TSTP Solution File: COM013+4 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : COM013+4 : TPTP v5.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : art04.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 05:45:47 EST 2010

% Result   : Theorem 0.32s
% Output   : CNFRefutation 0.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    3
% Syntax   : Number of formulae    :   54 (   7 unt;   0 def)
%            Number of atoms       :  380 (  31 equ)
%            Maximal formula atoms :   50 (   7 avg)
%            Number of connectives :  531 ( 205   ~; 200   |; 114   &)
%                                         (   0 <=>;  12  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   7 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   10 (   8 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :  105 (   1 sgn  50   !;  21   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(2,axiom,
    ( aRewritingSystem0(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/tmp_g9DpE/sel_COM013+4.p_1',m__587) ).

fof(9,axiom,
    ! [X1,X2] :
      ( ( aElement0(X1)
        & aRewritingSystem0(X2) )
     => ! [X3] :
          ( aReductOfIn0(X3,X1,X2)
         => aElement0(X3) ) ),
    file('/tmp/tmp_g9DpE/sel_COM013+4.p_1',mReduct) ).

fof(10,conjecture,
    ! [X1] :
      ( aElement0(X1)
     => ( ! [X2] :
            ( aElement0(X2)
           => ( iLess0(X2,X1)
             => ? [X3] :
                  ( aElement0(X3)
                  & ( X2 = X3
                    | ( ( aReductOfIn0(X3,X2,xR)
                        | ? [X4] :
                            ( aElement0(X4)
                            & aReductOfIn0(X4,X2,xR)
                            & sdtmndtplgtdt0(X4,xR,X3) ) )
                      & sdtmndtplgtdt0(X2,xR,X3) ) )
                  & sdtmndtasgtdt0(X2,xR,X3)
                  & ~ ? [X4] : aReductOfIn0(X4,X3,xR)
                  & aNormalFormOfIn0(X3,X2,xR) ) ) )
       => ? [X2] :
            ( ( aElement0(X2)
              & ( X1 = X2
                | aReductOfIn0(X2,X1,xR)
                | ? [X3] :
                    ( aElement0(X3)
                    & aReductOfIn0(X3,X1,xR)
                    & sdtmndtplgtdt0(X3,xR,X2) )
                | sdtmndtplgtdt0(X1,xR,X2)
                | sdtmndtasgtdt0(X1,xR,X2) )
              & ~ ? [X3] : aReductOfIn0(X3,X2,xR) )
            | aNormalFormOfIn0(X2,X1,xR) ) ) ),
    file('/tmp/tmp_g9DpE/sel_COM013+4.p_1',m__) ).

fof(16,negated_conjecture,
    ~ ! [X1] :
        ( aElement0(X1)
       => ( ! [X2] :
              ( aElement0(X2)
             => ( iLess0(X2,X1)
               => ? [X3] :
                    ( aElement0(X3)
                    & ( X2 = X3
                      | ( ( aReductOfIn0(X3,X2,xR)
                          | ? [X4] :
                              ( aElement0(X4)
                              & aReductOfIn0(X4,X2,xR)
                              & sdtmndtplgtdt0(X4,xR,X3) ) )
                        & sdtmndtplgtdt0(X2,xR,X3) ) )
                    & sdtmndtasgtdt0(X2,xR,X3)
                    & ~ ? [X4] : aReductOfIn0(X4,X3,xR)
                    & aNormalFormOfIn0(X3,X2,xR) ) ) )
         => ? [X2] :
              ( ( aElement0(X2)
                & ( X1 = X2
                  | aReductOfIn0(X2,X1,xR)
                  | ? [X3] :
                      ( aElement0(X3)
                      & aReductOfIn0(X3,X1,xR)
                      & sdtmndtplgtdt0(X3,xR,X2) )
                  | sdtmndtplgtdt0(X1,xR,X2)
                  | sdtmndtasgtdt0(X1,xR,X2) )
                & ~ ? [X3] : aReductOfIn0(X3,X2,xR) )
              | aNormalFormOfIn0(X2,X1,xR) ) ) ),
    inference(assume_negation,[status(cth)],[10]) ).

fof(20,plain,
    ( aRewritingSystem0(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)],[2]) ).

fof(21,plain,
    ( aRewritingSystem0(xR)
    & ! [X4,X5] :
        ( ~ aElement0(X4)
        | ~ aElement0(X5)
        | ( ~ aReductOfIn0(X5,X4,xR)
          & ! [X6] :
              ( ~ aElement0(X6)
              | ~ aReductOfIn0(X6,X4,xR)
              | ~ sdtmndtplgtdt0(X6,xR,X5) )
          & ~ sdtmndtplgtdt0(X4,xR,X5) )
        | iLess0(X5,X4) )
    & isTerminating0(xR) ),
    inference(variable_rename,[status(thm)],[20]) ).

