TSTP Solution File: SWC409+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC409+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art11.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 3.00GHz @ 3000MHz
% Memory   : 2006MB
% OS       : Linux 2.6.31.5-127.fc12.i686.PAE
% CPULimit : 300s
% DateTime : Sun Dec 26 11:49:21 EST 2010

% Result   : Theorem 0.95s
% Output   : CNFRefutation 0.95s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   46
%            Number of leaves      :   14
% Syntax   : Number of formulae    :  207 (  24 unt;   0 def)
%            Number of atoms       :  873 ( 238 equ)
%            Maximal formula atoms :   18 (   4 avg)
%            Number of connectives : 1095 ( 429   ~; 519   |; 104   &)
%                                         (   4 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   6 con; 0-2 aty)
%            Number of variables   :  279 (   0 sgn 136   !;  28   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ( memberP(X1,X2)
          <=> ? [X3] :
                ( ssList(X3)
                & ? [X4] :
                    ( ssList(X4)
                    & app(X3,cons(X2,X4)) = X1 ) ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax3) ).

fof(3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax26) ).

fof(6,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax84) ).

fof(7,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax83) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax82) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax81) ).

fof(10,axiom,
    ! [X1] :
      ( ssList(X1)
     => ( nil = X1
        | ? [X2] :
            ( ssList(X2)
            & ? [X3] :
                ( ssItem(X3)
                & cons(X3,X2) = X1 ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax20) ).

fof(11,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax38) ).

fof(12,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax16) ).

fof(13,axiom,
    ssList(nil),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax17) ).

fof(14,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(app(X2,X3),X1)
              <=> ( memberP(X2,X1)
                  | memberP(X3,X1) ) ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax36) ).

fof(15,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax28) ).

fof(20,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',ax37) ).

fof(21,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & app(X6,cons(X5,nil)) != X3
                            & app(cons(X5,nil),X6) = X4 ) )
                    | ! [X7] :
                        ( ssItem(X7)
                       => ( ~ memberP(X2,X7)
                          | memberP(X1,X7) ) )
                    | ( nil != X3
                      & nil = X4 ) ) ) ) ) ),
    file('/tmp/tmpekl4Yt/sel_SWC409+1.p_1',co1) ).

fof(22,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & app(X6,cons(X5,nil)) != X3
                              & app(cons(X5,nil),X6) = X4 ) )
                      | ! [X7] :
                          ( ssItem(X7)
                         => ( ~ memberP(X2,X7)
                            | memberP(X1,X7) ) )
                      | ( nil != X3
                        & nil = X4 ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[21]) ).

fof(23,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[11,theory(equality)]) ).

fof(24,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & app(X6,cons(X5,nil)) != X3
                              & app(cons(X5,nil),X6) = X4 ) )
                      | ! [X7] :
                          ( ssItem(X7)
                         => ( ~ memberP(X2,X7)
                            | memberP(X1,X7) ) )
                      | ( nil != X3
                        & nil = X4 ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[22,theory(equality)]) ).

fof(30,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)],[2]) ).

fof(31,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)],[30]) ).

fof(32,plain,
    ! [X5] :
      ( ~ ssList(X5)
      | ! [X6] :
          ( ~ ssItem(X6)
          | ( ( ~ memberP(X5,X6)
              | ( ssList(esk3_2(X5,X6))
                & ssList(esk4_2(X5,X6))
                & app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5 ) )
            & ( ! [X9] :
                  ( ~ ssList(X9)
                  | ! [X10] :
                      ( ~ ssList(X10)
                      | app(X9,cons(X6,X10)) != X5 ) )
              | memberP(X5,X6) ) ) ) ),
    inference(skolemize,[status(esa)],[31]) ).

fof(33,plain,
    ! [X5,X6,X9,X10] :
      ( ( ( ~ ssList(X10)
          | app(X9,cons(X6,X10)) != X5
          | ~ ssList(X9)
          | memberP(X5,X6) )
        & ( ~ memberP(X5,X6)
          | ( ssList(esk3_2(X5,X6))
            & ssList(esk4_2(X5,X6))
            & app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5 ) ) )
      | ~ ssItem(X6)
      | ~ ssList(X5) ),
    inference(shift_quantors,[status(thm)],[32]) ).

