TSTP Solution File: COM018+4 by SInE---0.4

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%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : COM018+4 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art09.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 : Sat Dec 25 05:48:13 EST 2010

% Result   : Theorem 0.24s
% Output   : CNFRefutation 0.24s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   34 (   7 unt;   0 def)
%            Number of atoms       :  437 (  39 equ)
%            Maximal formula atoms :   96 (  12 avg)
%            Number of connectives :  591 ( 188   ~; 229   |; 169   &)
%                                         (   0 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   9 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-3 aty)
%            Number of variables   :   83 (   1 sgn  55   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(4,axiom,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ? [X1] :
              ( aElement0(X1)
              & aReductOfIn0(X1,xu,xR)
              & sdtmndtplgtdt0(X1,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ? [X1] :
              ( aElement0(X1)
              & aReductOfIn0(X1,xv,xR)
              & sdtmndtplgtdt0(X1,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    file('/tmp/tmpy89yu7/sel_COM018+4.p_1',m__799) ).

fof(5,axiom,
    aRewritingSystem0(xR),
    file('/tmp/tmpy89yu7/sel_COM018+4.p_1',m__656) ).

fof(7,axiom,
    ! [X1] :
      ( ( aRewritingSystem0(X1)
        & isTerminating0(X1) )
     => ! [X2] :
          ( aElement0(X2)
         => ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
    file('/tmp/tmpy89yu7/sel_COM018+4.p_1',mTermNF) ).

fof(12,conjecture,
    ? [X1] :
      ( ( aElement0(X1)
        & ( xw = X1
          | aReductOfIn0(X1,xw,xR)
          | ? [X2] :
              ( aElement0(X2)
              & aReductOfIn0(X2,xw,xR)
              & sdtmndtplgtdt0(X2,xR,X1) )
          | sdtmndtplgtdt0(xw,xR,X1)
          | sdtmndtasgtdt0(xw,xR,X1) )
        & ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
      | aNormalFormOfIn0(X1,xw,xR) ),
    file('/tmp/tmpy89yu7/sel_COM018+4.p_1',m__) ).

fof(21,axiom,
    ( ! [X1,X2,X3] :
        ( ( aElement0(X1)
          & aElement0(X2)
          & aElement0(X3)
          & aReductOfIn0(X2,X1,xR)
          & aReductOfIn0(X3,X1,xR) )
       => ? [X4] :
            ( aElement0(X4)
            & ( X2 = X4
              | ( ( aReductOfIn0(X4,X2,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X2,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X2,xR,X4) ) )
            & sdtmndtasgtdt0(X2,xR,X4)
            & ( X3 = X4
              | ( ( aReductOfIn0(X4,X3,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X3,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X3,xR,X4) ) )
            & sdtmndtasgtdt0(X3,xR,X4) ) )
    & isLocallyConfluent0(xR)
    & ! [X1,X2] :
        ( ( aElement0(X1)
          & aElement0(X2) )
       => ( ( aReductOfIn0(X2,X1,xR)
            | ? [X3] :
                ( aElement0(X3)
                & aReductOfIn0(X3,X1,xR)
                & sdtmndtplgtdt0(X3,xR,X2) )
            | sdtmndtplgtdt0(X1,xR,X2) )
         => iLess0(X2,X1) ) )
    & isTerminating0(xR) ),
    file('/tmp/tmpy89yu7/sel_COM018+4.p_1',m__656_01) ).

fof(24,negated_conjecture,
    ~ ? [X1] :
        ( ( aElement0(X1)
          & ( xw = X1
            | aReductOfIn0(X1,xw,xR)
            | ? [X2] :
                ( aElement0(X2)
                & aReductOfIn0(X2,xw,xR)
                & sdtmndtplgtdt0(X2,xR,X1) )
            | sdtmndtplgtdt0(xw,xR,X1)
            | sdtmndtasgtdt0(xw,xR,X1) )
          & ~ ? [X2] : aReductOfIn0(X2,X1,xR) )
        | aNormalFormOfIn0(X1,xw,xR) ),
    inference(assume_negation,[status(cth)],[12]) ).

fof(322,plain,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ? [X2] :
              ( aElement0(X2)
              & aReductOfIn0(X2,xu,xR)
              & sdtmndtplgtdt0(X2,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ? [X3] :
              ( aElement0(X3)
              & aReductOfIn0(X3,xv,xR)
              & sdtmndtplgtdt0(X3,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(variable_rename,[status(thm)],[4]) ).

