TSTP Solution File: NUM483+3 by SInE---0.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SInE---0.4
% Problem  : NUM483+3 : TPTP v7.0.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : Source/sine.py -e eprover -t %d %s

% Computer : n118.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32218.625MB
% OS       : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan  8 15:21:30 EST 2018

% Result   : Theorem 1.85s
% Output   : CNFRefutation 1.85s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   39
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  142 (  19 unt;   0 def)
%            Number of atoms       :  788 (  99 equ)
%            Maximal formula atoms :   73 (   5 avg)
%            Number of connectives : 1033 ( 387   ~; 475   |; 154   &)
%                                         (   1 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   5 con; 0-2 aty)
%            Number of variables   :  164 (   3 sgn  84   !;  25   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(1,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m_MulZero) ).

fof(2,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( doDivides0(X1,X2)
          & doDivides0(X2,X3) )
       => doDivides0(X1,X3) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mDivTrans) ).

fof(7,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( doDivides0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & equal(X2,sdtasdt0(X1,X3)) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mDefDiv) ).

fof(10,axiom,
    ( ~ equal(xk,sz00)
    & ~ equal(xk,sz10) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m__1716_04) ).

fof(23,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ~ equal(X1,sz00)
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mMonMul2) ).

fof(24,axiom,
    aNaturalNumber0(xk),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m__1716) ).

fof(26,conjecture,
    ? [X1] :
      ( aNaturalNumber0(X1)
      & ( ? [X2] :
            ( aNaturalNumber0(X2)
            & equal(xk,sdtasdt0(X1,X2)) )
        | doDivides0(X1,xk) )
      & ( ( ~ equal(X1,sz00)
          & ~ equal(X1,sz10)
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & ? [X3] :
                    ( aNaturalNumber0(X3)
                    & equal(X1,sdtasdt0(X2,X3)) )
                & doDivides0(X2,X1) )
             => ( equal(X2,sz10)
                | equal(X2,X1) ) ) )
        | isPrime0(X1) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m__) ).

fof(29,axiom,
    ! [X1] :
      ( ( aNaturalNumber0(X1)
        & ~ equal(X1,sz00)
        & ~ equal(X1,sz10) )
     => ( iLess0(X1,xk)
       => ? [X2] :
            ( aNaturalNumber0(X2)
            & ? [X3] :
                ( aNaturalNumber0(X3)
                & equal(X1,sdtasdt0(X2,X3)) )
            & doDivides0(X2,X1)
            & ~ equal(X2,sz00)
            & ~ equal(X2,sz10)
            & ! [X3] :
                ( ( aNaturalNumber0(X3)
                  & ( ? [X4] :
                        ( aNaturalNumber0(X4)
                        & equal(X2,sdtasdt0(X3,X4)) )
                    | doDivides0(X3,X2) ) )
               => ( equal(X3,sz10)
                  | equal(X3,X2) ) )
            & isPrime0(X2) ) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m__1700) ).

fof(32,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mSortsB_02) ).

fof(34,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mSortsC) ).

fof(37,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( ~ equal(X1,X2)
          & sdtlseqdt0(X1,X2) )
       => iLess0(X1,X2) ) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mIH_03) ).

fof(38,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',mMulComm) ).

fof(39,axiom,
    ~ ( ! [X1] :
          ( ( aNaturalNumber0(X1)
            & ? [X2] :
                ( aNaturalNumber0(X2)
                & equal(xk,sdtasdt0(X1,X2)) )
            & doDivides0(X1,xk) )
         => ( equal(X1,sz10)
            | equal(X1,xk) ) )
      | isPrime0(xk) ),
    file('/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1',m__1725) ).

fof(43,negated_conjecture,
    ~ ? [X1] :
        ( aNaturalNumber0(X1)
        & ( ? [X2] :
              ( aNaturalNumber0(X2)
              & equal(xk,sdtasdt0(X1,X2)) )
          | doDivides0(X1,xk) )
        & ( ( ~ equal(X1,sz00)
            & ~ equal(X1,sz10)
            & ! [X2] :
                ( ( aNaturalNumber0(X2)
                  & ? [X3] :
                      ( aNaturalNumber0(X3)
                      & equal(X1,sdtasdt0(X2,X3)) )
                  & doDivides0(X2,X1) )
               => ( equal(X2,sz10)
                  | equal(X2,X1) ) ) )
          | isPrime0(X1) ) ),
    inference(assume_negation,[status(cth)],[26]) ).