fof(22,plain,
    ! [X4,X5,X6] :
      ( ( ( ( ~ aElement0(X6)
            | ~ aReductOfIn0(X6,X4,xR)
            | ~ sdtmndtplgtdt0(X6,xR,X5) )
          & ~ aReductOfIn0(X5,X4,xR)
          & ~ sdtmndtplgtdt0(X4,xR,X5) )
        | iLess0(X5,X4)
        | ~ aElement0(X4)
        | ~ aElement0(X5) )
      & aRewritingSystem0(xR)
      & isTerminating0(xR) ),
    inference(shift_quantors,[status(thm)],[21]) ).

fof(23,plain,
    ! [X4,X5,X6] :
      ( ( ~ aElement0(X6)
        | ~ aReductOfIn0(X6,X4,xR)
        | ~ sdtmndtplgtdt0(X6,xR,X5)
        | iLess0(X5,X4)
        | ~ aElement0(X4)
        | ~ aElement0(X5) )
      & ( ~ aReductOfIn0(X5,X4,xR)
        | iLess0(X5,X4)
        | ~ aElement0(X4)
        | ~ aElement0(X5) )
      & ( ~ sdtmndtplgtdt0(X4,xR,X5)
        | iLess0(X5,X4)
        | ~ aElement0(X4)
        | ~ aElement0(X5) )
      & aRewritingSystem0(xR)
      & isTerminating0(xR) ),
    inference(distribute,[status(thm)],[22]) ).

cnf(25,plain,
    aRewritingSystem0(xR),
    inference(split_conjunct,[status(thm)],[23]) ).

cnf(27,plain,
    ( iLess0(X1,X2)
    | ~ aElement0(X1)
    | ~ aElement0(X2)
    | ~ aReductOfIn0(X1,X2,xR) ),
    inference(split_conjunct,[status(thm)],[23]) ).

fof(89,plain,
    ! [X1,X2] :
      ( ~ aElement0(X1)
      | ~ aRewritingSystem0(X2)
      | ! [X3] :
          ( ~ aReductOfIn0(X3,X1,X2)
          | aElement0(X3) ) ),
    inference(fof_nnf,[status(thm)],[9]) ).

fof(90,plain,
    ! [X4,X5] :
      ( ~ aElement0(X4)
      | ~ aRewritingSystem0(X5)
      | ! [X6] :
          ( ~ aReductOfIn0(X6,X4,X5)
          | aElement0(X6) ) ),
    inference(variable_rename,[status(thm)],[89]) ).

fof(91,plain,
    ! [X4,X5,X6] :
      ( ~ aReductOfIn0(X6,X4,X5)
      | aElement0(X6)
      | ~ aElement0(X4)
      | ~ aRewritingSystem0(X5) ),
    inference(shift_quantors,[status(thm)],[90]) ).

cnf(92,plain,
    ( aElement0(X3)
    | ~ aRewritingSystem0(X1)
    | ~ aElement0(X2)
    | ~ aReductOfIn0(X3,X2,X1) ),
    inference(split_conjunct,[status(thm)],[91]) ).

fof(93,negated_conjecture,
    ? [X1] :
      ( aElement0(X1)
      & ! [X2] :
          ( ~ aElement0(X2)
          | ~ iLess0(X2,X1)
          | ? [X3] :
              ( aElement0(X3)
              & ( X2 = X3
                | ( ( aReductOfIn0(X3,X2,xR)
                    | ? [X4] :
                        ( aElement0(X4)
                        & aReductOfIn0(X4,X2,xR)
                        & sdtmndtplgtdt0(X4,xR,X3) ) )
                  & sdtmndtplgtdt0(X2,xR,X3) ) )
              & sdtmndtasgtdt0(X2,xR,X3)
              & ! [X4] : ~ aReductOfIn0(X4,X3,xR)
              & aNormalFormOfIn0(X3,X2,xR) ) )
      & ! [X2] :
          ( ( ~ aElement0(X2)
            | ( X1 != X2
              & ~ aReductOfIn0(X2,X1,xR)
              & ! [X3] :
                  ( ~ aElement0(X3)
                  | ~ aReductOfIn0(X3,X1,xR)
                  | ~ sdtmndtplgtdt0(X3,xR,X2) )
              & ~ sdtmndtplgtdt0(X1,xR,X2)
              & ~ sdtmndtasgtdt0(X1,xR,X2) )
            | ? [X3] : aReductOfIn0(X3,X2,xR) )
          & ~ aNormalFormOfIn0(X2,X1,xR) ) ),
    inference(fof_nnf,[status(thm)],[16]) ).