fof(323,plain,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ( aElement0(esk8_0)
            & aReductOfIn0(esk8_0,xu,xR)
            & sdtmndtplgtdt0(esk8_0,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ( aElement0(esk9_0)
            & aReductOfIn0(esk9_0,xv,xR)
            & sdtmndtplgtdt0(esk9_0,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(skolemize,[status(esa)],[322]) ).

fof(324,plain,
    ( aElement0(xw)
    & ( aElement0(esk8_0)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( aReductOfIn0(esk8_0,xu,xR)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( sdtmndtplgtdt0(esk8_0,xR,xw)
      | aReductOfIn0(xw,xu,xR)
      | xu = xw )
    & ( sdtmndtplgtdt0(xu,xR,xw)
      | xu = xw )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( aElement0(esk9_0)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( aReductOfIn0(esk9_0,xv,xR)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( sdtmndtplgtdt0(esk9_0,xR,xw)
      | aReductOfIn0(xw,xv,xR)
      | xv = xw )
    & ( sdtmndtplgtdt0(xv,xR,xw)
      | xv = xw )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(distribute,[status(thm)],[323]) ).

cnf(335,plain,
    aElement0(xw),
    inference(split_conjunct,[status(thm)],[324]) ).

cnf(336,plain,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[5]) ).

fof(341,plain,
    ! [X1] :
      ( ~ aRewritingSystem0(X1)
      | ~ isTerminating0(X1)
      | ! [X2] :
          ( ~ aElement0(X2)
          | ? [X3] : aNormalFormOfIn0(X3,X2,X1) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(342,plain,
    ! [X4] :
      ( ~ aRewritingSystem0(X4)
      | ~ isTerminating0(X4)
      | ! [X5] :
          ( ~ aElement0(X5)
          | ? [X6] : aNormalFormOfIn0(X6,X5,X4) ) ),
    inference(variable_rename,[status(thm)],[341]) ).

fof(343,plain,
    ! [X4] :
      ( ~ aRewritingSystem0(X4)
      | ~ isTerminating0(X4)
      | ! [X5] :
          ( ~ aElement0(X5)
          | aNormalFormOfIn0(esk10_2(X4,X5),X5,X4) ) ),
    inference(skolemize,[status(esa)],[342]) ).

fof(344,plain,
    ! [X4,X5] :
      ( ~ aElement0(X5)
      | aNormalFormOfIn0(esk10_2(X4,X5),X5,X4)
      | ~ aRewritingSystem0(X4)
      | ~ isTerminating0(X4) ),
    inference(shift_quantors,[status(thm)],[343]) ).

cnf(345,plain,
    ( aNormalFormOfIn0(esk10_2(X1,X2),X2,X1)
    | ~ isTerminating0(X1)
    | ~ aRewritingSystem0(X1)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[344]) ).

fof(380,negated_conjecture,
    ! [X1] :
      ( ( ~ aElement0(X1)
        | ( xw != X1
          & ~ aReductOfIn0(X1,xw,xR)
          & ! [X2] :
              ( ~ aElement0(X2)
              | ~ aReductOfIn0(X2,xw,xR)
              | ~ sdtmndtplgtdt0(X2,xR,X1) )
          & ~ sdtmndtplgtdt0(xw,xR,X1)
          & ~ sdtmndtasgtdt0(xw,xR,X1) )
        | ? [X2] : aReductOfIn0(X2,X1,xR) )
      & ~ aNormalFormOfIn0(X1,xw,xR) ),
    inference(fof_nnf,[status(thm)],[24]) ).

fof(381,negated_conjecture,
    ! [X3] :
      ( ( ~ aElement0(X3)
        | ( xw != X3
          & ~ aReductOfIn0(X3,xw,xR)
          & ! [X4] :
              ( ~ aElement0(X4)
              | ~ aReductOfIn0(X4,xw,xR)
              | ~ sdtmndtplgtdt0(X4,xR,X3) )
          & ~ sdtmndtplgtdt0(xw,xR,X3)
          & ~ sdtmndtasgtdt0(xw,xR,X3) )
        | ? [X5] : aReductOfIn0(X5,X3,xR) )
      & ~ aNormalFormOfIn0(X3,xw,xR) ),
    inference(variable_rename,[status(thm)],[380]) ).

