TSTP Solution File: SWC198+1 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC198+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art03.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 10:47:40 EST 2010

% Result   : Theorem 0.28s
% Output   : CNFRefutation 0.28s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   47 (   8 unt;   0 def)
%            Number of atoms       :  306 ( 100 equ)
%            Maximal formula atoms :   34 (   6 avg)
%            Number of connectives :  389 ( 130   ~; 138   |;  97   &)
%                                         (   1 <=>;  23  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Maximal term depth    :    2 (   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   :   88 (   1 sgn  47   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(12,axiom,
    ? [X1] :
      ( ssItem(X1)
      & ? [X2] :
          ( ssItem(X2)
          & X1 != X2 ) ),
    file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax2) ).

fof(16,axiom,
    ssList(nil),
    file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax17) ).

fof(18,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ! [X2] :
          ( ssItem(X2)
         => ! [X3] :
              ( ssList(X3)
             => ( memberP(cons(X2,X3),X1)
              <=> ( X1 = X2
                  | memberP(X3,X1) ) ) ) ) ),
    file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax37) ).

fof(19,axiom,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',ax38) ).

fof(24,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ssList(X4)
                 => ( X2 != X4
                    | X1 != X3
                    | ? [X5] :
                        ( ssItem(X5)
                        & ! [X6] :
                            ( ssItem(X6)
                           => ( ~ memberP(X1,X6)
                              | X5 = X6 ) ) )
                    | ( ! [X7] :
                          ( ssItem(X7)
                         => ( cons(X7,nil) != X3
                            | ~ memberP(X4,X7)
                            | ? [X8] :
                                ( ssItem(X8)
                                & X7 != X8
                                & memberP(X4,X8)
                                & leq(X7,X8) ) ) )
                      & ( nil != X4
                        | nil != X3 ) ) ) ) ) ) ),
    file('/tmp/tmpb1vMvR/sel_SWC198+1.p_1',co1) ).

fof(25,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ! [X6] :
                              ( ssItem(X6)
                             => ( ~ memberP(X1,X6)
                                | X5 = X6 ) ) )
                      | ( ! [X7] :
                            ( ssItem(X7)
                           => ( cons(X7,nil) != X3
                              | ~ memberP(X4,X7)
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & X7 != X8
                                  & memberP(X4,X8)
                                  & leq(X7,X8) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[24]) ).

fof(26,plain,
    ! [X1] :
      ( ssItem(X1)
     => ~ memberP(nil,X1) ),
    inference(fof_simplification,[status(thm)],[19,theory(equality)]) ).

fof(27,negated_conjecture,
    ~ ! [X1] :
        ( ssList(X1)
       => ! [X2] :
            ( ssList(X2)
           => ! [X3] :
                ( ssList(X3)
               => ! [X4] :
                    ( ssList(X4)
                   => ( X2 != X4
                      | X1 != X3
                      | ? [X5] :
                          ( ssItem(X5)
                          & ! [X6] :
                              ( ssItem(X6)
                             => ( ~ memberP(X1,X6)
                                | X5 = X6 ) ) )
                      | ( ! [X7] :
                            ( ssItem(X7)
                           => ( cons(X7,nil) != X3
                              | ~ memberP(X4,X7)
                              | ? [X8] :
                                  ( ssItem(X8)
                                  & X7 != X8
                                  & memberP(X4,X8)
                                  & leq(X7,X8) ) ) )
                        & ( nil != X4
                          | nil != X3 ) ) ) ) ) ) ),
    inference(fof_simplification,[status(thm)],[25,theory(equality)]) ).

fof(76,plain,
    ? [X3] :
      ( ssItem(X3)
      & ? [X4] :
          ( ssItem(X4)
          & X3 != X4 ) ),
    inference(variable_rename,[status(thm)],[12]) ).

fof(77,plain,
    ( ssItem(esk3_0)
    & ssItem(esk4_0)
    & esk3_0 != esk4_0 ),
    inference(skolemize,[status(esa)],[76]) ).

cnf(80,plain,
    ssItem(esk3_0),
    inference(split_conjunct,[status(thm)],[77]) ).

cnf(98,plain,
    ssList(nil),
    inference(split_conjunct,[status(thm)],[16]) ).

fof(106,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)],[18]) ).

