TSTP Solution File: SWC239+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC239+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art01.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 11:03:27 EST 2010

% Result   : Theorem 0.68s
% Output   : CNFRefutation 0.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   42
%            Number of leaves      :   10
% Syntax   : Number of formulae    :  114 (  12 unt;   0 def)
%            Number of atoms       :  563 ( 171 equ)
%            Maximal formula atoms :   54 (   4 avg)
%            Number of connectives :  737 ( 288   ~; 305   |; 107   &)
%                                         (   0 <=>;  37  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   6 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-3 aty)
%            Number of variables   :  202 (   0 sgn 105   !;  24   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(3,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => app(app(X1,X2),X3) = app(X1,app(X2,X3)) ) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax82) ).

fof(4,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax81) ).

fof(5,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( app(X2,X3) = app(X2,X1)
               => X3 = X1 ) ) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax80) ).

fof(7,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(nil,X1) = X1 ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax28) ).

fof(8,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssItem(X3)
             => cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax27) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax26) ).

fof(20,axiom,
    ssList(nil),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax17) ).

fof(24,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax38) ).

fof(28,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ssList(cons(X2,X1)) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',ax16) ).

fof(30,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | nil = X1
                    | ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & app(app(X6,cons(X5,nil)),X7) = X1
                                & ! [X8] :
                                    ( ssItem(X8)
                                   => ( ~ memberP(X6,X8)
                                      | ~ memberP(X7,X8)
                                      | ~ lt(X5,X8)
                                      | leq(X5,X8) ) ) ) ) )
                    | ( ! [X9] :
                          ( ssItem(X9)
                         => ( cons(X9,nil) != X3
                            | ~ memberP(X4,X9)
                            | ? [X10] :
                                ( ssItem(X10)
                                & X9 != X10
                                & memberP(X4,X10)
                                & leq(X9,X10) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/tmp/tmpXwpQ3I/sel_SWC239+1.p_1',co1) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) )
                      | ( ! [X9] :
                            ( ssItem(X9)
                           => ( cons(X9,nil) != X3
                              | ~ memberP(X4,X9)
                              | ? [X10] :
                                  ( ssItem(X10)
                                  & X9 != X10
                                  & memberP(X4,X10)
                                  & leq(X9,X10) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[30]) ).

fof(34,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[24,theory(equality)]) ).

fof(35,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | nil = X1
                      | ? [X5] :
                          ( ssItem(X5)
                          & ? [X6] :
                              ( ssList(X6)
                              & ? [X7] :
                                  ( ssList(X7)
                                  & app(app(X6,cons(X5,nil)),X7) = X1
                                  & ! [X8] :
                                      ( ssItem(X8)
                                     => ( ~ memberP(X6,X8)
                                        | ~ memberP(X7,X8)
                                        | ~ lt(X5,X8)
                                        | leq(X5,X8) ) ) ) ) )
                      | ( ! [X9] :
                            ( ssItem(X9)
                           => ( cons(X9,nil) != X3
                              | ~ memberP(X4,X9)
                              | ? [X10] :
                                  ( ssItem(X10)
                                  & X9 != X10
                                  & memberP(X4,X10)
                                  & leq(X9,X10) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).

fof(46,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)],[3]) ).

fof(47,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)],[46]) ).

fof(48,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)],[47]) ).

cnf(49,plain,
    ( app(app(X1,X2),X3) = app(X1,app(X2,X3))
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[48]) ).

fof(50,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | cons(X2,X1) = app(cons(X2,nil),X1) ) ),
    inference(fof_nnf,[status(thm)],[4]) ).

fof(51,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | cons(X4,X3) = app(cons(X4,nil),X3) ) ),
    inference(variable_rename,[status(thm)],[50]) ).

fof(52,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | cons(X4,X3) = app(cons(X4,nil),X3)
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[51]) ).

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

fof(54,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssList(X3)
              | app(X2,X3) != app(X2,X1)
              | X3 = X1 ) ) ),
    inference(fof_nnf,[status(thm)],[5]) ).

fof(55,plain,
    ! [X4] :
      ( ~ ssList(X4)
      | ! [X5] :
          ( ~ ssList(X5)
          | ! [X6] :
              ( ~ ssList(X6)
              | app(X5,X6) != app(X5,X4)
              | X6 = X4 ) ) ),
    inference(variable_rename,[status(thm)],[54]) ).

fof(56,plain,
    ! [X4,X5,X6] :
      ( ~ ssList(X6)
      | app(X5,X6) != app(X5,X4)
      | X6 = X4
      | ~ ssList(X5)
      | ~ ssList(X4) ),
    inference(shift_quantors,[status(thm)],[55]) ).

cnf(57,plain,
    ( X3 = X1
    | ~ ssList(X1)
    | ~ ssList(X2)
    | app(X2,X3) != app(X2,X1)
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[56]) ).

fof(62,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(nil,X1) = X1 ),
    inference(fof_nnf,[status(thm)],[7]) ).