fof(44,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( equal(sdtasdt0(X1,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X1)) ) ),
    inference(fof_nnf,[status(thm)],[1]) ).

fof(45,plain,
    ! [X2] :
      ( ~ aNaturalNumber0(X2)
      | ( equal(sdtasdt0(X2,sz00),sz00)
        & equal(sz00,sdtasdt0(sz00,X2)) ) ),
    inference(variable_rename,[status(thm)],[44]) ).

fof(46,plain,
    ! [X2] :
      ( ( equal(sdtasdt0(X2,sz00),sz00)
        | ~ aNaturalNumber0(X2) )
      & ( equal(sz00,sdtasdt0(sz00,X2))
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[45]) ).

cnf(47,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[46]) ).

fof(49,plain,
    ! [X1,X2,X3] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ~ aNaturalNumber0(X3)
      | ~ doDivides0(X1,X2)
      | ~ doDivides0(X2,X3)
      | doDivides0(X1,X3) ),
    inference(fof_nnf,[status(thm)],[2]) ).

fof(50,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ doDivides0(X4,X5)
      | ~ doDivides0(X5,X6)
      | doDivides0(X4,X6) ),
    inference(variable_rename,[status(thm)],[49]) ).

cnf(51,plain,
    ( doDivides0(X1,X2)
    | ~ doDivides0(X3,X2)
    | ~ doDivides0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[50]) ).

fof(69,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | ( ( ~ doDivides0(X1,X2)
          | ? [X3] :
              ( aNaturalNumber0(X3)
              & equal(X2,sdtasdt0(X1,X3)) ) )
        & ( ! [X3] :
              ( ~ aNaturalNumber0(X3)
              | ~ equal(X2,sdtasdt0(X1,X3)) )
          | doDivides0(X1,X2) ) ) ),
    inference(fof_nnf,[status(thm)],[7]) ).

fof(70,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & equal(X5,sdtasdt0(X4,X6)) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(variable_rename,[status(thm)],[69]) ).

fof(71,plain,
    ! [X4,X5] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ( ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) )
        & ( ! [X7] :
              ( ~ aNaturalNumber0(X7)
              | ~ equal(X5,sdtasdt0(X4,X7)) )
          | doDivides0(X4,X5) ) ) ),
    inference(skolemize,[status(esa)],[70]) ).

fof(72,plain,
    ! [X4,X5,X7] :
      ( ( ( ~ aNaturalNumber0(X7)
          | ~ equal(X5,sdtasdt0(X4,X7))
          | doDivides0(X4,X5) )
        & ( ~ doDivides0(X4,X5)
          | ( aNaturalNumber0(esk1_2(X4,X5))
            & equal(X5,sdtasdt0(X4,esk1_2(X4,X5))) ) ) )
      | ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5) ),
    inference(shift_quantors,[status(thm)],[71]) ).

fof(73,plain,
    ! [X4,X5,X7] :
      ( ( ~ aNaturalNumber0(X7)
        | ~ equal(X5,sdtasdt0(X4,X7))
        | doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( aNaturalNumber0(esk1_2(X4,X5))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( equal(X5,sdtasdt0(X4,esk1_2(X4,X5)))
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[72]) ).

cnf(74,plain,
    ( X1 = sdtasdt0(X2,esk1_2(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[73]) ).

cnf(75,plain,
    ( aNaturalNumber0(esk1_2(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[73]) ).

cnf(76,plain,
    ( doDivides0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | X1 != sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[73]) ).

cnf(86,plain,
    xk != sz00,
    inference(split_conjunct,[status(thm)],[10]) ).

fof(143,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(X1,sz00)
      | sdtlseqdt0(X2,sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[23]) ).

fof(144,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(X3,sz00)
      | sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[143]) ).

cnf(145,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X1,X2))
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[144]) ).

cnf(146,plain,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[24]) ).

fof(149,negated_conjecture,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | ( ! [X2] :
            ( ~ aNaturalNumber0(X2)
            | ~ equal(xk,sdtasdt0(X1,X2)) )
        & ~ doDivides0(X1,xk) )
      | ( ( equal(X1,sz00)
          | equal(X1,sz10)
          | ? [X2] :
              ( aNaturalNumber0(X2)
              & ? [X3] :
                  ( aNaturalNumber0(X3)
                  & equal(X1,sdtasdt0(X2,X3)) )
              & doDivides0(X2,X1)
              & ~ equal(X2,sz10)
              & ~ equal(X2,X1) ) )
        & ~ isPrime0(X1) ) ),
    inference(fof_nnf,[status(thm)],[43]) ).

