TSTP Solution File: SWC039+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC039+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art06.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 10:08:01 EST 2010

% Result   : Theorem 0.26s
% Output   : CNFRefutation 0.26s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   29
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   55 (  16 unt;   0 def)
%            Number of atoms       :  300 ( 134 equ)
%            Maximal formula atoms :   44 (   5 avg)
%            Number of connectives :  356 ( 111   ~; 125   |; 100   &)
%                                         (   1 <=>;  19  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   68 (   0 sgn  45   !;  18   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( ssList(X1)
     => app(X1,nil) = X1 ),
    file('/tmp/tmpleYoYK/sel_SWC039+1.p_1',ax84) ).

fof(2,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ( nil = app(X1,X2)
          <=> ( nil = X2
              & nil = X1 ) ) ) ),
    file('/tmp/tmpleYoYK/sel_SWC039+1.p_1',ax83) ).

fof(9,axiom,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ssList(app(X1,X2)) ) ),
    file('/tmp/tmpleYoYK/sel_SWC039+1.p_1',ax26) ).

fof(30,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( nil != X2
                    | X2 != X4
                    | X1 != X3
                    | nil = X1
                    | ( ! [X5] :
                          ( ssItem(X5)
                         => ! [X6] :
                              ( ssList(X6)
                             => ! [X7] :
                                  ( ssList(X7)
                                 => ( cons(X5,nil) != X3
                                    | app(app(X6,X3),X7) != X4
                                    | ? [X8] :
                                        ( ssItem(X8)
                                        & memberP(X6,X8)
                                        & lt(X5,X8) )
                                    | ? [X9] :
                                        ( ssItem(X9)
                                        & memberP(X7,X9)
                                        & lt(X9,X5) ) ) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/tmp/tmpleYoYK/sel_SWC039+1.p_1',co1) ).

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

fof(35,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | app(X1,nil) = X1 ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(36,plain,
    ! [X2] :
      ( ~ ssList(X2)
      | app(X2,nil) = X2 ),
    inference(variable_rename,[status(thm)],[35]) ).

cnf(37,plain,
    ( app(X1,nil) = X1
    | ~ ssList(X1) ),
    inference(split_conjunct,[status(thm)],[36]) ).

fof(38,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)],[2]) ).

fof(39,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)],[38]) ).

fof(40,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)],[39]) ).

fof(41,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)],[40]) ).

cnf(44,plain,
    ( nil = X2
    | ~ ssList(X1)
    | ~ ssList(X2)
    | nil != app(X1,X2) ),
    inference(split_conjunct,[status(thm)],[41]) ).

fof(68,plain,
    ! [X1] :
      ( ~ ssList(X1)
      | ! [X2] :
          ( ~ ssList(X2)
          | ssList(app(X1,X2)) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(69,plain,
    ! [X3] :
      ( ~ ssList(X3)
      | ! [X4] :
          ( ~ ssList(X4)
          | ssList(app(X3,X4)) ) ),
    inference(variable_rename,[status(thm)],[68]) ).

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

cnf(71,plain,
    ( ssList(app(X1,X2))
    | ~ ssList(X1)
    | ~ ssList(X2) ),
    inference(split_conjunct,[status(thm)],[70]) ).

fof(166,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & nil = X2
                  & X2 = X4
                  & X1 = X3
                  & nil != X1
                  & ( ? [X5] :
                        ( ssItem(X5)
                        & ? [X6] :
                            ( ssList(X6)
                            & ? [X7] :
                                ( ssList(X7)
                                & cons(X5,nil) = X3
                                & app(app(X6,X3),X7) = X4
                                & ! [X8] :
                                    ( ~ ssItem(X8)
                                    | ~ memberP(X6,X8)
                                    | ~ lt(X5,X8) )
                                & ! [X9] :
                                    ( ~ ssItem(X9)
                                    | ~ memberP(X7,X9)
                                    | ~ lt(X9,X5) ) ) ) )
                    | ( nil = X4
                      & nil = X3 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[31]) ).