fof(34,plain,
    ! [X5,X6,X9,X10] :
      ( ( ~ ssList(X10)
        | app(X9,cons(X6,X10)) != X5
        | ~ ssList(X9)
        | memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( ssList(esk3_2(X5,X6))
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( ssList(esk4_2(X5,X6))
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) )
      & ( app(esk3_2(X5,X6),cons(X6,esk4_2(X5,X6))) = X5
        | ~ memberP(X5,X6)
        | ~ ssItem(X6)
        | ~ ssList(X5) ) ),
    inference(distribute,[status(thm)],[33]) ).

cnf(35,plain,
    ( app(esk3_2(X1,X2),cons(X2,esk4_2(X1,X2))) = X1
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(36,plain,
    ( ssList(esk4_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

cnf(37,plain,
    ( ssList(esk3_2(X1,X2))
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ memberP(X1,X2) ),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(39,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[3]) ).

fof(40,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[39]) ).

fof(41,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[40]) ).

cnf(42,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(51,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(X1,nil) = X1 ),
    inference(fof_nnf,[status(thm)],[6]) ).

fof(52,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[51]) ).

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

fof(54,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)],[7]) ).

fof(55,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)],[54]) ).

fof(56,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)],[55]) ).

fof(57,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)],[56]) ).

cnf(58,plain,
    ( nil = app(X1,X2)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != X1
    | nil != X2 ),
    inference(split_conjunct,[status(thm)],[57]) ).

fof(61,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)],[8]) ).

fof(62,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)],[61]) ).

fof(63,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)],[62]) ).

cnf(64,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[63]) ).

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

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

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

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

fof(69,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | nil = X1
      | ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssItem(X3)
              & cons(X3,X2) = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[10]) ).

fof(70,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ? [X5] :
          ( ssList(X5)
          & ? [X6] :
              ( ssItem(X6)
              & cons(X6,X5) = X4 ) ) ),
    inference(variable_rename,[status(thm)],[69]) ).

fof(71,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | nil = X4
      | ( ssList(esk5_1(X4))
        & ssItem(esk6_1(X4))
        & cons(esk6_1(X4),esk5_1(X4)) = X4 ) ),
    inference(skolemize,[status(esa)],[70]) ).

fof(72,plain,
    ! [X4] :
      ( ( ssList(esk5_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( ssItem(esk6_1(X4))
        | nil = X4
        | ~ ssList(X4) )
      & ( cons(esk6_1(X4),esk5_1(X4)) = X4
        | nil = X4
        | ~ ssList(X4) ) ),
    inference(distribute,[status(thm)],[71]) ).

cnf(73,plain,
    ( nil = X1
    | cons(esk6_1(X1),esk5_1(X1)) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(74,plain,
    ( nil = X1
    | ssItem(esk6_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[72]) ).

cnf(75,plain,
    ( nil = X1
    | ssList(esk5_1(X1))
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[72]) ).

fof(76,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ memberP(nil,X1) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(77,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[76]) ).

cnf(78,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[77]) ).

fof(79,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[12]) ).

fof(80,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[79]) ).

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

cnf(82,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[81]) ).

cnf(83,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[13]) ).

fof(84,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)],[14]) ).

fof(85,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)],[84]) ).

fof(86,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)],[85]) ).

fof(87,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)],[86]) ).

cnf(88,plain,
    ( memberP(app(X2,X3),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ memberP(X3,X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

cnf(89,plain,
    ( memberP(app(X2,X3),X1)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ memberP(X2,X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

fof(91,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[15]) ).