fof(150,negated_conjecture,
    ! [X4] :
      ( ~ aNaturalNumber0(X4)
      | ( ! [X5] :
            ( ~ aNaturalNumber0(X5)
            | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ? [X6] :
              ( aNaturalNumber0(X6)
              & ? [X7] :
                  ( aNaturalNumber0(X7)
                  & equal(X4,sdtasdt0(X6,X7)) )
              & doDivides0(X6,X4)
              & ~ equal(X6,sz10)
              & ~ equal(X6,X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(variable_rename,[status(thm)],[149]) ).

fof(151,negated_conjecture,
    ! [X4] :
      ( ~ aNaturalNumber0(X4)
      | ( ! [X5] :
            ( ~ aNaturalNumber0(X5)
            | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ( aNaturalNumber0(esk3_1(X4))
            & aNaturalNumber0(esk4_1(X4))
            & equal(X4,sdtasdt0(esk3_1(X4),esk4_1(X4)))
            & doDivides0(esk3_1(X4),X4)
            & ~ equal(esk3_1(X4),sz10)
            & ~ equal(esk3_1(X4),X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(skolemize,[status(esa)],[150]) ).

fof(152,negated_conjecture,
    ! [X4,X5] :
      ( ( ( ~ aNaturalNumber0(X5)
          | ~ equal(xk,sdtasdt0(X4,X5)) )
        & ~ doDivides0(X4,xk) )
      | ~ aNaturalNumber0(X4)
      | ( ( equal(X4,sz00)
          | equal(X4,sz10)
          | ( aNaturalNumber0(esk3_1(X4))
            & aNaturalNumber0(esk4_1(X4))
            & equal(X4,sdtasdt0(esk3_1(X4),esk4_1(X4)))
            & doDivides0(esk3_1(X4),X4)
            & ~ equal(esk3_1(X4),sz10)
            & ~ equal(esk3_1(X4),X4) ) )
        & ~ isPrime0(X4) ) ),
    inference(shift_quantors,[status(thm)],[151]) ).

fof(153,negated_conjecture,
    ! [X4,X5] :
      ( ( aNaturalNumber0(esk3_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk4_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( equal(X4,sdtasdt0(esk3_1(X4),esk4_1(X4)))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( doDivides0(esk3_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk3_1(X4),sz10)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk3_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( ~ isPrime0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ equal(xk,sdtasdt0(X4,X5))
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk3_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( aNaturalNumber0(esk4_1(X4))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( equal(X4,sdtasdt0(esk3_1(X4),esk4_1(X4)))
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( doDivides0(esk3_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk3_1(X4),sz10)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ equal(esk3_1(X4),X4)
        | equal(X4,sz00)
        | equal(X4,sz10)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) )
      & ( ~ isPrime0(X4)
        | ~ doDivides0(X4,xk)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[152]) ).

cnf(154,negated_conjecture,
    ( ~ aNaturalNumber0(X1)
    | ~ doDivides0(X1,xk)
    | ~ isPrime0(X1) ),
    inference(split_conjunct,[status(thm)],[153]) ).

fof(176,plain,
    ! [X1] :
      ( ~ aNaturalNumber0(X1)
      | equal(X1,sz00)
      | equal(X1,sz10)
      | ~ iLess0(X1,xk)
      | ? [X2] :
          ( aNaturalNumber0(X2)
          & ? [X3] :
              ( aNaturalNumber0(X3)
              & equal(X1,sdtasdt0(X2,X3)) )
          & doDivides0(X2,X1)
          & ~ equal(X2,sz00)
          & ~ equal(X2,sz10)
          & ! [X3] :
              ( ~ aNaturalNumber0(X3)
              | ( ! [X4] :
                    ( ~ aNaturalNumber0(X4)
                    | ~ equal(X2,sdtasdt0(X3,X4)) )
                & ~ doDivides0(X3,X2) )
              | equal(X3,sz10)
              | equal(X3,X2) )
          & isPrime0(X2) ) ),
    inference(fof_nnf,[status(thm)],[29]) ).