fof(382,negated_conjecture,
    ! [X3] :
      ( ( ~ aElement0(X3)
        | ( xw != X3
          & ~ aReductOfIn0(X3,xw,xR)
          & ! [X4] :
              ( ~ aElement0(X4)
              | ~ aReductOfIn0(X4,xw,xR)
              | ~ sdtmndtplgtdt0(X4,xR,X3) )
          & ~ sdtmndtplgtdt0(xw,xR,X3)
          & ~ sdtmndtasgtdt0(xw,xR,X3) )
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ~ aNormalFormOfIn0(X3,xw,xR) ),
    inference(skolemize,[status(esa)],[381]) ).

fof(383,negated_conjecture,
    ! [X3,X4] :
      ( ( ( ( ~ aElement0(X4)
            | ~ aReductOfIn0(X4,xw,xR)
            | ~ sdtmndtplgtdt0(X4,xR,X3) )
          & xw != X3
          & ~ aReductOfIn0(X3,xw,xR)
          & ~ sdtmndtplgtdt0(xw,xR,X3)
          & ~ sdtmndtasgtdt0(xw,xR,X3) )
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ~ aNormalFormOfIn0(X3,xw,xR) ),
    inference(shift_quantors,[status(thm)],[382]) ).

fof(384,negated_conjecture,
    ! [X3,X4] :
      ( ( ~ aElement0(X4)
        | ~ aReductOfIn0(X4,xw,xR)
        | ~ sdtmndtplgtdt0(X4,xR,X3)
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ( xw != X3
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ( ~ aReductOfIn0(X3,xw,xR)
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ( ~ sdtmndtplgtdt0(xw,xR,X3)
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ( ~ sdtmndtasgtdt0(xw,xR,X3)
        | ~ aElement0(X3)
        | aReductOfIn0(esk17_1(X3),X3,xR) )
      & ~ aNormalFormOfIn0(X3,xw,xR) ),
    inference(distribute,[status(thm)],[383]) ).

cnf(385,negated_conjecture,
    ~ aNormalFormOfIn0(X1,xw,xR),
    inference(split_conjunct,[status(thm)],[384]) ).

fof(449,plain,
    ( ! [X1,X2,X3] :
        ( ~ aElement0(X1)
        | ~ aElement0(X2)
        | ~ aElement0(X3)
        | ~ aReductOfIn0(X2,X1,xR)
        | ~ aReductOfIn0(X3,X1,xR)
        | ? [X4] :
            ( aElement0(X4)
            & ( X2 = X4
              | ( ( aReductOfIn0(X4,X2,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X2,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X2,xR,X4) ) )
            & sdtmndtasgtdt0(X2,xR,X4)
            & ( X3 = X4
              | ( ( aReductOfIn0(X4,X3,xR)
                  | ? [X5] :
                      ( aElement0(X5)
                      & aReductOfIn0(X5,X3,xR)
                      & sdtmndtplgtdt0(X5,xR,X4) ) )
                & sdtmndtplgtdt0(X3,xR,X4) ) )
            & sdtmndtasgtdt0(X3,xR,X4) ) )
    & isLocallyConfluent0(xR)
    & ! [X1,X2] :
        ( ~ aElement0(X1)
        | ~ aElement0(X2)
        | ( ~ aReductOfIn0(X2,X1,xR)
          & ! [X3] :
              ( ~ aElement0(X3)
              | ~ aReductOfIn0(X3,X1,xR)
              | ~ sdtmndtplgtdt0(X3,xR,X2) )
          & ~ sdtmndtplgtdt0(X1,xR,X2) )
        | iLess0(X2,X1) )
    & isTerminating0(xR) ),
    inference(fof_nnf,[status(thm)],[21]) ).