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] :
          ( ~ ssList(X2)
          | ! [X3] :
              ( ~ ssItem(X3)
              | cons(X3,app(X2,X1)) = app(cons(X3,X2),X1) ) ) ),
    inference(fof_nnf,[status(thm)],[8]) ).

fof(66,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)],[65]) ).

fof(67,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)],[66]) ).

cnf(68,plain,
    ( cons(X3,app(X2,X1)) = app(cons(X3,X2),X1)
    | ~ ssList(X1)
    | ~ ssList(X2)
    | ~ ssItem(X3) ),
    inference(split_conjunct,[status(thm)],[67]) ).

fof(69,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(70,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[69]) ).

fof(71,plain,
    ! [X3,X4] :
      ( ~ ssList(X4)
      | ssList(app(X3,X4))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[70]) ).

cnf(72,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[71]) ).

cnf(121,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[20]) ).

fof(140,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ memberP(nil,X1) ),
    inference(fof_nnf,[status(thm)],[34]) ).

fof(141,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[140]) ).

cnf(142,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[141]) ).

fof(160,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssItem(X2)
          | ssList(cons(X2,X1)) ) ),
    inference(fof_nnf,[status(thm)],[28]) ).

fof(161,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssItem(X4)
          | ssList(cons(X4,X3)) ) ),
    inference(variable_rename,[status(thm)],[160]) ).

fof(162,plain,
    ! [X3,X4] :
      ( ~ ssItem(X4)
      | ssList(cons(X4,X3))
      | ~ ssList(X3) ),
    inference(shift_quantors,[status(thm)],[161]) ).

cnf(163,plain,
    ( ssList(cons(X2,X1))
    | ~ ssList(X1)
    | ~ ssItem(X2) ),
    inference(split_conjunct,[status(thm)],[162]) ).

fof(167,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & nil != X1
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ! [X6] :
                          ( ~ ssList(X6)
                          | ! [X7] :
                              ( ~ ssList(X7)
                              | app(app(X6,cons(X5,nil)),X7) != X1
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & memberP(X6,X8)
                                  & memberP(X7,X8)
                                  & lt(X5,X8)
                                  & ~ leq(X5,X8) ) ) ) )
                  & ( ? [X9] :
                        ( ssItem(X9)
                        & cons(X9,nil) = X3
                        & memberP(X4,X9)
                        & ! [X10] :
                            ( ~ ssItem(X10)
                            | X9 = X10
                            | ~ memberP(X4,X10)
                            | ~ leq(X9,X10) ) )
                    | ( nil = X4
                      & nil = X3 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[35]) ).

fof(168,negated_conjecture,
    ? [X11] :
      ( ssList(X11)
      & ? [X12] :
          ( ssList(X12)
          & ? [X13] :
              ( ssList(X13)
              & ? [X14] :
                  ( ssList(X14)
                  & X12 = X14
                  & X11 = X13
                  & nil != X11
                  & ! [X15] :
                      ( ~ ssItem(X15)
                      | ! [X16] :
                          ( ~ ssList(X16)
                          | ! [X17] :
                              ( ~ ssList(X17)
                              | app(app(X16,cons(X15,nil)),X17) != X11
                              | ? [X18] :
                                  ( ssItem(X18)
                                  & memberP(X16,X18)
                                  & memberP(X17,X18)
                                  & lt(X15,X18)
                                  & ~ leq(X15,X18) ) ) ) )
                  & ( ? [X19] :
                        ( ssItem(X19)
                        & cons(X19,nil) = X13
                        & memberP(X14,X19)
                        & ! [X20] :
                            ( ~ ssItem(X20)
                            | X19 = X20
                            | ~ memberP(X14,X20)
                            | ~ leq(X19,X20) ) )
                    | ( nil = X14
                      & nil = X13 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[167]) ).