fof(177,plain,
    ! [X5] :
      ( ~ aNaturalNumber0(X5)
      | equal(X5,sz00)
      | equal(X5,sz10)
      | ~ iLess0(X5,xk)
      | ? [X6] :
          ( aNaturalNumber0(X6)
          & ? [X7] :
              ( aNaturalNumber0(X7)
              & equal(X5,sdtasdt0(X6,X7)) )
          & doDivides0(X6,X5)
          & ~ equal(X6,sz00)
          & ~ equal(X6,sz10)
          & ! [X8] :
              ( ~ aNaturalNumber0(X8)
              | ( ! [X9] :
                    ( ~ aNaturalNumber0(X9)
                    | ~ equal(X6,sdtasdt0(X8,X9)) )
                & ~ doDivides0(X8,X6) )
              | equal(X8,sz10)
              | equal(X8,X6) )
          & isPrime0(X6) ) ),
    inference(variable_rename,[status(thm)],[176]) ).

fof(178,plain,
    ! [X5] :
      ( ~ aNaturalNumber0(X5)
      | equal(X5,sz00)
      | equal(X5,sz10)
      | ~ iLess0(X5,xk)
      | ( aNaturalNumber0(esk5_1(X5))
        & aNaturalNumber0(esk6_1(X5))
        & equal(X5,sdtasdt0(esk5_1(X5),esk6_1(X5)))
        & doDivides0(esk5_1(X5),X5)
        & ~ equal(esk5_1(X5),sz00)
        & ~ equal(esk5_1(X5),sz10)
        & ! [X8] :
            ( ~ aNaturalNumber0(X8)
            | ( ! [X9] :
                  ( ~ aNaturalNumber0(X9)
                  | ~ equal(esk5_1(X5),sdtasdt0(X8,X9)) )
              & ~ doDivides0(X8,esk5_1(X5)) )
            | equal(X8,sz10)
            | equal(X8,esk5_1(X5)) )
        & isPrime0(esk5_1(X5)) ) ),
    inference(skolemize,[status(esa)],[177]) ).

fof(179,plain,
    ! [X5,X8,X9] :
      ( ( ( ( ( ~ aNaturalNumber0(X9)
              | ~ equal(esk5_1(X5),sdtasdt0(X8,X9)) )
            & ~ doDivides0(X8,esk5_1(X5)) )
          | ~ aNaturalNumber0(X8)
          | equal(X8,sz10)
          | equal(X8,esk5_1(X5)) )
        & aNaturalNumber0(esk5_1(X5))
        & aNaturalNumber0(esk6_1(X5))
        & equal(X5,sdtasdt0(esk5_1(X5),esk6_1(X5)))
        & doDivides0(esk5_1(X5),X5)
        & ~ equal(esk5_1(X5),sz00)
        & ~ equal(esk5_1(X5),sz10)
        & isPrime0(esk5_1(X5)) )
      | ~ iLess0(X5,xk)
      | ~ aNaturalNumber0(X5)
      | equal(X5,sz00)
      | equal(X5,sz10) ),
    inference(shift_quantors,[status(thm)],[178]) ).

fof(180,plain,
    ! [X5,X8,X9] :
      ( ( ~ aNaturalNumber0(X9)
        | ~ equal(esk5_1(X5),sdtasdt0(X8,X9))
        | ~ aNaturalNumber0(X8)
        | equal(X8,sz10)
        | equal(X8,esk5_1(X5))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( ~ doDivides0(X8,esk5_1(X5))
        | ~ aNaturalNumber0(X8)
        | equal(X8,sz10)
        | equal(X8,esk5_1(X5))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( aNaturalNumber0(esk5_1(X5))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( aNaturalNumber0(esk6_1(X5))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( equal(X5,sdtasdt0(esk5_1(X5),esk6_1(X5)))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( doDivides0(esk5_1(X5),X5)
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( ~ equal(esk5_1(X5),sz00)
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( ~ equal(esk5_1(X5),sz10)
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) )
      & ( isPrime0(esk5_1(X5))
        | ~ iLess0(X5,xk)
        | ~ aNaturalNumber0(X5)
        | equal(X5,sz00)
        | equal(X5,sz10) ) ),
    inference(distribute,[status(thm)],[179]) ).

cnf(181,plain,
    ( X1 = sz10
    | X1 = sz00
    | isPrime0(esk5_1(X1))
    | ~ aNaturalNumber0(X1)
    | ~ iLess0(X1,xk) ),
    inference(split_conjunct,[status(thm)],[180]) ).