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

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

fof(112,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | ( ( ~ memberP(cons(X2,X3),X1)
                  | X1 = X2
                  | memberP(X3,X1) )
                & ( ( X1 != X2
                    & ~ memberP(X3,X1) )
                  | memberP(cons(X2,X3),X1) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[20]) ).

fof(113,plain,
    ! [X4] :
      ( ~ ssItem(X4)
      | ! [X5] :
          ( ~ ssItem(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | ( ( ~ memberP(cons(X5,X6),X4)
                  | X4 = X5
                  | memberP(X6,X4) )
                & ( ( X4 != X5
                    & ~ memberP(X6,X4) )
                  | memberP(cons(X5,X6),X4) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[112]) ).

fof(114,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | ( ( ~ memberP(cons(X5,X6),X4)
          | X4 = X5
          | memberP(X6,X4) )
        & ( ( X4 != X5
            & ~ memberP(X6,X4) )
          | memberP(cons(X5,X6),X4) ) )
      | ~ ssItem(X5)
      | ~ ssItem(X4) ),
    inference(shift_quantors,[status(thm)],[113]) ).

fof(115,plain,
    ! [X4,X5,X6] :
      ( ( ~ memberP(cons(X5,X6),X4)
        | X4 = X5
        | memberP(X6,X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) )
      & ( X4 != X5
        | memberP(cons(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) )
      & ( ~ memberP(X6,X4)
        | memberP(cons(X5,X6),X4)
        | ~ ssList(X6)
        | ~ ssItem(X5)
        | ~ ssItem(X4) ) ),
    inference(distribute,[status(thm)],[114]) ).

cnf(117,plain,
    ( memberP(cons(X2,X3),X1)
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | X1 != X2 ),
    inference(split_conjunct,[status(thm)],[115]) ).

cnf(118,plain,
    ( memberP(X3,X1)
    | X1 = X2
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ memberP(cons(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[115]) ).

fof(119,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | app(X6,cons(X5,nil)) = X3
                          | app(cons(X5,nil),X6) != X4 ) )
                  & ? [X7] :
                      ( ssItem(X7)
                      & memberP(X2,X7)
                      & ~ memberP(X1,X7) )
                  & ( nil = X3
                    | nil != X4 ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(120,negated_conjecture,
    ? [X8] :
      ( ssList(X8)
      & ? [X9] :
          ( ssList(X9)
          & ? [X10] :
              ( ssList(X10)
              & ? [X11] :
                  ( ssList(X11)
                  & X9 = X11
                  & X8 = X10
                  & ! [X12] :
                      ( ~ ssItem(X12)
                      | ! [X13] :
                          ( ~ ssList(X13)
                          | app(X13,cons(X12,nil)) = X10
                          | app(cons(X12,nil),X13) != X11 ) )
                  & ? [X14] :
                      ( ssItem(X14)
                      & memberP(X9,X14)
                      & ~ memberP(X8,X14) )
                  & ( nil = X10
                    | nil != X11 ) ) ) ) ),
    inference(variable_rename,[status(thm)],[119]) ).

fof(121,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ! [X12] :
        ( ~ ssItem(X12)
        | ! [X13] :
            ( ~ ssList(X13)
            | app(X13,cons(X12,nil)) = esk9_0
            | app(cons(X12,nil),X13) != esk10_0 ) )
    & ssItem(esk11_0)
    & memberP(esk8_0,esk11_0)
    & ~ memberP(esk7_0,esk11_0)
    & ( nil = esk9_0
      | nil != esk10_0 ) ),
    inference(skolemize,[status(esa)],[120]) ).

fof(122,negated_conjecture,
    ! [X12,X13] :
      ( ( ~ ssList(X13)
        | app(X13,cons(X12,nil)) = esk9_0
        | app(cons(X12,nil),X13) != esk10_0
        | ~ ssItem(X12) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssItem(esk11_0)
      & memberP(esk8_0,esk11_0)
      & ~ memberP(esk7_0,esk11_0)
      & ( nil = esk9_0
        | nil != esk10_0 )
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[121]) ).

