TSTP Solution File: SWC378+1 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : SWC378+1 : TPTP v5.0.0. Released v2.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art02.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 11:40:30 EST 2010

% Result   : Theorem 0.30s
% Output   : CNFRefutation 0.30s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   48
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   72 (  15 unt;   0 def)
%            Number of atoms       :  335 (  30 equ)
%            Maximal formula atoms :   16 (   4 avg)
%            Number of connectives :  400 ( 137   ~; 197   |;  50   &)
%                                         (   1 <=>;  15  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   19 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :   83 (   0 sgn  36   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
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/tmpgk8LGP/sel_SWC378+1.p_1',ax36) ).

fof(21,conjecture,
    ! [X1] :
      ( ssList(X1)
     => ! [X2] :
          ( ssList(X2)
         => ! [X3] :
              ( ssList(X3)
             => ! [X4] :
                  ( ~ ssList(X4)
                  | X2 != X4
                  | X1 != X3
                  | ! [X5] :
                      ( ssList(X5)
                     => ! [X6] :
                          ( ~ ssList(X6)
                          | app(X5,X6) != X4
                          | app(X6,X5) != X3 ) )
                  | ! [X7] :
                      ( ~ ssItem(X7)
                      | ( ~ memberP(X2,X7)
                        & ~ memberP(X1,X7) )
                      | ( memberP(X2,X7)
                        & memberP(X1,X7) ) ) ) ) ) ),
    file('/tmp/tmpgk8LGP/sel_SWC378+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] :
                        ( ssList(X5)
                       => ! [X6] :
                            ( ~ ssList(X6)
                            | app(X5,X6) != X4
                            | app(X6,X5) != X3 ) )
                    | ! [X7] :
                        ( ~ ssItem(X7)
                        | ( ~ memberP(X2,X7)
                          & ~ memberP(X1,X7) )
                        | ( memberP(X2,X7)
                          & memberP(X1,X7) ) ) ) ) ) ),
    inference(assume_negation,[status(cth)],[21]) ).

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

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]) ).

cnf(90,plain,
    ( memberP(X3,X1)
    | memberP(X2,X1)
    | ~ ssItem(X1)
    | ~ ssList(X2)
    | ~ ssList(X3)
    | ~ memberP(app(X2,X3),X1) ),
    inference(split_conjunct,[status(thm)],[87]) ).

fof(119,negated_conjecture,
    ? [X1] :
      ( ssList(X1)
      & ? [X2] :
          ( ssList(X2)
          & ? [X3] :
              ( ssList(X3)
              & ? [X4] :
                  ( ssList(X4)
                  & X2 = X4
                  & X1 = X3
                  & ? [X5] :
                      ( ssList(X5)
                      & ? [X6] :
                          ( ssList(X6)
                          & app(X5,X6) = X4
                          & app(X6,X5) = X3 ) )
                  & ? [X7] :
                      ( ssItem(X7)
                      & ( memberP(X2,X7)
                        | memberP(X1,X7) )
                      & ( ~ memberP(X2,X7)
                        | ~ memberP(X1,X7) ) ) ) ) ) ),
    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] :
                      ( ssList(X12)
                      & ? [X13] :
                          ( ssList(X13)
                          & app(X12,X13) = X11
                          & app(X13,X12) = X10 ) )
                  & ? [X14] :
                      ( ssItem(X14)
                      & ( memberP(X9,X14)
                        | memberP(X8,X14) )
                      & ( ~ memberP(X9,X14)
                        | ~ memberP(X8,X14) ) ) ) ) ) ),
    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
    & ssList(esk11_0)
    & ssList(esk12_0)
    & app(esk11_0,esk12_0) = esk10_0
    & app(esk12_0,esk11_0) = esk9_0
    & ssItem(esk13_0)
    & ( memberP(esk8_0,esk13_0)
      | memberP(esk7_0,esk13_0) )
    & ( ~ memberP(esk8_0,esk13_0)
      | ~ memberP(esk7_0,esk13_0) ) ),
    inference(skolemize,[status(esa)],[120]) ).

cnf(122,negated_conjecture,
    ( ~ memberP(esk7_0,esk13_0)
    | ~ memberP(esk8_0,esk13_0) ),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(123,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | memberP(esk8_0,esk13_0) ),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(124,negated_conjecture,
    ssItem(esk13_0),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(125,negated_conjecture,
    app(esk12_0,esk11_0) = esk9_0,
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(126,negated_conjecture,
    app(esk11_0,esk12_0) = esk10_0,
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(127,negated_conjecture,
    ssList(esk12_0),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(128,negated_conjecture,
    ssList(esk11_0),
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(129,negated_conjecture,
    esk7_0 = esk9_0,
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(130,negated_conjecture,
    esk8_0 = esk10_0,
    inference(split_conjunct,[status(thm)],[121]) ).

cnf(139,negated_conjecture,
    app(esk11_0,esk12_0) = esk8_0,
    inference(rw,[status(thm)],[126,130,theory(equality)]) ).