fof(167,negated_conjecture,
    ? [X10] :
      ( ssList(X10)
      & ? [X11] :
          ( ssList(X11)
          & ? [X12] :
              ( ssList(X12)
              & ? [X13] :
                  ( ssList(X13)
                  & nil = X11
                  & X11 = X13
                  & X10 = X12
                  & nil != X10
                  & ( ? [X14] :
                        ( ssItem(X14)
                        & ? [X15] :
                            ( ssList(X15)
                            & ? [X16] :
                                ( ssList(X16)
                                & cons(X14,nil) = X12
                                & app(app(X15,X12),X16) = X13
                                & ! [X17] :
                                    ( ~ ssItem(X17)
                                    | ~ memberP(X15,X17)
                                    | ~ lt(X14,X17) )
                                & ! [X18] :
                                    ( ~ ssItem(X18)
                                    | ~ memberP(X16,X18)
                                    | ~ lt(X18,X14) ) ) ) )
                    | ( nil = X13
                      & nil = X12 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[166]) ).

fof(168,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & nil = esk8_0
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & nil != esk7_0
    & ( ( ssItem(esk11_0)
        & ssList(esk12_0)
        & ssList(esk13_0)
        & cons(esk11_0,nil) = esk9_0
        & app(app(esk12_0,esk9_0),esk13_0) = esk10_0
        & ! [X17] :
            ( ~ ssItem(X17)
            | ~ memberP(esk12_0,X17)
            | ~ lt(esk11_0,X17) )
        & ! [X18] :
            ( ~ ssItem(X18)
            | ~ memberP(esk13_0,X18)
            | ~ lt(X18,esk11_0) ) )
      | ( nil = esk10_0
        & nil = esk9_0 ) ) ),
    inference(skolemize,[status(esa)],[167]) ).

fof(169,negated_conjecture,
    ! [X17,X18] :
      ( ( ( ( ~ ssItem(X18)
            | ~ memberP(esk13_0,X18)
            | ~ lt(X18,esk11_0) )
          & ( ~ ssItem(X17)
            | ~ memberP(esk12_0,X17)
            | ~ lt(esk11_0,X17) )
          & cons(esk11_0,nil) = esk9_0
          & app(app(esk12_0,esk9_0),esk13_0) = esk10_0
          & ssList(esk13_0)
          & ssList(esk12_0)
          & ssItem(esk11_0) )
        | ( nil = esk10_0
          & nil = esk9_0 ) )
      & nil = esk8_0
      & 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)],[168]) ).

fof(170,negated_conjecture,
    ! [X17,X18] :
      ( ( nil = esk10_0
        | ~ ssItem(X18)
        | ~ memberP(esk13_0,X18)
        | ~ lt(X18,esk11_0) )
      & ( nil = esk9_0
        | ~ ssItem(X18)
        | ~ memberP(esk13_0,X18)
        | ~ lt(X18,esk11_0) )
      & ( nil = esk10_0
        | ~ ssItem(X17)
        | ~ memberP(esk12_0,X17)
        | ~ lt(esk11_0,X17) )
      & ( nil = esk9_0
        | ~ ssItem(X17)
        | ~ memberP(esk12_0,X17)
        | ~ lt(esk11_0,X17) )
      & ( nil = esk10_0
        | cons(esk11_0,nil) = esk9_0 )
      & ( nil = esk9_0
        | cons(esk11_0,nil) = esk9_0 )
      & ( nil = esk10_0
        | app(app(esk12_0,esk9_0),esk13_0) = esk10_0 )
      & ( nil = esk9_0
        | app(app(esk12_0,esk9_0),esk13_0) = esk10_0 )
      & ( nil = esk10_0
        | ssList(esk13_0) )
      & ( nil = esk9_0
        | ssList(esk13_0) )
      & ( nil = esk10_0
        | ssList(esk12_0) )
      & ( nil = esk9_0
        | ssList(esk12_0) )
      & ( nil = esk10_0
        | ssItem(esk11_0) )
      & ( nil = esk9_0
        | ssItem(esk11_0) )
      & nil = esk8_0
      & 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)],[169]) ).

cnf(173,negated_conjecture,
    ssList(esk9_0),
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(175,negated_conjecture,
    nil != esk7_0,
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(176,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(177,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(178,negated_conjecture,
    nil = esk8_0,
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(181,negated_conjecture,
    ( ssList(esk12_0)
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(183,negated_conjecture,
    ( ssList(esk13_0)
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(185,negated_conjecture,
    ( app(app(esk12_0,esk9_0),esk13_0) = esk10_0
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[170]) ).