cnf(124,negated_conjecture,
    ssList(esk8_0),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(128,negated_conjecture,
    ~ memberP(esk7_0,esk11_0),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(129,negated_conjecture,
    memberP(esk8_0,esk11_0),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(130,negated_conjecture,
    ssItem(esk11_0),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(131,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(132,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(133,negated_conjecture,
    ( app(X2,cons(X1,nil)) = esk9_0
    | ~ ssItem(X1)
    | app(cons(X1,nil),X2) != esk10_0
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[122]) ).

cnf(135,negated_conjecture,
    ssList(esk10_0),
    inference(rw,[status(thm)],[124,132,theory(equality)]) ).

cnf(136,negated_conjecture,
    memberP(esk10_0,esk11_0),
    inference(rw,[status(thm)],[129,132,theory(equality)]) ).

cnf(137,negated_conjecture,
    ~ memberP(esk9_0,esk11_0),
    inference(rw,[status(thm)],[128,131,theory(equality)]) ).

cnf(150,negated_conjecture,
    ( ssList(esk3_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[37,136,theory(equality)]) ).

cnf(151,negated_conjecture,
    ( ssList(esk3_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0)
    | $false ),
    inference(rw,[status(thm)],[150,130,theory(equality)]) ).

cnf(152,negated_conjecture,
    ( ssList(esk3_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0) ),
    inference(cn,[status(thm)],[151,theory(equality)]) ).

cnf(153,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(er,[status(thm)],[58,theory(equality)]) ).

cnf(154,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[153,83,theory(equality)]) ).

cnf(155,plain,
    ( app(X1,nil) = nil
    | nil != X1
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[154,theory(equality)]) ).

cnf(156,negated_conjecture,
    ( ssList(esk4_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[36,136,theory(equality)]) ).

cnf(157,negated_conjecture,
    ( ssList(esk4_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0)
    | $false ),
    inference(rw,[status(thm)],[156,130,theory(equality)]) ).

cnf(158,negated_conjecture,
    ( ssList(esk4_2(esk10_0,esk11_0))
    | ~ ssList(esk10_0) ),
    inference(cn,[status(thm)],[157,theory(equality)]) ).

cnf(159,plain,
    ( memberP(cons(X1,X2),X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(er,[status(thm)],[117,theory(equality)]) ).

cnf(169,negated_conjecture,
    ( memberP(app(X1,esk10_0),esk11_0)
    | ~ ssList(esk10_0)
    | ~ ssList(X1)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[88,136,theory(equality)]) ).

cnf(170,negated_conjecture,
    ( memberP(app(X1,esk10_0),esk11_0)
    | ~ ssList(esk10_0)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[169,130,theory(equality)]) ).

cnf(171,negated_conjecture,
    ( memberP(app(X1,esk10_0),esk11_0)
    | ~ ssList(esk10_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[170,theory(equality)]) ).

cnf(205,plain,
    ( X1 = esk6_1(X2)
    | memberP(esk5_1(X2),X1)
    | nil = X2
    | ~ memberP(X2,X1)
    | ~ ssList(esk5_1(X2))
    | ~ ssItem(esk6_1(X2))
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[118,73,theory(equality)]) ).

cnf(220,negated_conjecture,
    ( app(X1,cons(X2,nil)) = esk9_0
    | cons(X2,X1) != esk10_0
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(spm,[status(thm)],[133,68,theory(equality)]) ).

cnf(238,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(nil)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[53,64,theory(equality)]) ).

cnf(240,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[64,93,theory(equality)]) ).

cnf(241,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X3)
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[42,64,theory(equality)]) ).

cnf(253,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | $false
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[238,83,theory(equality)]) ).

cnf(254,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[253,theory(equality)]) ).

cnf(257,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[240,83,theory(equality)]) ).

cnf(258,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[257,theory(equality)]) ).

cnf(267,negated_conjecture,
    ( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
    | ~ ssList(esk10_0)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[35,136,theory(equality)]) ).

cnf(268,negated_conjecture,
    ( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
    | ~ ssList(esk10_0)
    | $false ),
    inference(rw,[status(thm)],[267,130,theory(equality)]) ).

cnf(269,negated_conjecture,
    ( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
    | ~ ssList(esk10_0) ),
    inference(cn,[status(thm)],[268,theory(equality)]) ).