cnf(184,plain,
    ( X1 = sz10
    | X1 = sz00
    | doDivides0(esk5_1(X1),X1)
    | ~ aNaturalNumber0(X1)
    | ~ iLess0(X1,xk) ),
    inference(split_conjunct,[status(thm)],[180]) ).

cnf(187,plain,
    ( X1 = sz10
    | X1 = sz00
    | aNaturalNumber0(esk5_1(X1))
    | ~ aNaturalNumber0(X1)
    | ~ iLess0(X1,xk) ),
    inference(split_conjunct,[status(thm)],[180]) ).

fof(200,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(fof_nnf,[status(thm)],[32]) ).

fof(201,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[200]) ).

cnf(202,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[201]) ).

cnf(215,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[34]) ).

fof(224,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(X1,X2)
      | ~ sdtlseqdt0(X1,X2)
      | iLess0(X1,X2) ),
    inference(fof_nnf,[status(thm)],[37]) ).

fof(225,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(X3,X4)
      | ~ sdtlseqdt0(X3,X4)
      | iLess0(X3,X4) ),
    inference(variable_rename,[status(thm)],[224]) ).

cnf(226,plain,
    ( iLess0(X1,X2)
    | X1 = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[225]) ).

fof(227,plain,
    ! [X1,X2] :
      ( ~ aNaturalNumber0(X1)
      | ~ aNaturalNumber0(X2)
      | equal(sdtasdt0(X1,X2),sdtasdt0(X2,X1)) ),
    inference(fof_nnf,[status(thm)],[38]) ).

fof(228,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | equal(sdtasdt0(X3,X4),sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[227]) ).

cnf(229,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[228]) ).

fof(230,plain,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & ? [X2] :
            ( aNaturalNumber0(X2)
            & equal(xk,sdtasdt0(X1,X2)) )
        & doDivides0(X1,xk)
        & ~ equal(X1,sz10)
        & ~ equal(X1,xk) )
    & ~ isPrime0(xk) ),
    inference(fof_nnf,[status(thm)],[39]) ).

fof(231,plain,
    ( ? [X3] :
        ( aNaturalNumber0(X3)
        & ? [X4] :
            ( aNaturalNumber0(X4)
            & equal(xk,sdtasdt0(X3,X4)) )
        & doDivides0(X3,xk)
        & ~ equal(X3,sz10)
        & ~ equal(X3,xk) )
    & ~ isPrime0(xk) ),
    inference(variable_rename,[status(thm)],[230]) ).

fof(232,plain,
    ( aNaturalNumber0(esk8_0)
    & aNaturalNumber0(esk9_0)
    & equal(xk,sdtasdt0(esk8_0,esk9_0))
    & doDivides0(esk8_0,xk)
    & ~ equal(esk8_0,sz10)
    & ~ equal(esk8_0,xk)
    & ~ isPrime0(xk) ),
    inference(skolemize,[status(esa)],[231]) ).

cnf(234,plain,
    esk8_0 != xk,
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(235,plain,
    esk8_0 != sz10,
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(236,plain,
    doDivides0(esk8_0,xk),
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(237,plain,
    xk = sdtasdt0(esk8_0,esk9_0),
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(238,plain,
    aNaturalNumber0(esk9_0),
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(239,plain,
    aNaturalNumber0(esk8_0),
    inference(split_conjunct,[status(thm)],[232]) ).

cnf(379,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sdtasdt0(X1,X2)) ),
    inference(er,[status(thm)],[76,theory(equality)]) ).

cnf(382,plain,
    ( doDivides0(sz00,X1)
    | sz00 != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[76,47,theory(equality)]) ).

cnf(392,plain,
    ( doDivides0(sz00,X1)
    | sz00 != X1
    | ~ aNaturalNumber0(X2)
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[382,215,theory(equality)]) ).

cnf(393,plain,
    ( doDivides0(sz00,X1)
    | sz00 != X1
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[392,theory(equality)]) ).

cnf(400,plain,
    ( sz00 = esk9_0
    | sdtlseqdt0(esk8_0,xk)
    | ~ aNaturalNumber0(esk9_0)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[145,237,theory(equality)]) ).

cnf(406,plain,
    ( sz00 = esk9_0
    | sdtlseqdt0(esk8_0,xk)
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[400,238,theory(equality)]) ).