fof(169,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & nil != esk7_0
    & ! [X15] :
        ( ~ ssItem(X15)
        | ! [X16] :
            ( ~ ssList(X16)
            | ! [X17] :
                ( ~ ssList(X17)
                | app(app(X16,cons(X15,nil)),X17) != esk7_0
                | ( ssItem(esk11_3(X15,X16,X17))
                  & memberP(X16,esk11_3(X15,X16,X17))
                  & memberP(X17,esk11_3(X15,X16,X17))
                  & lt(X15,esk11_3(X15,X16,X17))
                  & ~ leq(X15,esk11_3(X15,X16,X17)) ) ) ) )
    & ( ( ssItem(esk12_0)
        & cons(esk12_0,nil) = esk9_0
        & memberP(esk10_0,esk12_0)
        & ! [X20] :
            ( ~ ssItem(X20)
            | esk12_0 = X20
            | ~ memberP(esk10_0,X20)
            | ~ leq(esk12_0,X20) ) )
      | ( nil = esk10_0
        & nil = esk9_0 ) ) ),
    inference(skolemize,[status(esa)],[168]) ).

fof(170,negated_conjecture,
    ! [X15,X16,X17,X20] :
      ( ( ( ( ~ ssItem(X20)
            | esk12_0 = X20
            | ~ memberP(esk10_0,X20)
            | ~ leq(esk12_0,X20) )
          & cons(esk12_0,nil) = esk9_0
          & memberP(esk10_0,esk12_0)
          & ssItem(esk12_0) )
        | ( nil = esk10_0
          & nil = esk9_0 ) )
      & ( ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ( ssItem(esk11_3(X15,X16,X17))
          & memberP(X16,esk11_3(X15,X16,X17))
          & memberP(X17,esk11_3(X15,X16,X17))
          & lt(X15,esk11_3(X15,X16,X17))
          & ~ leq(X15,esk11_3(X15,X16,X17)) )
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & nil != esk7_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[169]) ).

fof(171,negated_conjecture,
    ! [X15,X16,X17,X20] :
      ( ( nil = esk10_0
        | ~ ssItem(X20)
        | esk12_0 = X20
        | ~ memberP(esk10_0,X20)
        | ~ leq(esk12_0,X20) )
      & ( nil = esk9_0
        | ~ ssItem(X20)
        | esk12_0 = X20
        | ~ memberP(esk10_0,X20)
        | ~ leq(esk12_0,X20) )
      & ( nil = esk10_0
        | cons(esk12_0,nil) = esk9_0 )
      & ( nil = esk9_0
        | cons(esk12_0,nil) = esk9_0 )
      & ( nil = esk10_0
        | memberP(esk10_0,esk12_0) )
      & ( nil = esk9_0
        | memberP(esk10_0,esk12_0) )
      & ( nil = esk10_0
        | ssItem(esk12_0) )
      & ( nil = esk9_0
        | ssItem(esk12_0) )
      & ( ssItem(esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( memberP(X16,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( memberP(X17,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( lt(X15,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & ( ~ leq(X15,esk11_3(X15,X16,X17))
        | ~ ssList(X17)
        | app(app(X16,cons(X15,nil)),X17) != esk7_0
        | ~ ssList(X16)
        | ~ ssItem(X15) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & nil != esk7_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[170]) ).

cnf(172,negated_conjecture,
    ssList(esk7_0),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(176,negated_conjecture,
    nil != esk7_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(177,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(181,negated_conjecture,
    ( memberP(X3,esk11_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk7_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(183,negated_conjecture,
    ( ssItem(esk11_3(X1,X2,X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | app(app(X2,cons(X1,nil)),X3) != esk7_0
    | ~ ssList(X3) ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(184,negated_conjecture,
    ( ssItem(esk12_0)
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(188,negated_conjecture,
    ( cons(esk12_0,nil) = esk9_0
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[171]) ).

cnf(195,negated_conjecture,
    ( esk7_0 = nil
    | ssItem(esk12_0) ),
    inference(rw,[status(thm)],[184,177,theory(equality)]) ).

cnf(196,negated_conjecture,
    ssItem(esk12_0),
    inference(sr,[status(thm)],[195,176,theory(equality)]) ).

cnf(198,negated_conjecture,
    ( esk7_0 = nil
    | cons(esk12_0,nil) = esk9_0 ),
    inference(rw,[status(thm)],[188,177,theory(equality)]) ).

cnf(199,negated_conjecture,
    ( esk7_0 = nil
    | cons(esk12_0,nil) = esk7_0 ),
    inference(rw,[status(thm)],[198,177,theory(equality)]) ).

cnf(200,negated_conjecture,
    cons(esk12_0,nil) = esk7_0,
    inference(sr,[status(thm)],[199,176,theory(equality)]) ).

cnf(245,negated_conjecture,
    ( app(esk7_0,X1) = cons(esk12_0,X1)
    | ~ ssItem(esk12_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[53,200,theory(equality)]) ).

cnf(250,negated_conjecture,
    ( app(esk7_0,X1) = cons(esk12_0,X1)
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[245,196,theory(equality)]) ).