cnf(284,negated_conjecture,
    ( ssList(esk3_2(esk10_0,esk11_0))
    | $false ),
    inference(rw,[status(thm)],[152,135,theory(equality)]) ).

cnf(285,negated_conjecture,
    ssList(esk3_2(esk10_0,esk11_0)),
    inference(cn,[status(thm)],[284,theory(equality)]) ).

cnf(286,negated_conjecture,
    ( ssList(esk4_2(esk10_0,esk11_0))
    | $false ),
    inference(rw,[status(thm)],[158,135,theory(equality)]) ).

cnf(287,negated_conjecture,
    ssList(esk4_2(esk10_0,esk11_0)),
    inference(cn,[status(thm)],[286,theory(equality)]) ).

cnf(288,plain,
    ( app(nil,nil) = nil
    | ~ ssList(nil) ),
    inference(er,[status(thm)],[155,theory(equality)]) ).

cnf(289,plain,
    ( app(nil,nil) = nil
    | $false ),
    inference(rw,[status(thm)],[288,83,theory(equality)]) ).

cnf(290,plain,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[289,theory(equality)]) ).

cnf(357,negated_conjecture,
    ( memberP(app(X1,esk10_0),esk11_0)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[171,135,theory(equality)]) ).

cnf(358,negated_conjecture,
    ( memberP(app(X1,esk10_0),esk11_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[357,theory(equality)]) ).

cnf(364,negated_conjecture,
    ( memberP(app(X1,app(X2,esk10_0)),esk11_0)
    | ~ ssList(app(X2,esk10_0))
    | ~ ssList(X1)
    | ~ ssItem(esk11_0)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[88,358,theory(equality)]) ).

cnf(381,negated_conjecture,
    ( memberP(app(X1,app(X2,esk10_0)),esk11_0)
    | ~ ssList(app(X2,esk10_0))
    | ~ ssList(X1)
    | $false
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[364,130,theory(equality)]) ).

cnf(382,negated_conjecture,
    ( memberP(app(X1,app(X2,esk10_0)),esk11_0)
    | ~ ssList(app(X2,esk10_0))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[381,theory(equality)]) ).

cnf(397,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(cons(X2,X3))
    | ~ ssList(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[88,159,theory(equality)]) ).

cnf(813,negated_conjecture,
    ( app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0
    | $false ),
    inference(rw,[status(thm)],[269,135,theory(equality)]) ).

cnf(814,negated_conjecture,
    app(esk3_2(esk10_0,esk11_0),cons(esk11_0,esk4_2(esk10_0,esk11_0))) = esk10_0,
    inference(cn,[status(thm)],[813,theory(equality)]) ).

cnf(928,plain,
    ( X1 = esk6_1(X2)
    | nil = X2
    | memberP(esk5_1(X2),X1)
    | ~ memberP(X2,X1)
    | ~ ssList(esk5_1(X2))
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[205,74]) ).

cnf(929,plain,
    ( X1 = esk6_1(X2)
    | nil = X2
    | memberP(esk5_1(X2),X1)
    | ~ memberP(X2,X1)
    | ~ ssList(X2)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[928,75]) ).

cnf(930,negated_conjecture,
    ( esk11_0 = esk6_1(esk10_0)
    | nil = esk10_0
    | memberP(esk5_1(esk10_0),esk11_0)
    | ~ ssList(esk10_0)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[929,136,theory(equality)]) ).

cnf(935,negated_conjecture,
    ( esk11_0 = esk6_1(esk10_0)
    | nil = esk10_0
    | memberP(esk5_1(esk10_0),esk11_0)
    | $false
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[930,135,theory(equality)]) ).

cnf(936,negated_conjecture,
    ( esk11_0 = esk6_1(esk10_0)
    | nil = esk10_0
    | memberP(esk5_1(esk10_0),esk11_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[935,130,theory(equality)]) ).