cnf(407,plain,
    ( sz00 = esk9_0
    | sdtlseqdt0(esk8_0,xk)
    | $false
    | $false ),
    inference(rw,[status(thm)],[406,239,theory(equality)]) ).

cnf(408,plain,
    ( sz00 = esk9_0
    | sdtlseqdt0(esk8_0,xk) ),
    inference(cn,[status(thm)],[407,theory(equality)]) ).

cnf(417,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk8_0)
    | ~ aNaturalNumber0(esk8_0)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[51,236,theory(equality)]) ).

cnf(420,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk8_0)
    | $false
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[417,239,theory(equality)]) ).

cnf(421,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk8_0)
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[420,146,theory(equality)]) ).

cnf(422,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk8_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[421,theory(equality)]) ).

cnf(452,plain,
    ( X1 = sz00
    | ~ aNaturalNumber0(esk1_2(sz00,X1))
    | ~ doDivides0(sz00,X1)
    | ~ aNaturalNumber0(sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[47,74,theory(equality)]) ).

cnf(461,plain,
    ( X1 = sz00
    | ~ aNaturalNumber0(esk1_2(sz00,X1))
    | ~ doDivides0(sz00,X1)
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[452,215,theory(equality)]) ).

cnf(462,plain,
    ( X1 = sz00
    | ~ aNaturalNumber0(esk1_2(sz00,X1))
    | ~ doDivides0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[461,theory(equality)]) ).

cnf(466,plain,
    ( sz10 = X1
    | sz00 = X1
    | aNaturalNumber0(esk5_1(X1))
    | X1 = xk
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X1,xk)
    | ~ aNaturalNumber0(xk) ),
    inference(spm,[status(thm)],[187,226,theory(equality)]) ).

cnf(467,plain,
    ( sz10 = X1
    | sz00 = X1
    | aNaturalNumber0(esk5_1(X1))
    | X1 = xk
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X1,xk)
    | $false ),
    inference(rw,[status(thm)],[466,146,theory(equality)]) ).

cnf(468,plain,
    ( sz10 = X1
    | sz00 = X1
    | aNaturalNumber0(esk5_1(X1))
    | X1 = xk
    | ~ aNaturalNumber0(X1)
    | ~ sdtlseqdt0(X1,xk) ),
    inference(cn,[status(thm)],[467,theory(equality)]) ).

cnf(472,plain,
    ( sz10 = X1
    | sz00 = X1
    | ~ doDivides0(esk5_1(X1),xk)
    | ~ aNaturalNumber0(esk5_1(X1))
    | ~ iLess0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[154,181,theory(equality)]) ).

cnf(1249,plain,
    ( doDivides0(esk5_1(esk8_0),xk)
    | sz10 = esk8_0
    | sz00 = esk8_0
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ iLess0(esk8_0,xk)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[422,184,theory(equality)]) ).

cnf(1262,plain,
    ( doDivides0(esk5_1(esk8_0),xk)
    | sz10 = esk8_0
    | sz00 = esk8_0
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ iLess0(esk8_0,xk)
    | $false ),
    inference(rw,[status(thm)],[1249,239,theory(equality)]) ).

cnf(1263,plain,
    ( doDivides0(esk5_1(esk8_0),xk)
    | sz10 = esk8_0
    | sz00 = esk8_0
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ iLess0(esk8_0,xk) ),
    inference(cn,[status(thm)],[1262,theory(equality)]) ).

cnf(1264,plain,
    ( doDivides0(esk5_1(esk8_0),xk)
    | esk8_0 = sz00
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ iLess0(esk8_0,xk) ),
    inference(sr,[status(thm)],[1263,235,theory(equality)]) ).

cnf(1315,plain,
    ( doDivides0(sz00,X1)
    | sz00 != X1
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[393,215,theory(equality)]) ).

cnf(1371,plain,
    ( doDivides0(sz00,xk)
    | ~ aNaturalNumber0(sz00)
    | sz00 != esk8_0
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[422,1315,theory(equality)]) ).

cnf(1380,plain,
    ( doDivides0(sz00,xk)
    | $false
    | sz00 != esk8_0
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[1371,215,theory(equality)]) ).

cnf(1381,plain,
    ( doDivides0(sz00,xk)
    | $false
    | sz00 != esk8_0
    | $false ),
    inference(rw,[status(thm)],[1380,239,theory(equality)]) ).