cnf(140,negated_conjecture,
    app(esk12_0,esk11_0) = esk7_0,
    inference(rw,[status(thm)],[125,129,theory(equality)]) ).

cnf(271,negated_conjecture,
    ( memberP(esk11_0,X1)
    | memberP(esk12_0,X1)
    | ~ memberP(esk8_0,X1)
    | ~ ssList(esk12_0)
    | ~ ssList(esk11_0)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[90,139,theory(equality)]) ).

cnf(272,negated_conjecture,
    ( memberP(esk12_0,X1)
    | memberP(esk11_0,X1)
    | ~ memberP(esk7_0,X1)
    | ~ ssList(esk11_0)
    | ~ ssList(esk12_0)
    | ~ ssItem(X1) ),
    inference(spm,[status(thm)],[90,140,theory(equality)]) ).

cnf(276,negated_conjecture,
    ( memberP(esk11_0,X1)
    | memberP(esk12_0,X1)
    | ~ memberP(esk8_0,X1)
    | $false
    | ~ ssList(esk11_0)
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[271,127,theory(equality)]) ).

cnf(277,negated_conjecture,
    ( memberP(esk11_0,X1)
    | memberP(esk12_0,X1)
    | ~ memberP(esk8_0,X1)
    | $false
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[276,128,theory(equality)]) ).

cnf(278,negated_conjecture,
    ( memberP(esk11_0,X1)
    | memberP(esk12_0,X1)
    | ~ memberP(esk8_0,X1)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[277,theory(equality)]) ).

cnf(279,negated_conjecture,
    ( memberP(esk12_0,X1)
    | memberP(esk11_0,X1)
    | ~ memberP(esk7_0,X1)
    | $false
    | ~ ssList(esk12_0)
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[272,128,theory(equality)]) ).

cnf(280,negated_conjecture,
    ( memberP(esk12_0,X1)
    | memberP(esk11_0,X1)
    | ~ memberP(esk7_0,X1)
    | $false
    | $false
    | ~ ssItem(X1) ),
    inference(rw,[status(thm)],[279,127,theory(equality)]) ).

cnf(281,negated_conjecture,
    ( memberP(esk12_0,X1)
    | memberP(esk11_0,X1)
    | ~ memberP(esk7_0,X1)
    | ~ ssItem(X1) ),
    inference(cn,[status(thm)],[280,theory(equality)]) ).

cnf(643,negated_conjecture,
    ( memberP(esk12_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | memberP(esk7_0,esk13_0)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[278,123,theory(equality)]) ).

cnf(644,negated_conjecture,
    ( memberP(esk12_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | memberP(esk7_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[643,124,theory(equality)]) ).

cnf(645,negated_conjecture,
    ( memberP(esk12_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | memberP(esk7_0,esk13_0) ),
    inference(cn,[status(thm)],[644,theory(equality)]) ).

cnf(649,negated_conjecture,
    ( memberP(app(esk12_0,X1),esk13_0)
    | memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(X1)
    | ~ ssList(esk12_0)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[89,645,theory(equality)]) ).

cnf(661,negated_conjecture,
    ( memberP(app(esk12_0,X1),esk13_0)
    | memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(X1)
    | $false
    | ~ ssItem(esk13_0) ),
    inference(rw,[status(thm)],[649,127,theory(equality)]) ).

cnf(662,negated_conjecture,
    ( memberP(app(esk12_0,X1),esk13_0)
    | memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[661,124,theory(equality)]) ).

cnf(663,negated_conjecture,
    ( memberP(app(esk12_0,X1),esk13_0)
    | memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[662,theory(equality)]) ).

cnf(753,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(esk11_0) ),
    inference(spm,[status(thm)],[663,140,theory(equality)]) ).

cnf(762,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[753,128,theory(equality)]) ).

cnf(763,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | memberP(esk11_0,esk13_0) ),
    inference(cn,[status(thm)],[762,theory(equality)]) ).

cnf(784,negated_conjecture,
    ( memberP(app(X1,esk11_0),esk13_0)
    | memberP(esk7_0,esk13_0)
    | ~ ssList(esk11_0)
    | ~ ssList(X1)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[88,763,theory(equality)]) ).

cnf(794,negated_conjecture,
    ( memberP(app(X1,esk11_0),esk13_0)
    | memberP(esk7_0,esk13_0)
    | $false
    | ~ ssList(X1)
    | ~ ssItem(esk13_0) ),
    inference(rw,[status(thm)],[784,128,theory(equality)]) ).

cnf(795,negated_conjecture,
    ( memberP(app(X1,esk11_0),esk13_0)
    | memberP(esk7_0,esk13_0)
    | $false
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[794,124,theory(equality)]) ).

cnf(796,negated_conjecture,
    ( memberP(app(X1,esk11_0),esk13_0)
    | memberP(esk7_0,esk13_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[795,theory(equality)]) ).