cnf(196,negated_conjecture,
    esk10_0 = nil,
    inference(rw,[status(thm)],[177,178,theory(equality)]) ).

cnf(199,negated_conjecture,
    esk9_0 != nil,
    inference(rw,[status(thm)],[175,176,theory(equality)]) ).

cnf(200,negated_conjecture,
    ssList(esk12_0),
    inference(sr,[status(thm)],[181,199,theory(equality)]) ).

cnf(201,negated_conjecture,
    ssList(esk13_0),
    inference(sr,[status(thm)],[183,199,theory(equality)]) ).

cnf(212,negated_conjecture,
    ( esk9_0 = nil
    | app(app(esk12_0,esk9_0),esk13_0) = nil ),
    inference(rw,[status(thm)],[185,196,theory(equality)]) ).

cnf(213,negated_conjecture,
    app(app(esk12_0,esk9_0),esk13_0) = nil,
    inference(sr,[status(thm)],[212,199,theory(equality)]) ).

cnf(258,negated_conjecture,
    ( nil = esk13_0
    | ~ ssList(esk13_0)
    | ~ ssList(app(esk12_0,esk9_0)) ),
    inference(spm,[status(thm)],[44,213,theory(equality)]) ).

cnf(261,negated_conjecture,
    ( nil = esk13_0
    | $false
    | ~ ssList(app(esk12_0,esk9_0)) ),
    inference(rw,[status(thm)],[258,201,theory(equality)]) ).

cnf(262,negated_conjecture,
    ( nil = esk13_0
    | ~ ssList(app(esk12_0,esk9_0)) ),
    inference(cn,[status(thm)],[261,theory(equality)]) ).

cnf(485,negated_conjecture,
    ( esk13_0 = nil
    | ~ ssList(esk9_0)
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[262,71,theory(equality)]) ).

cnf(487,negated_conjecture,
    ( esk13_0 = nil
    | $false
    | ~ ssList(esk12_0) ),
    inference(rw,[status(thm)],[485,173,theory(equality)]) ).

cnf(488,negated_conjecture,
    ( esk13_0 = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[487,200,theory(equality)]) ).

cnf(489,negated_conjecture,
    esk13_0 = nil,
    inference(cn,[status(thm)],[488,theory(equality)]) ).

cnf(494,negated_conjecture,
    app(app(esk12_0,esk9_0),nil) = nil,
    inference(rw,[status(thm)],[213,489,theory(equality)]) ).

cnf(499,negated_conjecture,
    ( nil = app(esk12_0,esk9_0)
    | ~ ssList(app(esk12_0,esk9_0)) ),
    inference(spm,[status(thm)],[37,494,theory(equality)]) ).

cnf(545,negated_conjecture,
    ( app(esk12_0,esk9_0) = nil
    | ~ ssList(esk9_0)
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[499,71,theory(equality)]) ).

cnf(546,negated_conjecture,
    ( app(esk12_0,esk9_0) = nil
    | $false
    | ~ ssList(esk12_0) ),
    inference(rw,[status(thm)],[545,173,theory(equality)]) ).

cnf(547,negated_conjecture,
    ( app(esk12_0,esk9_0) = nil
    | $false
    | $false ),
    inference(rw,[status(thm)],[546,200,theory(equality)]) ).

cnf(548,negated_conjecture,
    app(esk12_0,esk9_0) = nil,
    inference(cn,[status(thm)],[547,theory(equality)]) ).

cnf(550,negated_conjecture,
    ( nil = esk9_0
    | ~ ssList(esk9_0)
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[44,548,theory(equality)]) ).

cnf(569,negated_conjecture,
    ( nil = esk9_0
    | $false
    | ~ ssList(esk12_0) ),
    inference(rw,[status(thm)],[550,173,theory(equality)]) ).

cnf(570,negated_conjecture,
    ( nil = esk9_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[569,200,theory(equality)]) ).

cnf(571,negated_conjecture,
    nil = esk9_0,
    inference(cn,[status(thm)],[570,theory(equality)]) ).

cnf(572,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[571,199,theory(equality)]) ).

cnf(573,negated_conjecture,
    $false,
    572,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC039+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpleYoYK/sel_SWC039+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC039+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC039+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC039+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
% 
%------------------------------------------------------------------------------