cnf(1382,plain,
    ( doDivides0(sz00,xk)
    | sz00 != esk8_0 ),
    inference(cn,[status(thm)],[1381,theory(equality)]) ).

cnf(2282,plain,
    ( doDivides0(X1,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[379,202]) ).

cnf(2288,plain,
    ( doDivides0(X1,sdtasdt0(X2,X1))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[2282,229,theory(equality)]) ).

cnf(2691,plain,
    ( doDivides0(esk9_0,xk)
    | ~ aNaturalNumber0(esk8_0)
    | ~ aNaturalNumber0(esk9_0) ),
    inference(spm,[status(thm)],[2288,237,theory(equality)]) ).

cnf(2707,plain,
    ( doDivides0(esk9_0,xk)
    | $false
    | ~ aNaturalNumber0(esk9_0) ),
    inference(rw,[status(thm)],[2691,239,theory(equality)]) ).

cnf(2708,plain,
    ( doDivides0(esk9_0,xk)
    | $false
    | $false ),
    inference(rw,[status(thm)],[2707,238,theory(equality)]) ).

cnf(2709,plain,
    doDivides0(esk9_0,xk),
    inference(cn,[status(thm)],[2708,theory(equality)]) ).

cnf(2720,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk9_0)
    | ~ aNaturalNumber0(esk9_0)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[51,2709,theory(equality)]) ).

cnf(2732,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk9_0)
    | $false
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2720,238,theory(equality)]) ).

cnf(2733,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk9_0)
    | $false
    | $false
    | ~ aNaturalNumber0(X1) ),
    inference(rw,[status(thm)],[2732,146,theory(equality)]) ).

cnf(2734,plain,
    ( doDivides0(X1,xk)
    | ~ doDivides0(X1,esk9_0)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[2733,theory(equality)]) ).

cnf(2798,plain,
    ( doDivides0(sz00,xk)
    | ~ aNaturalNumber0(sz00)
    | sz00 != esk9_0
    | ~ aNaturalNumber0(esk9_0) ),
    inference(spm,[status(thm)],[2734,1315,theory(equality)]) ).

cnf(2820,plain,
    ( doDivides0(sz00,xk)
    | $false
    | sz00 != esk9_0
    | ~ aNaturalNumber0(esk9_0) ),
    inference(rw,[status(thm)],[2798,215,theory(equality)]) ).

cnf(2821,plain,
    ( doDivides0(sz00,xk)
    | $false
    | sz00 != esk9_0
    | $false ),
    inference(rw,[status(thm)],[2820,238,theory(equality)]) ).

cnf(2822,plain,
    ( doDivides0(sz00,xk)
    | sz00 != esk9_0 ),
    inference(cn,[status(thm)],[2821,theory(equality)]) ).

cnf(3327,plain,
    ( X1 = sz00
    | ~ doDivides0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(sz00) ),
    inference(spm,[status(thm)],[462,75,theory(equality)]) ).

cnf(3328,plain,
    ( X1 = sz00
    | ~ doDivides0(sz00,X1)
    | ~ aNaturalNumber0(X1)
    | $false ),
    inference(rw,[status(thm)],[3327,215,theory(equality)]) ).

cnf(3329,plain,
    ( X1 = sz00
    | ~ doDivides0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[3328,theory(equality)]) ).

cnf(3335,plain,
    ( xk = sz00
    | ~ aNaturalNumber0(xk)
    | esk8_0 != sz00 ),
    inference(spm,[status(thm)],[3329,1382,theory(equality)]) ).

cnf(3340,plain,
    ( xk = sz00
    | ~ aNaturalNumber0(xk)
    | esk9_0 != sz00 ),
    inference(spm,[status(thm)],[3329,2822,theory(equality)]) ).

cnf(3349,plain,
    ( xk = sz00
    | $false
    | esk8_0 != sz00 ),
    inference(rw,[status(thm)],[3335,146,theory(equality)]) ).

cnf(3350,plain,
    ( xk = sz00
    | esk8_0 != sz00 ),
    inference(cn,[status(thm)],[3349,theory(equality)]) ).

cnf(3351,plain,
    esk8_0 != sz00,
    inference(sr,[status(thm)],[3350,86,theory(equality)]) ).

cnf(3362,plain,
    ( xk = sz00
    | $false
    | esk9_0 != sz00 ),
    inference(rw,[status(thm)],[3340,146,theory(equality)]) ).