fof(94,negated_conjecture,
    ? [X5] :
      ( aElement0(X5)
      & ! [X6] :
          ( ~ aElement0(X6)
          | ~ iLess0(X6,X5)
          | ? [X7] :
              ( aElement0(X7)
              & ( X6 = X7
                | ( ( aReductOfIn0(X7,X6,xR)
                    | ? [X8] :
                        ( aElement0(X8)
                        & aReductOfIn0(X8,X6,xR)
                        & sdtmndtplgtdt0(X8,xR,X7) ) )
                  & sdtmndtplgtdt0(X6,xR,X7) ) )
              & sdtmndtasgtdt0(X6,xR,X7)
              & ! [X9] : ~ aReductOfIn0(X9,X7,xR)
              & aNormalFormOfIn0(X7,X6,xR) ) )
      & ! [X10] :
          ( ( ~ aElement0(X10)
            | ( X5 != X10
              & ~ aReductOfIn0(X10,X5,xR)
              & ! [X11] :
                  ( ~ aElement0(X11)
                  | ~ aReductOfIn0(X11,X5,xR)
                  | ~ sdtmndtplgtdt0(X11,xR,X10) )
              & ~ sdtmndtplgtdt0(X5,xR,X10)
              & ~ sdtmndtasgtdt0(X5,xR,X10) )
            | ? [X12] : aReductOfIn0(X12,X10,xR) )
          & ~ aNormalFormOfIn0(X10,X5,xR) ) ),
    inference(variable_rename,[status(thm)],[93]) ).

fof(95,negated_conjecture,
    ( aElement0(esk13_0)
    & ! [X6] :
        ( ~ aElement0(X6)
        | ~ iLess0(X6,esk13_0)
        | ( aElement0(esk14_1(X6))
          & ( X6 = esk14_1(X6)
            | ( ( aReductOfIn0(esk14_1(X6),X6,xR)
                | ( aElement0(esk15_1(X6))
                  & aReductOfIn0(esk15_1(X6),X6,xR)
                  & sdtmndtplgtdt0(esk15_1(X6),xR,esk14_1(X6)) ) )
              & sdtmndtplgtdt0(X6,xR,esk14_1(X6)) ) )
          & sdtmndtasgtdt0(X6,xR,esk14_1(X6))
          & ! [X9] : ~ aReductOfIn0(X9,esk14_1(X6),xR)
          & aNormalFormOfIn0(esk14_1(X6),X6,xR) ) )
    & ! [X10] :
        ( ( ~ aElement0(X10)
          | ( esk13_0 != X10
            & ~ aReductOfIn0(X10,esk13_0,xR)
            & ! [X11] :
                ( ~ aElement0(X11)
                | ~ aReductOfIn0(X11,esk13_0,xR)
                | ~ sdtmndtplgtdt0(X11,xR,X10) )
            & ~ sdtmndtplgtdt0(esk13_0,xR,X10)
            & ~ sdtmndtasgtdt0(esk13_0,xR,X10) )
          | aReductOfIn0(esk16_1(X10),X10,xR) )
        & ~ aNormalFormOfIn0(X10,esk13_0,xR) ) ),
    inference(skolemize,[status(esa)],[94]) ).

fof(96,negated_conjecture,
    ! [X6,X9,X10,X11] :
      ( ( ( ( ~ aElement0(X11)
            | ~ aReductOfIn0(X11,esk13_0,xR)
            | ~ sdtmndtplgtdt0(X11,xR,X10) )
          & esk13_0 != X10
          & ~ aReductOfIn0(X10,esk13_0,xR)
          & ~ sdtmndtplgtdt0(esk13_0,xR,X10)
          & ~ sdtmndtasgtdt0(esk13_0,xR,X10) )
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ~ aNormalFormOfIn0(X10,esk13_0,xR)
      & ( ( ~ aReductOfIn0(X9,esk14_1(X6),xR)
          & aElement0(esk14_1(X6))
          & ( X6 = esk14_1(X6)
            | ( ( aReductOfIn0(esk14_1(X6),X6,xR)
                | ( aElement0(esk15_1(X6))
                  & aReductOfIn0(esk15_1(X6),X6,xR)
                  & sdtmndtplgtdt0(esk15_1(X6),xR,esk14_1(X6)) ) )
              & sdtmndtplgtdt0(X6,xR,esk14_1(X6)) ) )
          & sdtmndtasgtdt0(X6,xR,esk14_1(X6))
          & aNormalFormOfIn0(esk14_1(X6),X6,xR) )
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & aElement0(esk13_0) ),
    inference(shift_quantors,[status(thm)],[95]) ).