fof(107,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)],[106]) ).

fof(108,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)],[107]) ).

fof(109,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)],[108]) ).

cnf(112,plain,
    ( memberP(X3,X1)
    | X1 = X2
    | ~ ssItem(X1)
    | ~ ssItem(X2)
    | ~ ssList(X3)
    | ~ memberP(cons(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[109]) ).

fof(113,plain,
    ! [X1] :
      ( ~ ssItem(X1)
      | ~ memberP(nil,X1) ),
    inference(fof_nnf,[status(thm)],[26]) ).

fof(114,plain,
    ! [X2] :
      ( ~ ssItem(X2)
      | ~ memberP(nil,X2) ),
    inference(variable_rename,[status(thm)],[113]) ).

cnf(115,plain,
    ( ~ memberP(nil,X1)
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[114]) ).

fof(133,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ! [X5] :
                      ( ~ ssItem(X5)
                      | ? [X6] :
                          ( ssItem(X6)
                          & memberP(X1,X6)
                          & X5 != X6 ) )
                  & ( ? [X7] :
                        ( ssItem(X7)
                        & cons(X7,nil) = X3
                        & memberP(X4,X7)
                        & ! [X8] :
                            ( ~ ssItem(X8)
                            | X7 = X8
                            | ~ memberP(X4,X8)
                            | ~ leq(X7,X8) ) )
                    | ( nil = X4
                      & nil = X3 ) ) ) ) ) ),
    inference(fof_nnf,[status(thm)],[27]) ).

fof(134,negated_conjecture,
    ? [X9] :
      ( ssList(X9)
      & ? [X10] :
          ( ssList(X10)
          & ? [X11] :
              ( ssList(X11)
              & ? [X12] :
                  ( ssList(X12)
                  & X10 = X12
                  & X9 = X11
                  & ! [X13] :
                      ( ~ ssItem(X13)
                      | ? [X14] :
                          ( ssItem(X14)
                          & memberP(X9,X14)
                          & X13 != X14 ) )
                  & ( ? [X15] :
                        ( ssItem(X15)
                        & cons(X15,nil) = X11
                        & memberP(X12,X15)
                        & ! [X16] :
                            ( ~ ssItem(X16)
                            | X15 = X16
                            | ~ memberP(X12,X16)
                            | ~ leq(X15,X16) ) )
                    | ( nil = X12
                      & nil = X11 ) ) ) ) ) ),
    inference(variable_rename,[status(thm)],[133]) ).

fof(135,negated_conjecture,
    ( ssList(esk7_0)
    & ssList(esk8_0)
    & ssList(esk9_0)
    & ssList(esk10_0)
    & esk8_0 = esk10_0
    & esk7_0 = esk9_0
    & ! [X13] :
        ( ~ ssItem(X13)
        | ( ssItem(esk11_1(X13))
          & memberP(esk7_0,esk11_1(X13))
          & X13 != esk11_1(X13) ) )
    & ( ( ssItem(esk12_0)
        & cons(esk12_0,nil) = esk9_0
        & memberP(esk10_0,esk12_0)
        & ! [X16] :
            ( ~ ssItem(X16)
            | esk12_0 = X16
            | ~ memberP(esk10_0,X16)
            | ~ leq(esk12_0,X16) ) )
      | ( nil = esk10_0
        & nil = esk9_0 ) ) ),
    inference(skolemize,[status(esa)],[134]) ).

fof(136,negated_conjecture,
    ! [X13,X16] :
      ( ( ( ( ~ ssItem(X16)
            | esk12_0 = X16
            | ~ memberP(esk10_0,X16)
            | ~ leq(esk12_0,X16) )
          & cons(esk12_0,nil) = esk9_0
          & memberP(esk10_0,esk12_0)
          & ssItem(esk12_0) )
        | ( nil = esk10_0
          & nil = esk9_0 ) )
      & ( ~ ssItem(X13)
        | ( ssItem(esk11_1(X13))
          & memberP(esk7_0,esk11_1(X13))
          & X13 != esk11_1(X13) ) )
      & 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)],[135]) ).