fof(450,plain,
    ( ! [X6,X7,X8] :
        ( ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR)
        | ? [X9] :
            ( aElement0(X9)
            & ( X7 = X9
              | ( ( aReductOfIn0(X9,X7,xR)
                  | ? [X10] :
                      ( aElement0(X10)
                      & aReductOfIn0(X10,X7,xR)
                      & sdtmndtplgtdt0(X10,xR,X9) ) )
                & sdtmndtplgtdt0(X7,xR,X9) ) )
            & sdtmndtasgtdt0(X7,xR,X9)
            & ( X8 = X9
              | ( ( aReductOfIn0(X9,X8,xR)
                  | ? [X11] :
                      ( aElement0(X11)
                      & aReductOfIn0(X11,X8,xR)
                      & sdtmndtplgtdt0(X11,xR,X9) ) )
                & sdtmndtplgtdt0(X8,xR,X9) ) )
            & sdtmndtasgtdt0(X8,xR,X9) ) )
    & isLocallyConfluent0(xR)
    & ! [X12,X13] :
        ( ~ aElement0(X12)
        | ~ aElement0(X13)
        | ( ~ aReductOfIn0(X13,X12,xR)
          & ! [X14] :
              ( ~ aElement0(X14)
              | ~ aReductOfIn0(X14,X12,xR)
              | ~ sdtmndtplgtdt0(X14,xR,X13) )
          & ~ sdtmndtplgtdt0(X12,xR,X13) )
        | iLess0(X13,X12) )
    & isTerminating0(xR) ),
    inference(variable_rename,[status(thm)],[449]) ).

fof(451,plain,
    ( ! [X6,X7,X8] :
        ( ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR)
        | ( aElement0(esk24_3(X6,X7,X8))
          & ( X7 = esk24_3(X6,X7,X8)
            | ( ( aReductOfIn0(esk24_3(X6,X7,X8),X7,xR)
                | ( aElement0(esk25_3(X6,X7,X8))
                  & aReductOfIn0(esk25_3(X6,X7,X8),X7,xR)
                  & sdtmndtplgtdt0(esk25_3(X6,X7,X8),xR,esk24_3(X6,X7,X8)) ) )
              & sdtmndtplgtdt0(X7,xR,esk24_3(X6,X7,X8)) ) )
          & sdtmndtasgtdt0(X7,xR,esk24_3(X6,X7,X8))
          & ( X8 = esk24_3(X6,X7,X8)
            | ( ( aReductOfIn0(esk24_3(X6,X7,X8),X8,xR)
                | ( aElement0(esk26_3(X6,X7,X8))
                  & aReductOfIn0(esk26_3(X6,X7,X8),X8,xR)
                  & sdtmndtplgtdt0(esk26_3(X6,X7,X8),xR,esk24_3(X6,X7,X8)) ) )
              & sdtmndtplgtdt0(X8,xR,esk24_3(X6,X7,X8)) ) )
          & sdtmndtasgtdt0(X8,xR,esk24_3(X6,X7,X8)) ) )
    & isLocallyConfluent0(xR)
    & ! [X12,X13] :
        ( ~ aElement0(X12)
        | ~ aElement0(X13)
        | ( ~ aReductOfIn0(X13,X12,xR)
          & ! [X14] :
              ( ~ aElement0(X14)
              | ~ aReductOfIn0(X14,X12,xR)
              | ~ sdtmndtplgtdt0(X14,xR,X13) )
          & ~ sdtmndtplgtdt0(X12,xR,X13) )
        | iLess0(X13,X12) )
    & isTerminating0(xR) ),
    inference(skolemize,[status(esa)],[450]) ).

fof(452,plain,
    ! [X6,X7,X8,X12,X13,X14] :
      ( ( ( ( ~ aElement0(X14)
            | ~ aReductOfIn0(X14,X12,xR)
            | ~ sdtmndtplgtdt0(X14,xR,X13) )
          & ~ aReductOfIn0(X13,X12,xR)
          & ~ sdtmndtplgtdt0(X12,xR,X13) )
        | iLess0(X13,X12)
        | ~ aElement0(X12)
        | ~ aElement0(X13) )
      & ( ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR)
        | ( aElement0(esk24_3(X6,X7,X8))
          & ( X7 = esk24_3(X6,X7,X8)
            | ( ( aReductOfIn0(esk24_3(X6,X7,X8),X7,xR)
                | ( aElement0(esk25_3(X6,X7,X8))
                  & aReductOfIn0(esk25_3(X6,X7,X8),X7,xR)
                  & sdtmndtplgtdt0(esk25_3(X6,X7,X8),xR,esk24_3(X6,X7,X8)) ) )
              & sdtmndtplgtdt0(X7,xR,esk24_3(X6,X7,X8)) ) )
          & sdtmndtasgtdt0(X7,xR,esk24_3(X6,X7,X8))
          & ( X8 = esk24_3(X6,X7,X8)
            | ( ( aReductOfIn0(esk24_3(X6,X7,X8),X8,xR)
                | ( aElement0(esk26_3(X6,X7,X8))
                  & aReductOfIn0(esk26_3(X6,X7,X8),X8,xR)
                  & sdtmndtplgtdt0(esk26_3(X6,X7,X8),xR,esk24_3(X6,X7,X8)) ) )
              & sdtmndtplgtdt0(X8,xR,esk24_3(X6,X7,X8)) ) )
          & sdtmndtasgtdt0(X8,xR,esk24_3(X6,X7,X8)) ) )
      & isLocallyConfluent0(xR)
      & isTerminating0(xR) ),
    inference(shift_quantors,[status(thm)],[451]) ).