cnf(251,negated_conjecture,
    ( app(esk7_0,X1) = cons(esk12_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[250,theory(equality)]) ).

cnf(319,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[49,64,theory(equality)]) ).

cnf(338,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[319,121,theory(equality)]) ).

cnf(339,plain,
    ( app(X1,X2) = app(nil,app(X1,X2))
    | ~ ssList(X2)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[338,theory(equality)]) ).

cnf(345,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssItem(X1)
    | ~ ssList(app(X2,X3))
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(spm,[status(thm)],[163,68,theory(equality)]) ).

cnf(381,negated_conjecture,
    ( ssItem(esk11_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(nil)
    | ~ ssList(cons(X1,nil)) ),
    inference(spm,[status(thm)],[183,64,theory(equality)]) ).

cnf(391,negated_conjecture,
    ( ssItem(esk11_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | $false
    | ~ ssList(cons(X1,nil)) ),
    inference(rw,[status(thm)],[381,121,theory(equality)]) ).

cnf(392,negated_conjecture,
    ( ssItem(esk11_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(cons(X1,nil)) ),
    inference(cn,[status(thm)],[391,theory(equality)]) ).

cnf(424,negated_conjecture,
    ( ~ ssItem(esk11_3(X1,X2,nil))
    | app(app(X2,cons(X1,nil)),nil) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(nil)
    | ~ ssList(X2) ),
    inference(spm,[status(thm)],[142,181,theory(equality)]) ).

cnf(427,negated_conjecture,
    ( ~ ssItem(esk11_3(X1,X2,nil))
    | app(app(X2,cons(X1,nil)),nil) != esk7_0
    | ~ ssItem(X1)
    | $false
    | ~ ssList(X2) ),
    inference(rw,[status(thm)],[424,121,theory(equality)]) ).

cnf(428,negated_conjecture,
    ( ~ ssItem(esk11_3(X1,X2,nil))
    | app(app(X2,cons(X1,nil)),nil) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[427,theory(equality)]) ).

cnf(452,negated_conjecture,
    ( app(esk7_0,nil) = esk7_0
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[200,251,theory(equality)]) ).

cnf(467,negated_conjecture,
    ( app(esk7_0,nil) = esk7_0
    | $false ),
    inference(rw,[status(thm)],[452,121,theory(equality)]) ).

cnf(468,negated_conjecture,
    app(esk7_0,nil) = esk7_0,
    inference(cn,[status(thm)],[467,theory(equality)]) ).

cnf(504,negated_conjecture,
    ( nil = X1
    | esk7_0 != app(esk7_0,X1)
    | ~ ssList(X1)
    | ~ ssList(esk7_0)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[57,468,theory(equality)]) ).

cnf(508,negated_conjecture,
    ( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
    | ~ ssList(X1)
    | ~ ssList(nil)
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[49,468,theory(equality)]) ).

cnf(527,negated_conjecture,
    ( nil = X1
    | esk7_0 != app(esk7_0,X1)
    | ~ ssList(X1)
    | $false
    | ~ ssList(nil) ),
    inference(rw,[status(thm)],[504,172,theory(equality)]) ).

cnf(528,negated_conjecture,
    ( nil = X1
    | esk7_0 != app(esk7_0,X1)
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[527,121,theory(equality)]) ).

cnf(529,negated_conjecture,
    ( nil = X1
    | esk7_0 != app(esk7_0,X1)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[528,theory(equality)]) ).

cnf(539,negated_conjecture,
    ( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
    | ~ ssList(X1)
    | $false
    | ~ ssList(esk7_0) ),
    inference(rw,[status(thm)],[508,121,theory(equality)]) ).

cnf(540,negated_conjecture,
    ( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[539,172,theory(equality)]) ).

cnf(541,negated_conjecture,
    ( app(esk7_0,X1) = app(esk7_0,app(nil,X1))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[540,theory(equality)]) ).

cnf(602,negated_conjecture,
    ( nil = app(nil,X1)
    | app(esk7_0,X1) != esk7_0
    | ~ ssList(app(nil,X1))
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[529,541,theory(equality)]) ).

cnf(1466,negated_conjecture,
    ( app(nil,X1) = nil
    | app(esk7_0,X1) != esk7_0
    | ~ ssList(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[602,72,theory(equality)]) ).

cnf(1467,negated_conjecture,
    ( app(nil,X1) = nil
    | app(esk7_0,X1) != esk7_0
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[1466,121,theory(equality)]) ).