cnf(814,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[796,140,theory(equality)]) ).

cnf(825,negated_conjecture,
    ( memberP(esk7_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[814,127,theory(equality)]) ).

cnf(826,negated_conjecture,
    memberP(esk7_0,esk13_0),
    inference(cn,[status(thm)],[825,theory(equality)]) ).

cnf(855,negated_conjecture,
    ( memberP(esk11_0,esk13_0)
    | memberP(esk12_0,esk13_0)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[281,826,theory(equality)]) ).

cnf(865,negated_conjecture,
    ( $false
    | ~ memberP(esk8_0,esk13_0) ),
    inference(rw,[status(thm)],[122,826,theory(equality)]) ).

cnf(866,negated_conjecture,
    ~ memberP(esk8_0,esk13_0),
    inference(cn,[status(thm)],[865,theory(equality)]) ).

cnf(886,negated_conjecture,
    ( memberP(esk11_0,esk13_0)
    | memberP(esk12_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[855,124,theory(equality)]) ).

cnf(887,negated_conjecture,
    ( memberP(esk11_0,esk13_0)
    | memberP(esk12_0,esk13_0) ),
    inference(cn,[status(thm)],[886,theory(equality)]) ).

cnf(916,negated_conjecture,
    ( memberP(app(X1,esk12_0),esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(esk12_0)
    | ~ ssList(X1)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[88,887,theory(equality)]) ).

cnf(926,negated_conjecture,
    ( memberP(app(X1,esk12_0),esk13_0)
    | memberP(esk11_0,esk13_0)
    | $false
    | ~ ssList(X1)
    | ~ ssItem(esk13_0) ),
    inference(rw,[status(thm)],[916,127,theory(equality)]) ).

cnf(927,negated_conjecture,
    ( memberP(app(X1,esk12_0),esk13_0)
    | memberP(esk11_0,esk13_0)
    | $false
    | ~ ssList(X1)
    | $false ),
    inference(rw,[status(thm)],[926,124,theory(equality)]) ).

cnf(928,negated_conjecture,
    ( memberP(app(X1,esk12_0),esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[927,theory(equality)]) ).

cnf(1068,negated_conjecture,
    ( memberP(esk8_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | ~ ssList(esk11_0) ),
    inference(spm,[status(thm)],[928,139,theory(equality)]) ).

cnf(1079,negated_conjecture,
    ( memberP(esk8_0,esk13_0)
    | memberP(esk11_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[1068,128,theory(equality)]) ).

cnf(1080,negated_conjecture,
    ( memberP(esk8_0,esk13_0)
    | memberP(esk11_0,esk13_0) ),
    inference(cn,[status(thm)],[1079,theory(equality)]) ).

cnf(1081,negated_conjecture,
    memberP(esk11_0,esk13_0),
    inference(sr,[status(thm)],[1080,866,theory(equality)]) ).

cnf(1107,negated_conjecture,
    ( memberP(app(esk11_0,X1),esk13_0)
    | ~ ssList(X1)
    | ~ ssList(esk11_0)
    | ~ ssItem(esk13_0) ),
    inference(spm,[status(thm)],[89,1081,theory(equality)]) ).

cnf(1123,negated_conjecture,
    ( memberP(app(esk11_0,X1),esk13_0)
    | ~ ssList(X1)
    | $false
    | ~ ssItem(esk13_0) ),
    inference(rw,[status(thm)],[1107,128,theory(equality)]) ).

cnf(1124,negated_conjecture,
    ( memberP(app(esk11_0,X1),esk13_0)
    | ~ ssList(X1)
    | $false
    | $false ),
    inference(rw,[status(thm)],[1123,124,theory(equality)]) ).

cnf(1125,negated_conjecture,
    ( memberP(app(esk11_0,X1),esk13_0)
    | ~ ssList(X1) ),
    inference(cn,[status(thm)],[1124,theory(equality)]) ).

cnf(1170,negated_conjecture,
    ( memberP(esk8_0,esk13_0)
    | ~ ssList(esk12_0) ),
    inference(spm,[status(thm)],[1125,139,theory(equality)]) ).

cnf(1179,negated_conjecture,
    ( memberP(esk8_0,esk13_0)
    | $false ),
    inference(rw,[status(thm)],[1170,127,theory(equality)]) ).

cnf(1180,negated_conjecture,
    memberP(esk8_0,esk13_0),
    inference(cn,[status(thm)],[1179,theory(equality)]) ).

cnf(1181,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[1180,866,theory(equality)]) ).

cnf(1182,negated_conjecture,
    $false,
    1181,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/SWC/SWC378+1.p
% --creating new selector for [SWC001+0.ax]
% -running prover on /tmp/tmpgk8LGP/sel_SWC378+1.p_1 with time limit 29
% -prover status Theorem
% Problem SWC378+1.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/SWC/SWC378+1.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/SWC/SWC378+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
% 
%------------------------------------------------------------------------------