TSTP Solution File: SWC010+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC010+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art05.cs.miami.edu
% Model    : i686 i686
% CPU      : Intel(R) Pentium(R) 4 CPU 2.80GHz @ 2793MHz
% Memory   : 2018MB
% OS       : Linux 2.6.26.8-57.fc8
% CPULimit : 300s
% DateTime : Sun Dec 26 10:04:56 EST 2010

% Result   : Theorem 0.21s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    1
% Syntax   : Number of formulae    :   39 (  10 unt;   0 def)
%            Number of atoms       :  290 (  79 equ)
%            Maximal formula atoms :   52 (   7 avg)
%            Number of connectives :  372 ( 121   ~; 129   |; 101   &)
%                                         (   0 <=>;  21  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   7 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   79 (   0 sgn  41   !;  26   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(30,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ( ( ~ neq(X2,nil)
                        | ? [X5] :
                            ( ssItem(X5)
                            & ? [X6] :
                                ( ssList(X6)
                                & ? [X7] :
                                    ( ssList(X7)
                                    & app(app(X6,cons(X5,nil)),X7) = X2
                                    & app(X6,X7) = X1 ) ) )
                        | ! [X8] :
                            ( ssItem(X8)
                           => ! [X9] :
                                ( ssList(X9)
                               => ! [X10] :
                                    ( ssList(X10)
                                   => ( app(app(X9,cons(X8,nil)),X10) != X4
                                      | app(X9,X10) != X3
                                      | ? [X11] :
                                          ( ssItem(X11)
                                          & X8 != X11
                                          & memberP(X4,X11)
                                          & geq(X11,X8) ) ) ) ) ) )
                      & ( ~ neq(X2,nil)
                        | neq(X4,nil) ) ) ) ) ) ) ),
    file('/tmp/tmpr_nUuU/sel_SWC010+1.p_1',co1) ).

fof(31,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssItem(X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & ? [X7] :
                                      ( ssList(X7)
                                      & app(app(X6,cons(X5,nil)),X7) = X2
                                      & app(X6,X7) = X1 ) ) )
                          | ! [X8] :
                              ( ssItem(X8)
                             => ! [X9] :
                                  ( ssList(X9)
                                 => ! [X10] :
                                      ( ssList(X10)
                                     => ( app(app(X9,cons(X8,nil)),X10) != X4
                                        | app(X9,X10) != X3
                                        | ? [X11] :
                                            ( ssItem(X11)
                                            & X8 != X11
                                            & memberP(X4,X11)
                                            & geq(X11,X8) ) ) ) ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[30]) ).

fof(33,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ( ( ~ neq(X2,nil)
                          | ? [X5] :
                              ( ssItem(X5)
                              & ? [X6] :
                                  ( ssList(X6)
                                  & ? [X7] :
                                      ( ssList(X7)
                                      & app(app(X6,cons(X5,nil)),X7) = X2
                                      & app(X6,X7) = X1 ) ) )
                          | ! [X8] :
                              ( ssItem(X8)
                             => ! [X9] :
                                  ( ssList(X9)
                                 => ! [X10] :
                                      ( ssList(X10)
                                     => ( app(app(X9,cons(X8,nil)),X10) != X4
                                        | app(X9,X10) != X3
                                        | ? [X11] :
                                            ( ssItem(X11)
                                            & X8 != X11
                                            & memberP(X4,X11)
                                            & geq(X11,X8) ) ) ) ) ) )
                        & ( ~ neq(X2,nil)
                          | neq(X4,nil) ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[31,theory(equality)]) ).

fof(168,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ( ( neq(X2,nil)
                      & ! [X5] :
                          ( ~ ssItem(X5)
                          | ! [X6] :
                              ( ~ ssList(X6)
                              | ! [X7] :
                                  ( ~ ssList(X7)
                                  | app(app(X6,cons(X5,nil)),X7) != X2
                                  | app(X6,X7) != X1 ) ) )
                      & ? [X8] :
                          ( ssItem(X8)
                          & ? [X9] :
                              ( ssList(X9)
                              & ? [X10] :
                                  ( ssList(X10)
                                  & app(app(X9,cons(X8,nil)),X10) = X4
                                  & app(X9,X10) = X3
                                  & ! [X11] :
                                      ( ~ ssItem(X11)
                                      | X8 = X11
                                      | ~ memberP(X4,X11)
                                      | ~ geq(X11,X8) ) ) ) ) )
                    | ( neq(X2,nil)
                      & ~ neq(X4,nil) ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[33]) ).

