6262,negated_conjecture,
    ( tl(esk10_0) = app(tl(esk10_0),nil)
    | nil = esk10_0 ),
    inference(cn,[status(thm)],[6261,theory(equality)]) ).

cnf(6591,negated_conjecture,
    ( nil = esk10_0
    | ssList(tl(esk10_0))
    | ~ ssList(nil)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[889,6262,theory(equality)]) ).

cnf(6647,negated_conjecture,
    ( nil = esk10_0
    | ssList(tl(esk10_0))
    | $false
    | ~ ssList(esk10_0) ),
    inference(rw,[status(thm)],[6591,142,theory(equality)]) ).

cnf(6648,negated_conjecture,
    ( nil = esk10_0
    | ssList(tl(esk10_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[6647,172,theory(equality)]) ).

cnf(6649,negated_conjecture,
    ( nil = esk10_0
    | ssList(tl(esk10_0)) ),
    inference(cn,[status(thm)],[6648,theory(equality)]) ).

cnf(10981,plain,
    ( app(nil,tl(cons(X1,X2))) != cons(X1,X2)
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[621,1103]) ).

cnf(20366,plain,
    ( cons(hd(X1),nil) = X2
    | nil = X1
    | app(X2,tl(X1)) != X1
    | ~ ssItem(hd(X1))
    | ~ ssList(cons(hd(X1),nil))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[795,71]) ).

cnf(20367,plain,
    ( cons(hd(X1),nil) = X2
    | nil = X1
    | app(X2,tl(X1)) != X1
    | ~ ssItem(hd(X1))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[20366,3838]) ).

cnf(20368,plain,
    ( cons(hd(X1),nil) = X2
    | nil = X1
    | app(X2,tl(X1)) != X1
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[20367,97]) ).

cnf(20386,negated_conjecture,
    ( cons(hd(esk10_0),nil) = esk7_0
    | nil = esk10_0
    | ~ ssList(esk7_0)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[20368,6044,theory(equality)]) ).

cnf(20402,negated_conjecture,
    ( cons(hd(esk10_0),nil) = esk7_0
    | nil = esk10_0
    | $false
    | ~ ssList(esk10_0) ),
    inference(rw,[status(thm)],[20386,158,theory(equality)]) ).

cnf(20403,negated_conjecture,
    ( cons(hd(esk10_0),nil) = esk7_0
    | nil = esk10_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[20402,172,theory(equality)]) ).

cnf(20404,negated_conjecture,
    ( cons(hd(esk10_0),nil) = esk7_0
    | nil = esk10_0 ),
    inference(cn,[status(thm)],[20403,theory(equality)]) ).

cnf(20428,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[68,20404,theory(equality)]) ).

cnf(20431,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[94,20404,theory(equality)]) ).

cnf(20437,negated_conjecture,
    ( esk10_0 = nil
    | app(esk7_0,X1) != esk10_0
    | ~ ssItem(hd(esk10_0))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[316,20404,theory(equality)]) ).

cnf(20497,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0
    | ~ ssItem(hd(esk10_0))
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[10981,20404,theory(equality)]) ).

cnf(20522,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[20428,142,theory(equality)]) ).

cnf(20523,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0)) ),
    inference(cn,[status(thm)],[20522,theory(equality)]) ).

cnf(20528,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[20431,142,theory(equality)]) ).

cnf(20529,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil
    | ~ ssItem(hd(esk10_0)) ),
    inference(cn,[status(thm)],[20528,theory(equality)]) ).

cnf(20630,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0
    | ~ ssItem(hd(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[20497,142,theory(equality)]) ).

cnf(20631,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0
    | ~ ssItem(hd(esk10_0)) ),
    inference(cn,[status(thm)],[20630,theory(equality)]) ).

cnf(20783,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[20523,97,theory(equality)]) ).

cnf(20784,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[20783,172,theory(equality)]) ).

cnf(20785,negated_conjecture,
    ( tl(esk7_0) = nil
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[20784,theory(equality)]) ).

cnf(21647,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[20631,97,theory(equality)]) ).

cnf(21648,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0
    | $false ),
    inference(rw,[status(thm)],[21647,172,theory(equality)]) ).

cnf(21649,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,tl(esk7_0)) != esk7_0 ),
    inference(cn,[status(thm)],[21648,theory(equality)]) ).

cnf(21654,negated_conjecture,
    ( esk10_0 = nil
    | app(nil,nil) != esk7_0 ),
    inference(spm,[status(thm)],[21649,20785,theory(equality)]) ).

cnf(21657,negated_conjecture,
    ( esk10_0 = nil
    | nil != esk7_0 ),
    inference(rw,[status(thm)],[21654,332,theory(equality)]) ).

cnf(22737,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[20529,97,theory(equality)]) ).

cnf(22738,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[22737,172,theory(equality)]) ).

cnf(22739,negated_conjecture,
    ( hd(esk7_0) = hd(esk10_0)
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[22738,theory(equality)]) ).

cnf(22749,negated_conjecture,
    ( nil = esk7_0
    | ssItem(hd(esk10_0))
    | esk10_0 = nil
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[97,22739,theory(equality)]) ).

cnf(22759,negated_conjecture,
    ( nil = esk7_0
    | ssItem(hd(esk10_0))
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[22749,158,theory(equality)]) ).

cnf(22760,negated_conjecture,
    ( nil = esk7_0
    | ssItem(hd(esk10_0))
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[22759,theory(equality)]) ).

cnf(22775,negated_conjecture,
    ( esk10_0 = nil
    | ssItem(hd(esk10_0)) ),
    inference(csr,[status(thm)],[22760,21657]) ).

cnf(921402,negated_conjecture,
    ( esk10_0 = nil
    | app(esk7_0,X1) != esk10_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[20437,22775]) ).

cnf(921407,negated_conjecture,
    ( esk10_0 = nil
    | ~ ssList(tl(esk10_0)) ),
    inference(spm,[status(thm)],[921402,6044,theory(equality)]) ).

cnf(921486,negated_conjecture,
    esk10_0 = nil,
    inference(csr,[status(thm)],[921407,6649]) ).

cnf(921489,negated_conjecture,
    neq(nil,nil),
    inference(rw,[status(thm)],[173,921486,theory(equality)]) ).

cnf(923816,negated_conjecture,
    ~ ssList(nil),
    inference(spm,[status(thm)],[186,921489,theory(equality)]) ).

cnf(923818,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[923816,142,theory(equality)]) ).

cnf(923819,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[923818,theory(equality)]) ).

cnf(923820,negated_conjecture,
    $false,
    923819,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC015+1.p
% --creating new selector for [SWC001+0.ax]
% eprover: CPU time limit exceeded, terminating
% -running prover on /tmp/tmpsLcjbr/sel_SWC015+1.p_1 with time limit 29
% -prover status ResourceOut
% -running prover on /tmp/tmpsLcjbr/sel_SWC015+1.p_2 with time limit 81
% -prover status Theorem
% Problem SWC015+1.p solved in phase 1.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC015+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC015+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
% 
%------------------------------------------------------------------------------