fof(97,negated_conjecture,
    ! [X6,X9,X10,X11] :
      ( ( ~ aElement0(X11)
        | ~ aReductOfIn0(X11,esk13_0,xR)
        | ~ sdtmndtplgtdt0(X11,xR,X10)
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ( esk13_0 != X10
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ( ~ aReductOfIn0(X10,esk13_0,xR)
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ( ~ sdtmndtplgtdt0(esk13_0,xR,X10)
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ( ~ sdtmndtasgtdt0(esk13_0,xR,X10)
        | ~ aElement0(X10)
        | aReductOfIn0(esk16_1(X10),X10,xR) )
      & ~ aNormalFormOfIn0(X10,esk13_0,xR)
      & ( ~ aReductOfIn0(X9,esk14_1(X6),xR)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( aElement0(esk14_1(X6))
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( aElement0(esk15_1(X6))
        | aReductOfIn0(esk14_1(X6),X6,xR)
        | X6 = esk14_1(X6)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( aReductOfIn0(esk15_1(X6),X6,xR)
        | aReductOfIn0(esk14_1(X6),X6,xR)
        | X6 = esk14_1(X6)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( sdtmndtplgtdt0(esk15_1(X6),xR,esk14_1(X6))
        | aReductOfIn0(esk14_1(X6),X6,xR)
        | X6 = esk14_1(X6)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( sdtmndtplgtdt0(X6,xR,esk14_1(X6))
        | X6 = esk14_1(X6)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( sdtmndtasgtdt0(X6,xR,esk14_1(X6))
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & ( aNormalFormOfIn0(esk14_1(X6),X6,xR)
        | ~ iLess0(X6,esk13_0)
        | ~ aElement0(X6) )
      & aElement0(esk13_0) ),
    inference(distribute,[status(thm)],[96]) ).

cnf(98,negated_conjecture,
    aElement0(esk13_0),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(101,negated_conjecture,
    ( X1 = esk14_1(X1)
    | sdtmndtplgtdt0(X1,xR,esk14_1(X1))
    | ~ aElement0(X1)
    | ~ iLess0(X1,esk13_0) ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(105,negated_conjecture,
    ( aElement0(esk14_1(X1))
    | ~ aElement0(X1)
    | ~ iLess0(X1,esk13_0) ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(106,negated_conjecture,
    ( ~ aElement0(X1)
    | ~ iLess0(X1,esk13_0)
    | ~ aReductOfIn0(X2,esk14_1(X1),xR) ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(110,negated_conjecture,
    ( aReductOfIn0(esk16_1(X1),X1,xR)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR) ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(111,negated_conjecture,
    ( aReductOfIn0(esk16_1(X1),X1,xR)
    | ~ aElement0(X1)
    | esk13_0 != X1 ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(112,negated_conjecture,
    ( aReductOfIn0(esk16_1(X1),X1,xR)
    | ~ aElement0(X1)
    | ~ sdtmndtplgtdt0(X2,xR,X1)
    | ~ aReductOfIn0(X2,esk13_0,xR)
    | ~ aElement0(X2) ),
    inference(split_conjunct,[status(thm)],[97]) ).

cnf(135,negated_conjecture,
    ( ~ iLess0(X1,esk13_0)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
    | ~ aElement0(esk14_1(X1)) ),
    inference(spm,[status(thm)],[106,110,theory(equality)]) ).

cnf(138,negated_conjecture,
    ( aElement0(esk16_1(X1))
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(X1)
    | esk13_0 != X1 ),
    inference(spm,[status(thm)],[92,111,theory(equality)]) ).

cnf(142,negated_conjecture,
    ( aElement0(esk16_1(X1))
    | $false
    | ~ aElement0(X1)
    | esk13_0 != X1 ),
    inference(rw,[status(thm)],[138,25,theory(equality)]) ).

cnf(143,negated_conjecture,
    ( aElement0(esk16_1(X1))
    | ~ aElement0(X1)
    | esk13_0 != X1 ),
    inference(cn,[status(thm)],[142,theory(equality)]) ).

cnf(153,plain,
    ( aElement0(esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(esk13_0) ),
    inference(spm,[status(thm)],[105,27,theory(equality)]) ).