fof(169,negated_conjecture,
    ? [X12] :
      ( ssList(X12)
      & ? [X13] :
          ( ssList(X13)
          & ? [X14] :
              ( ssList(X14)
              & ? [X15] :
                  ( ssList(X15)
                  & X13 = X15
                  & X12 = X14
                  & ( ( neq(X13,nil)
                      & ! [X16] :
                          ( ~ ssItem(X16)
                          | ! [X17] :
                              ( ~ ssList(X17)
                              | ! [X18] :
                                  ( ~ ssList(X18)
                                  | app(app(X17,cons(X16,nil)),X18) != X13
                                  | app(X17,X18) != X12 ) ) )
                      & ? [X19] :
                          ( ssItem(X19)
                          & ? [X20] :
                              ( ssList(X20)
                              & ? [X21] :
                                  ( ssList(X21)
                                  & app(app(X20,cons(X19,nil)),X21) = X15
                                  & app(X20,X21) = X14
                                  & ! [X22] :
                                      ( ~ ssItem(X22)
                                      | X19 = X22
                                      | ~ memberP(X15,X22)
                                      | ~ geq(X22,X19) ) ) ) ) )
                    | ( neq(X13,nil)
                      & ~ neq(X15,nil) ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[168]) ).

fof(170,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ( ( neq(esk8_0,nil)
        & ! [X16] :
            ( ~ ssItem(X16)
            | ! [X17] :
                ( ~ ssList(X17)
                | ! [X18] :
                    ( ~ ssList(X18)
                    | app(app(X17,cons(X16,nil)),X18) != esk8_0
                    | app(X17,X18) != esk7_0 ) ) )
        & ssItem(esk11_0)
        & ssList(esk12_0)
        & ssList(esk13_0)
        & app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
        & app(esk12_0,esk13_0) = esk9_0
        & ! [X22] :
            ( ~ ssItem(X22)
            | esk11_0 = X22
            | ~ memberP(esk10_0,X22)
            | ~ geq(X22,esk11_0) ) )
      | ( neq(esk8_0,nil)
        & ~ neq(esk10_0,nil) ) ) ),
    inference(skolemize,[status(esa)],[169]) ).

fof(171,negated_conjecture,
    ! [X16,X17,X18,X22] :
      ( ( ( ( ~ ssItem(X22)
            | esk11_0 = X22
            | ~ memberP(esk10_0,X22)
            | ~ geq(X22,esk11_0) )
          & app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
          & app(esk12_0,esk13_0) = esk9_0
          & ssList(esk13_0)
          & ssList(esk12_0)
          & ssItem(esk11_0)
          & ( ~ ssList(X18)
            | app(app(X17,cons(X16,nil)),X18) != esk8_0
            | app(X17,X18) != esk7_0
            | ~ ssList(X17)
            | ~ ssItem(X16) )
          & neq(esk8_0,nil) )
        | ( neq(esk8_0,nil)
          & ~ neq(esk10_0,nil) ) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(shift_quantors,[status(thm)],[170]) ).

fof(172,negated_conjecture,
    ! [X16,X17,X18,X22] :
      ( ( neq(esk8_0,nil)
        | ~ ssItem(X22)
        | esk11_0 = X22
        | ~ memberP(esk10_0,X22)
        | ~ geq(X22,esk11_0) )
      & ( ~ neq(esk10_0,nil)
        | ~ ssItem(X22)
        | esk11_0 = X22
        | ~ memberP(esk10_0,X22)
        | ~ geq(X22,esk11_0) )
      & ( neq(esk8_0,nil)
        | app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0 )
      & ( ~ neq(esk10_0,nil)
        | app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0 )
      & ( neq(esk8_0,nil)
        | app(esk12_0,esk13_0) = esk9_0 )
      & ( ~ neq(esk10_0,nil)
        | app(esk12_0,esk13_0) = esk9_0 )
      & ( neq(esk8_0,nil)
        | ssList(esk13_0) )
      & ( ~ neq(esk10_0,nil)
        | ssList(esk13_0) )
      & ( neq(esk8_0,nil)
        | ssList(esk12_0) )
      & ( ~ neq(esk10_0,nil)
        | ssList(esk12_0) )
      & ( neq(esk8_0,nil)
        | ssItem(esk11_0) )
      & ( ~ neq(esk10_0,nil)
        | ssItem(esk11_0) )
      & ( neq(esk8_0,nil)
        | ~ ssList(X18)
        | app(app(X17,cons(X16,nil)),X18) != esk8_0
        | app(X17,X18) != esk7_0
        | ~ ssList(X17)
        | ~ ssItem(X16) )
      & ( ~ neq(esk10_0,nil)
        | ~ ssList(X18)
        | app(app(X17,cons(X16,nil)),X18) != esk8_0
        | app(X17,X18) != esk7_0
        | ~ ssList(X17)
        | ~ ssItem(X16) )
      & ( neq(esk8_0,nil)
        | neq(esk8_0,nil) )
      & ( ~ neq(esk10_0,nil)
        | neq(esk8_0,nil) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[171]) ).