cnf(937,negated_conjecture,
    ( esk11_0 = esk6_1(esk10_0)
    | nil = esk10_0
    | memberP(esk5_1(esk10_0),esk11_0) ),
    inference(cn,[status(thm)],[936,theory(equality)]) ).

cnf(950,negated_conjecture,
    ( memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(X1)
    | ~ ssList(esk5_1(esk10_0))
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[89,937,theory(equality)]) ).

cnf(961,negated_conjecture,
    ( memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(X1)
    | ~ ssList(esk5_1(esk10_0))
    | $false ),
    inference(rw,[status(thm)],[950,130,theory(equality)]) ).

cnf(962,negated_conjecture,
    ( memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(X1)
    | ~ ssList(esk5_1(esk10_0)) ),
    inference(cn,[status(thm)],[961,theory(equality)]) ).

cnf(1053,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0)))
    | ~ ssList(esk3_2(esk10_0,esk11_0)) ),
    inference(spm,[status(thm)],[258,814,theory(equality)]) ).

cnf(1084,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0)))
    | $false ),
    inference(rw,[status(thm)],[1053,285,theory(equality)]) ).

cnf(1085,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | ~ ssList(cons(esk11_0,esk4_2(esk10_0,esk11_0))) ),
    inference(cn,[status(thm)],[1084,theory(equality)]) ).

cnf(1130,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | ~ ssList(esk4_2(esk10_0,esk11_0))
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[1085,82,theory(equality)]) ).

cnf(1131,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | $false
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[1130,287,theory(equality)]) ).

cnf(1132,negated_conjecture,
    ( app(nil,esk10_0) = esk10_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[1131,130,theory(equality)]) ).

cnf(1133,negated_conjecture,
    app(nil,esk10_0) = esk10_0,
    inference(cn,[status(thm)],[1132,theory(equality)]) ).

cnf(1142,negated_conjecture,
    ( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
    | ~ ssList(X1)
    | ~ ssList(esk10_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[64,1133,theory(equality)]) ).

cnf(1179,negated_conjecture,
    ( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
    | ~ ssList(X1)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[1142,135,theory(equality)]) ).

cnf(1180,negated_conjecture,
    ( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1179,83,theory(equality)]) ).

cnf(1181,negated_conjecture,
    ( app(esk10_0,X1) = app(nil,app(esk10_0,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1180,theory(equality)]) ).

cnf(1437,negated_conjecture,
    ( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
    | nil = X1
    | X1 != esk10_0
    | ~ ssList(esk5_1(X1))
    | ~ ssItem(esk6_1(X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[220,73,theory(equality)]) ).

cnf(1847,plain,
    ( app(X1,app(X2,nil)) = app(X1,X2)
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[254,42]) ).

cnf(1886,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[258,1847,theory(equality)]) ).

cnf(1926,plain,
    ( app(nil,X1) = app(X1,nil)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[1886,83,theory(equality)]) ).

cnf(1927,plain,
    ( app(nil,X1) = app(X1,nil)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1926,theory(equality)]) ).

cnf(2031,plain,
    ( ssList(app(X1,app(X2,X3)))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[241,42]) ).

cnf(2034,negated_conjecture,
    ( ssList(app(X1,esk10_0))
    | ~ ssList(esk10_0)
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[2031,1133,theory(equality)]) ).

cnf(2063,negated_conjecture,
    ( ssList(app(X1,esk10_0))
    | $false
    | ~ ssList(nil)
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2034,135,theory(equality)]) ).

cnf(2064,negated_conjecture,
    ( ssList(app(X1,esk10_0))
    | $false
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[2063,83,theory(equality)]) ).

cnf(2065,negated_conjecture,
    ( ssList(app(X1,esk10_0))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[2064,theory(equality)]) ).

cnf(4606,negated_conjecture,
    ( memberP(app(X1,app(X2,esk10_0)),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[382,2065]) ).

cnf(4626,negated_conjecture,
    ( memberP(app(esk10_0,esk10_0),esk11_0)
    | ~ ssList(nil)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[4606,1181,theory(equality)]) ).