fof(453,plain,
    ! [X6,X7,X8,X12,X13,X14] :
      ( ( ~ aElement0(X14)
        | ~ aReductOfIn0(X14,X12,xR)
        | ~ sdtmndtplgtdt0(X14,xR,X13)
        | iLess0(X13,X12)
        | ~ aElement0(X12)
        | ~ aElement0(X13) )
      & ( ~ aReductOfIn0(X13,X12,xR)
        | iLess0(X13,X12)
        | ~ aElement0(X12)
        | ~ aElement0(X13) )
      & ( ~ sdtmndtplgtdt0(X12,xR,X13)
        | iLess0(X13,X12)
        | ~ aElement0(X12)
        | ~ aElement0(X13) )
      & ( aElement0(esk24_3(X6,X7,X8))
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( aElement0(esk25_3(X6,X7,X8))
        | aReductOfIn0(esk24_3(X6,X7,X8),X7,xR)
        | X7 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( aReductOfIn0(esk25_3(X6,X7,X8),X7,xR)
        | aReductOfIn0(esk24_3(X6,X7,X8),X7,xR)
        | X7 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtplgtdt0(esk25_3(X6,X7,X8),xR,esk24_3(X6,X7,X8))
        | aReductOfIn0(esk24_3(X6,X7,X8),X7,xR)
        | X7 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtplgtdt0(X7,xR,esk24_3(X6,X7,X8))
        | X7 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtasgtdt0(X7,xR,esk24_3(X6,X7,X8))
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( aElement0(esk26_3(X6,X7,X8))
        | aReductOfIn0(esk24_3(X6,X7,X8),X8,xR)
        | X8 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( aReductOfIn0(esk26_3(X6,X7,X8),X8,xR)
        | aReductOfIn0(esk24_3(X6,X7,X8),X8,xR)
        | X8 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtplgtdt0(esk26_3(X6,X7,X8),xR,esk24_3(X6,X7,X8))
        | aReductOfIn0(esk24_3(X6,X7,X8),X8,xR)
        | X8 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtplgtdt0(X8,xR,esk24_3(X6,X7,X8))
        | X8 = esk24_3(X6,X7,X8)
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & ( sdtmndtasgtdt0(X8,xR,esk24_3(X6,X7,X8))
        | ~ aElement0(X6)
        | ~ aElement0(X7)
        | ~ aElement0(X8)
        | ~ aReductOfIn0(X7,X6,xR)
        | ~ aReductOfIn0(X8,X6,xR) )
      & isLocallyConfluent0(xR)
      & isTerminating0(xR) ),
    inference(distribute,[status(thm)],[452]) ).

cnf(454,plain,
    isTerminating0(xR),
    inference(split_conjunct,[status(thm)],[453]) ).

cnf(862,negated_conjecture,
    ( ~ isTerminating0(xR)
    | ~ aElement0(xw)
    | ~ aRewritingSystem0(xR) ),
    inference(spm,[status(thm)],[385,345,theory(equality)]) ).

cnf(866,negated_conjecture,
    ( $false
    | ~ aElement0(xw)
    | ~ aRewritingSystem0(xR) ),
    inference(rw,[status(thm)],[862,454,theory(equality)]) ).

cnf(867,negated_conjecture,
    ( $false
    | $false
    | ~ aRewritingSystem0(xR) ),
    inference(rw,[status(thm)],[866,335,theory(equality)]) ).

cnf(868,negated_conjecture,
    ( $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[867,336,theory(equality)]) ).

cnf(869,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[868,theory(equality)]) ).

cnf(870,negated_conjecture,
    $false,
    869,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM018+4.p
% --creating new selector for []
% -running prover on /tmp/tmpy89yu7/sel_COM018+4.p_1 with time limit 29
% -prover status Theorem
% Problem COM018+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM018+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM018+4.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
% 
%------------------------------------------------------------------------------