cnf(177,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(178,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(180,negated_conjecture,
    ( neq(esk8_0,nil)
    | neq(esk8_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(181,negated_conjecture,
    ( ~ ssItem(X1)
    | ~ ssList(X2)
    | app(X2,X3) != esk7_0
    | app(app(X2,cons(X1,nil)),X3) != esk8_0
    | ~ ssList(X3)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(183,negated_conjecture,
    ( ssItem(esk11_0)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(185,negated_conjecture,
    ( ssList(esk12_0)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(187,negated_conjecture,
    ( ssList(esk13_0)
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(189,negated_conjecture,
    ( app(esk12_0,esk13_0) = esk9_0
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(191,negated_conjecture,
    ( app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
    | ~ neq(esk10_0,nil) ),
    inference(split_conjunct,[status(thm)],[172]) ).

cnf(198,negated_conjecture,
    neq(esk10_0,nil),
    inference(rw,[status(thm)],[180,178,theory(equality)]) ).

cnf(202,negated_conjecture,
    ( ssItem(esk11_0)
    | $false ),
    inference(rw,[status(thm)],[183,198,theory(equality)]) ).

cnf(203,negated_conjecture,
    ssItem(esk11_0),
    inference(cn,[status(thm)],[202,theory(equality)]) ).

cnf(204,negated_conjecture,
    ( ssList(esk12_0)
    | $false ),
    inference(rw,[status(thm)],[185,198,theory(equality)]) ).

cnf(205,negated_conjecture,
    ssList(esk12_0),
    inference(cn,[status(thm)],[204,theory(equality)]) ).

cnf(206,negated_conjecture,
    ( ssList(esk13_0)
    | $false ),
    inference(rw,[status(thm)],[187,198,theory(equality)]) ).

cnf(207,negated_conjecture,
    ssList(esk13_0),
    inference(cn,[status(thm)],[206,theory(equality)]) ).

cnf(213,negated_conjecture,
    ( app(esk12_0,esk13_0) = esk7_0
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[189,177,theory(equality)]) ).

cnf(214,negated_conjecture,
    ( app(esk12_0,esk13_0) = esk7_0
    | $false ),
    inference(rw,[status(thm)],[213,198,theory(equality)]) ).

cnf(215,negated_conjecture,
    app(esk12_0,esk13_0) = esk7_0,
    inference(cn,[status(thm)],[214,theory(equality)]) ).

cnf(228,negated_conjecture,
    ( app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0
    | $false ),
    inference(rw,[status(thm)],[191,198,theory(equality)]) ).

cnf(229,negated_conjecture,
    app(app(esk12_0,cons(esk11_0,nil)),esk13_0) = esk10_0,
    inference(cn,[status(thm)],[228,theory(equality)]) ).

cnf(497,negated_conjecture,
    ( app(X2,X3) != esk7_0
    | app(app(X2,cons(X1,nil)),X3) != esk10_0
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | ~ neq(esk10_0,nil) ),
    inference(rw,[status(thm)],[181,178,theory(equality)]) ).

cnf(498,negated_conjecture,
    ( app(X2,X3) != esk7_0
    | app(app(X2,cons(X1,nil)),X3) != esk10_0
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2)
    | $false ),
    inference(rw,[status(thm)],[497,198,theory(equality)]) ).

cnf(499,negated_conjecture,
    ( app(X2,X3) != esk7_0
    | app(app(X2,cons(X1,nil)),X3) != esk10_0
    | ~ ssItem(X1)
    | ~ ssList(X3)
    | ~ ssList(X2) ),
    inference(cn,[status(thm)],[498,theory(equality)]) ).

cnf(500,negated_conjecture,
    ( app(esk12_0,esk13_0) != esk7_0
    | ~ ssList(esk13_0)
    | ~ ssList(esk12_0)
    | ~ ssItem(esk11_0) ),
    inference(spm,[status(thm)],[499,229,theory(equality)]) ).

cnf(508,negated_conjecture,
    ( $false
    | ~ ssList(esk13_0)
    | ~ ssList(esk12_0)
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[500,215,theory(equality)]) ).

cnf(509,negated_conjecture,
    ( $false
    | $false
    | ~ ssList(esk12_0)
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[508,207,theory(equality)]) ).

cnf(510,negated_conjecture,
    ( $false
    | $false
    | $false
    | ~ ssItem(esk11_0) ),
    inference(rw,[status(thm)],[509,205,theory(equality)]) ).

cnf(511,negated_conjecture,
    ( $false
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[510,203,theory(equality)]) ).

cnf(512,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[511,theory(equality)]) ).

cnf(513,negated_conjecture,
    $false,
    512,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC010+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpr_nUuU/sel_SWC010+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC010+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC010+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC010+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
% 
%------------------------------------------------------------------------------