cnf(4672,negated_conjecture,
    ( memberP(app(esk10_0,esk10_0),esk11_0)
    | $false
    | ~ ssList(esk10_0) ),
    inference(rw,[status(thm)],[4626,83,theory(equality)]) ).

cnf(4673,negated_conjecture,
    ( memberP(app(esk10_0,esk10_0),esk11_0)
    | $false
    | $false ),
    inference(rw,[status(thm)],[4672,135,theory(equality)]) ).

cnf(4674,negated_conjecture,
    memberP(app(esk10_0,esk10_0),esk11_0),
    inference(cn,[status(thm)],[4673,theory(equality)]) ).

cnf(4695,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(app(esk10_0,esk10_0))
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[89,4674,theory(equality)]) ).

cnf(4707,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(app(esk10_0,esk10_0))
    | $false ),
    inference(rw,[status(thm)],[4695,130,theory(equality)]) ).

cnf(4708,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(app(esk10_0,esk10_0)) ),
    inference(cn,[status(thm)],[4707,theory(equality)]) ).

cnf(5107,plain,
    ( memberP(app(X1,cons(X2,X3)),X2)
    | ~ ssList(X1)
    | ~ ssList(X3)
    | ~ ssItem(X2) ),
    inference(csr,[status(thm)],[397,82]) ).

cnf(5991,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[4708,42,theory(equality)]) ).

cnf(5994,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[5991,135,theory(equality)]) ).

cnf(5995,negated_conjecture,
    ( memberP(app(app(esk10_0,esk10_0),X1),esk11_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[5994,theory(equality)]) ).

cnf(6012,negated_conjecture,
    ( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
    | ~ ssList(nil)
    | ~ ssList(app(esk10_0,esk10_0)) ),
    inference(spm,[status(thm)],[5995,1927,theory(equality)]) ).

cnf(6036,negated_conjecture,
    ( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
    | $false
    | ~ ssList(app(esk10_0,esk10_0)) ),
    inference(rw,[status(thm)],[6012,83,theory(equality)]) ).

cnf(6037,negated_conjecture,
    ( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
    | ~ ssList(app(esk10_0,esk10_0)) ),
    inference(cn,[status(thm)],[6036,theory(equality)]) ).

cnf(6133,negated_conjecture,
    ( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[6037,42,theory(equality)]) ).

cnf(6136,negated_conjecture,
    ( memberP(app(nil,app(esk10_0,esk10_0)),esk11_0)
    | $false ),
    inference(rw,[status(thm)],[6133,135,theory(equality)]) ).

cnf(6137,negated_conjecture,
    memberP(app(nil,app(esk10_0,esk10_0)),esk11_0),
    inference(cn,[status(thm)],[6136,theory(equality)]) ).

cnf(10924,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[962,75,theory(equality)]) ).

cnf(10925,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[10924,135,theory(equality)]) ).

cnf(10926,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | memberP(app(esk5_1(esk10_0),X1),esk11_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[10925,theory(equality)]) ).

cnf(19201,negated_conjecture,
    ( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
    | nil = X1
    | X1 != esk10_0
    | ~ ssList(esk5_1(X1))
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[1437,74]) ).

cnf(19202,negated_conjecture,
    ( app(esk5_1(X1),cons(esk6_1(X1),nil)) = esk9_0
    | nil = X1
    | X1 != esk10_0
    | ~ ssList(X1) ),
    inference(csr,[status(thm)],[19201,75]) ).

cnf(19203,negated_conjecture,
    ( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
    | nil = esk10_0
    | ~ ssList(esk10_0) ),
    inference(er,[status(thm)],[19202,theory(equality)]) ).

cnf(19204,negated_conjecture,
    ( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
    | nil = esk10_0
    | $false ),
    inference(rw,[status(thm)],[19203,135,theory(equality)]) ).

cnf(19205,negated_conjecture,
    ( app(esk5_1(esk10_0),cons(esk6_1(esk10_0),nil)) = esk9_0
    | nil = esk10_0 ),
    inference(cn,[status(thm)],[19204,theory(equality)]) ).