cnf(1468,negated_conjecture,
    ( app(nil,X1) = nil
    | app(esk7_0,X1) != esk7_0
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1467,theory(equality)]) ).

cnf(1469,negated_conjecture,
    ( app(nil,nil) = nil
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[1468,468,theory(equality)]) ).

cnf(1475,negated_conjecture,
    ( app(nil,nil) = nil
    | $false ),
    inference(rw,[status(thm)],[1469,121,theory(equality)]) ).

cnf(1476,negated_conjecture,
    app(nil,nil) = nil,
    inference(cn,[status(thm)],[1475,theory(equality)]) ).

cnf(1490,negated_conjecture,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[68,1476,theory(equality)]) ).

cnf(1516,negated_conjecture,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[1490,121,theory(equality)]) ).

cnf(1517,negated_conjecture,
    ( cons(X1,nil) = app(cons(X1,nil),nil)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[1516,theory(equality)]) ).

cnf(2575,negated_conjecture,
    ( app(nil,esk7_0) = esk7_0
    | ~ ssList(nil)
    | ~ ssList(esk7_0) ),
    inference(spm,[status(thm)],[339,468,theory(equality)]) ).

cnf(2630,negated_conjecture,
    ( app(nil,esk7_0) = esk7_0
    | $false
    | ~ ssList(esk7_0) ),
    inference(rw,[status(thm)],[2575,121,theory(equality)]) ).

cnf(2631,negated_conjecture,
    ( app(nil,esk7_0) = esk7_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[2630,172,theory(equality)]) ).

cnf(2632,negated_conjecture,
    app(nil,esk7_0) = esk7_0,
    inference(cn,[status(thm)],[2631,theory(equality)]) ).

cnf(7869,plain,
    ( ssList(app(cons(X1,X2),X3))
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3) ),
    inference(csr,[status(thm)],[345,72]) ).

cnf(7880,negated_conjecture,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[7869,1517,theory(equality)]) ).

cnf(7907,negated_conjecture,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[7880,121,theory(equality)]) ).

cnf(7908,negated_conjecture,
    ( ssList(cons(X1,nil))
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[7907,theory(equality)]) ).

cnf(9882,negated_conjecture,
    ( ssItem(esk11_3(X1,nil,X2))
    | app(cons(X1,nil),X2) != esk7_0
    | ~ ssItem(X1)
    | ~ ssList(X2) ),
    inference(csr,[status(thm)],[392,7908]) ).

cnf(12362,negated_conjecture,
    ( app(app(X1,esk7_0),nil) != esk7_0
    | ~ ssItem(esk11_3(esk12_0,X1,nil))
    | ~ ssItem(esk12_0)
    | ~ ssList(X1) ),
    inference(spm,[status(thm)],[428,200,theory(equality)]) ).

cnf(12381,negated_conjecture,
    ( app(app(X1,esk7_0),nil) != esk7_0
    | ~ ssItem(esk11_3(esk12_0,X1,nil))
    | $false
    | ~ ssList(X1) ),
    inference(rw,[status(thm)],[12362,196,theory(equality)]) ).

cnf(12382,negated_conjecture,
    ( app(app(X1,esk7_0),nil) != esk7_0
    | ~ ssItem(esk11_3(esk12_0,X1,nil))
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[12381,theory(equality)]) ).

cnf(12409,negated_conjecture,
    ( app(app(nil,esk7_0),nil) != esk7_0
    | ~ ssList(nil)
    | app(cons(esk12_0,nil),nil) != esk7_0
    | ~ ssItem(esk12_0) ),
    inference(spm,[status(thm)],[12382,9882,theory(equality)]) ).

cnf(12417,negated_conjecture,
    ( $false
    | ~ ssList(nil)
    | app(cons(esk12_0,nil),nil) != esk7_0
    | ~ ssItem(esk12_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[12409,2632,theory(equality)]),468,theory(equality)]) ).

cnf(12418,negated_conjecture,
    ( $false
    | $false
    | app(cons(esk12_0,nil),nil) != esk7_0
    | ~ ssItem(esk12_0) ),
    inference(rw,[status(thm)],[12417,121,theory(equality)]) ).

cnf(12419,negated_conjecture,
    ( $false
    | $false
    | $false
    | ~ ssItem(esk12_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[12418,200,theory(equality)]),468,theory(equality)]) ).

cnf(12420,negated_conjecture,
    ( $false
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[12419,196,theory(equality)]) ).

cnf(12421,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[12420,theory(equality)]) ).

cnf(12422,negated_conjecture,
    $false,
    12421,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC239+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpXwpQ3I/sel_SWC239+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC239+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC239+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC239+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
% 
%------------------------------------------------------------------------------