cnf(156,plain,
    ( aElement0(esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | $false ),
    inference(rw,[status(thm)],[153,98,theory(equality)]) ).

cnf(157,plain,
    ( aElement0(esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR) ),
    inference(cn,[status(thm)],[156,theory(equality)]) ).

cnf(169,plain,
    ( esk14_1(X1) = X1
    | sdtmndtplgtdt0(X1,xR,esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(esk13_0) ),
    inference(spm,[status(thm)],[101,27,theory(equality)]) ).

cnf(171,plain,
    ( esk14_1(X1) = X1
    | sdtmndtplgtdt0(X1,xR,esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | $false ),
    inference(rw,[status(thm)],[169,98,theory(equality)]) ).

cnf(172,plain,
    ( esk14_1(X1) = X1
    | sdtmndtplgtdt0(X1,xR,esk14_1(X1))
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR) ),
    inference(cn,[status(thm)],[171,theory(equality)]) ).

cnf(314,negated_conjecture,
    ( ~ iLess0(X1,esk13_0)
    | ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[135,105]) ).

cnf(315,plain,
    ( ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(esk13_0) ),
    inference(spm,[status(thm)],[314,27,theory(equality)]) ).

cnf(317,plain,
    ( ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | $false ),
    inference(rw,[status(thm)],[315,98,theory(equality)]) ).

cnf(318,plain,
    ( ~ aReductOfIn0(esk14_1(X1),esk13_0,xR)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR) ),
    inference(cn,[status(thm)],[317,theory(equality)]) ).

cnf(382,plain,
    ( aReductOfIn0(esk16_1(esk14_1(X1)),esk14_1(X1),xR)
    | esk14_1(X1) = X1
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1)
    | ~ aElement0(esk14_1(X1)) ),
    inference(spm,[status(thm)],[112,172,theory(equality)]) ).

cnf(636,plain,
    ( esk14_1(X1) = X1
    | aReductOfIn0(esk16_1(esk14_1(X1)),esk14_1(X1),xR)
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1) ),
    inference(csr,[status(thm)],[382,157]) ).

cnf(637,plain,
    ( esk14_1(X1) = X1
    | ~ iLess0(X1,esk13_0)
    | ~ aElement0(X1)
    | ~ aReductOfIn0(X1,esk13_0,xR) ),
    inference(spm,[status(thm)],[106,636,theory(equality)]) ).

cnf(645,plain,
    ( esk14_1(X1) = X1
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1)
    | ~ aElement0(esk13_0) ),
    inference(spm,[status(thm)],[637,27,theory(equality)]) ).

cnf(649,plain,
    ( esk14_1(X1) = X1
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1)
    | $false ),
    inference(rw,[status(thm)],[645,98,theory(equality)]) ).

cnf(650,plain,
    ( esk14_1(X1) = X1
    | ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1) ),
    inference(cn,[status(thm)],[649,theory(equality)]) ).

cnf(663,plain,
    ( ~ aReductOfIn0(X1,esk13_0,xR)
    | ~ aElement0(X1) ),
    inference(spm,[status(thm)],[318,650,theory(equality)]) ).

cnf(676,negated_conjecture,
    ( ~ aElement0(esk16_1(esk13_0))
    | ~ aElement0(esk13_0) ),
    inference(spm,[status(thm)],[663,111,theory(equality)]) ).

cnf(682,negated_conjecture,
    ( ~ aElement0(esk16_1(esk13_0))
    | $false ),
    inference(rw,[status(thm)],[676,98,theory(equality)]) ).

cnf(683,negated_conjecture,
    ~ aElement0(esk16_1(esk13_0)),
    inference(cn,[status(thm)],[682,theory(equality)]) ).

cnf(696,negated_conjecture,
    ~ aElement0(esk13_0),
    inference(spm,[status(thm)],[683,143,theory(equality)]) ).

cnf(699,negated_conjecture,
    $false,
    inference(rw,[status(thm)],[696,98,theory(equality)]) ).

cnf(700,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[699,theory(equality)]) ).

cnf(701,negated_conjecture,
    $false,
    700,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % SZS status Started for /home/graph/tptp/TPTP/Problems/COM/COM013+4.p
% --creating new selector for []
% -running prover on /tmp/tmp_g9DpE/sel_COM013+4.p_1 with time limit 29
% -prover status Theorem
% Problem COM013+4.p solved in phase 0.
% % SZS status Theorem for /home/graph/tptp/TPTP/Problems/COM/COM013+4.p
% % SZS status Ended for /home/graph/tptp/TPTP/Problems/COM/COM013+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
% 
%------------------------------------------------------------------------------