cnf(19256,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | memberP(esk9_0,esk11_0)
    | ~ ssList(cons(esk6_1(esk10_0),nil)) ),
    inference(spm,[status(thm)],[10926,19205,theory(equality)]) ).

cnf(19285,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(cons(esk6_1(esk10_0),nil)) ),
    inference(sr,[status(thm)],[19256,137,theory(equality)]) ).

cnf(19286,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(nil)
    | ~ ssItem(esk6_1(esk10_0)) ),
    inference(spm,[status(thm)],[19285,82,theory(equality)]) ).

cnf(19288,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | $false
    | ~ ssItem(esk6_1(esk10_0)) ),
    inference(rw,[status(thm)],[19286,83,theory(equality)]) ).

cnf(19289,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssItem(esk6_1(esk10_0)) ),
    inference(cn,[status(thm)],[19288,theory(equality)]) ).

cnf(19290,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[19289,74,theory(equality)]) ).

cnf(19291,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[19290,135,theory(equality)]) ).

cnf(19292,negated_conjecture,
    ( esk6_1(esk10_0) = esk11_0
    | esk10_0 = nil ),
    inference(cn,[status(thm)],[19291,theory(equality)]) ).

cnf(19305,negated_conjecture,
    ( app(esk5_1(esk10_0),cons(esk11_0,nil)) = esk9_0
    | esk10_0 = nil ),
    inference(spm,[status(thm)],[19205,19292,theory(equality)]) ).

cnf(19686,negated_conjecture,
    ( memberP(esk9_0,esk11_0)
    | esk10_0 = nil
    | ~ ssList(esk5_1(esk10_0))
    | ~ ssList(nil)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[5107,19305,theory(equality)]) ).

cnf(19727,negated_conjecture,
    ( memberP(esk9_0,esk11_0)
    | esk10_0 = nil
    | ~ ssList(esk5_1(esk10_0))
    | $false
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[19686,83,theory(equality)]) ).

cnf(19728,negated_conjecture,
    ( memberP(esk9_0,esk11_0)
    | esk10_0 = nil
    | ~ ssList(esk5_1(esk10_0))
    | $false
    | $false ),
    inference(rw,[status(thm)],[19727,130,theory(equality)]) ).

cnf(19729,negated_conjecture,
    ( memberP(esk9_0,esk11_0)
    | esk10_0 = nil
    | ~ ssList(esk5_1(esk10_0)) ),
    inference(cn,[status(thm)],[19728,theory(equality)]) ).

cnf(19730,negated_conjecture,
    ( esk10_0 = nil
    | ~ ssList(esk5_1(esk10_0)) ),
    inference(sr,[status(thm)],[19729,137,theory(equality)]) ).

cnf(19738,negated_conjecture,
    ( esk10_0 = nil
    | ~ ssList(esk10_0) ),
    inference(spm,[status(thm)],[19730,75,theory(equality)]) ).

cnf(19739,negated_conjecture,
    ( esk10_0 = nil
    | $false ),
    inference(rw,[status(thm)],[19738,135,theory(equality)]) ).

cnf(19740,negated_conjecture,
    esk10_0 = nil,
    inference(cn,[status(thm)],[19739,theory(equality)]) ).

cnf(19745,negated_conjecture,
    memberP(nil,esk11_0),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[6137,19740,theory(equality)]),19740,theory(equality)]),290,theory(equality)]),290,theory(equality)]) ).

cnf(20078,negated_conjecture,
    ~ ssItem(esk11_0),
    inference(spm,[status(thm)],[78,19745,theory(equality)]) ).

cnf(20085,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[20078,130,theory(equality)]) ).

cnf(20086,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[20085,theory(equality)]) ).

cnf(20087,negated_conjecture,
    $false,
    20086,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% /home/graph/tptp/Systems/SInE---0.4/Source/sine.py:10: DeprecationWarning: the sets module is deprecated
%   from sets import Set
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC409+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpekl4Yt/sel_SWC409+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC409+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC409+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC409+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
% 
%------------------------------------------------------------------------------