fof(137,negated_conjecture,
    ! [X13,X16] :
      ( ( nil = esk10_0
        | ~ ssItem(X16)
        | esk12_0 = X16
        | ~ memberP(esk10_0,X16)
        | ~ leq(esk12_0,X16) )
      & ( nil = esk9_0
        | ~ ssItem(X16)
        | esk12_0 = X16
        | ~ memberP(esk10_0,X16)
        | ~ leq(esk12_0,X16) )
      & ( 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_1(X13))
        | ~ ssItem(X13) )
      & ( memberP(esk7_0,esk11_1(X13))
        | ~ ssItem(X13) )
      & ( X13 != esk11_1(X13)
        | ~ ssItem(X13) )
      & esk8_0 = esk10_0
      & esk7_0 = esk9_0
      & ssList(esk10_0)
      & ssList(esk9_0)
      & ssList(esk8_0)
      & ssList(esk7_0) ),
    inference(distribute,[status(thm)],[136]) ).

cnf(142,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(144,negated_conjecture,
    ( ~ ssItem(X1)
    | X1 != esk11_1(X1) ),
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(145,negated_conjecture,
    ( memberP(esk7_0,esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(146,negated_conjecture,
    ( ssItem(esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(147,negated_conjecture,
    ( ssItem(esk12_0)
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(151,negated_conjecture,
    ( cons(esk12_0,nil) = esk9_0
    | nil = esk9_0 ),
    inference(split_conjunct,[status(thm)],[137]) ).

cnf(157,negated_conjecture,
    ( memberP(esk9_0,esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[145,142,theory(equality)]) ).

cnf(231,negated_conjecture,
    ( X1 = esk12_0
    | memberP(nil,X1)
    | esk9_0 = nil
    | ~ memberP(esk9_0,X1)
    | ~ ssItem(esk12_0)
    | ~ ssItem(X1)
    | ~ ssList(nil) ),
    inference(spm,[status(thm)],[112,151,theory(equality)]) ).

cnf(234,negated_conjecture,
    ( X1 = esk12_0
    | memberP(nil,X1)
    | esk9_0 = nil
    | ~ memberP(esk9_0,X1)
    | ~ ssItem(esk12_0)
    | ~ ssItem(X1)
    | $false ),
    inference(rw,[status(thm)],[231,98,theory(equality)]) ).

cnf(235,negated_conjecture,
    ( X1 = esk12_0
    | memberP(nil,X1)
    | esk9_0 = nil
    | ~ memberP(esk9_0,X1)
    | ~ ssItem(esk12_0)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[234,theory(equality)]) ).

cnf(641,negated_conjecture,
    ( esk9_0 = nil
    | X1 = esk12_0
    | memberP(nil,X1)
    | ~ memberP(esk9_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[235,147]) ).

cnf(642,negated_conjecture,
    ( esk9_0 = nil
    | X1 = esk12_0
    | ~ memberP(esk9_0,X1)
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[641,115]) ).

cnf(643,negated_conjecture,
    ( esk9_0 = nil
    | esk11_1(X1) = esk12_0
    | ~ ssItem(esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[642,157,theory(equality)]) ).

cnf(663,negated_conjecture,
    ( esk11_1(X1) = esk12_0
    | esk9_0 = nil
    | ~ ssItem(X1) ),
    inference(csr,[status(thm)],[643,146]) ).

cnf(665,negated_conjecture,
    ( esk9_0 = nil
    | esk12_0 != X1
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[144,663,theory(equality)]) ).

cnf(671,negated_conjecture,
    ( esk9_0 = nil
    | ~ ssItem(esk12_0) ),
    inference(er,[status(thm)],[665,theory(equality)]) ).

cnf(672,negated_conjecture,
    esk9_0 = nil,
    inference(csr,[status(thm)],[671,147]) ).

cnf(717,negated_conjecture,
    ( memberP(nil,esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[157,672,theory(equality)]) ).

cnf(740,negated_conjecture,
    ( ~ ssItem(esk11_1(X1))
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[115,717,theory(equality)]) ).

cnf(768,negated_conjecture,
    ~ ssItem(X1),
    inference(csr,[status(thm)],[740,146]) ).

cnf(771,plain,
    $false,
    inference(sr,[status(thm)],[80,768,theory(equality)]) ).

cnf(772,plain,
    $false,
    771,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC198+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpb1vMvR/sel_SWC198+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC198+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC198+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC198+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
% 
%------------------------------------------------------------------------------