cnf(3363,plain,
    ( xk = sz00
    | esk9_0 != sz00 ),
    inference(cn,[status(thm)],[3362,theory(equality)]) ).

cnf(3364,plain,
    esk9_0 != sz00,
    inference(sr,[status(thm)],[3363,86,theory(equality)]) ).

cnf(3485,plain,
    sdtlseqdt0(esk8_0,xk),
    inference(sr,[status(thm)],[408,3364,theory(equality)]) ).

cnf(4608,plain,
    ( sz10 = X1
    | sz00 = X1
    | ~ iLess0(X1,xk)
    | ~ doDivides0(esk5_1(X1),xk)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[472,187]) ).

cnf(89659,plain,
    ( doDivides0(esk5_1(esk8_0),xk)
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ iLess0(esk8_0,xk) ),
    inference(sr,[status(thm)],[1264,3351,theory(equality)]) ).

cnf(89668,plain,
    ( sz00 = esk8_0
    | sz10 = esk8_0
    | ~ iLess0(esk8_0,xk)
    | ~ aNaturalNumber0(esk8_0)
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(spm,[status(thm)],[4608,89659,theory(equality)]) ).

cnf(89687,plain,
    ( sz00 = esk8_0
    | sz10 = esk8_0
    | ~ iLess0(esk8_0,xk)
    | $false
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(rw,[status(thm)],[89668,239,theory(equality)]) ).

cnf(89688,plain,
    ( sz00 = esk8_0
    | sz10 = esk8_0
    | ~ iLess0(esk8_0,xk)
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(cn,[status(thm)],[89687,theory(equality)]) ).

cnf(89689,plain,
    ( esk8_0 = sz10
    | ~ iLess0(esk8_0,xk)
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(sr,[status(thm)],[89688,3351,theory(equality)]) ).

cnf(89690,plain,
    ( ~ iLess0(esk8_0,xk)
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(sr,[status(thm)],[89689,235,theory(equality)]) ).

cnf(90855,plain,
    ( esk8_0 = xk
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | ~ sdtlseqdt0(esk8_0,xk)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[89690,226,theory(equality)]) ).

cnf(90856,plain,
    ( esk8_0 = xk
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | $false
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[90855,3485,theory(equality)]) ).

cnf(90857,plain,
    ( esk8_0 = xk
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | $false
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[90856,146,theory(equality)]) ).

cnf(90858,plain,
    ( esk8_0 = xk
    | ~ aNaturalNumber0(esk5_1(esk8_0))
    | $false
    | $false
    | $false ),
    inference(rw,[status(thm)],[90857,239,theory(equality)]) ).

cnf(90859,plain,
    ( esk8_0 = xk
    | ~ aNaturalNumber0(esk5_1(esk8_0)) ),
    inference(cn,[status(thm)],[90858,theory(equality)]) ).

cnf(90860,plain,
    ~ aNaturalNumber0(esk5_1(esk8_0)),
    inference(sr,[status(thm)],[90859,234,theory(equality)]) ).

cnf(90888,plain,
    ( esk8_0 = xk
    | sz00 = esk8_0
    | sz10 = esk8_0
    | ~ sdtlseqdt0(esk8_0,xk)
    | ~ aNaturalNumber0(esk8_0) ),
    inference(spm,[status(thm)],[90860,468,theory(equality)]) ).

cnf(90894,plain,
    ( esk8_0 = xk
    | sz00 = esk8_0
    | sz10 = esk8_0
    | $false
    | ~ aNaturalNumber0(esk8_0) ),
    inference(rw,[status(thm)],[90888,3485,theory(equality)]) ).

cnf(90895,plain,
    ( esk8_0 = xk
    | sz00 = esk8_0
    | sz10 = esk8_0
    | $false
    | $false ),
    inference(rw,[status(thm)],[90894,239,theory(equality)]) ).

cnf(90896,plain,
    ( esk8_0 = xk
    | sz00 = esk8_0
    | sz10 = esk8_0 ),
    inference(cn,[status(thm)],[90895,theory(equality)]) ).

cnf(90897,plain,
    ( esk8_0 = sz00
    | esk8_0 = sz10 ),
    inference(sr,[status(thm)],[90896,234,theory(equality)]) ).

cnf(90898,plain,
    esk8_0 = sz10,
    inference(sr,[status(thm)],[90897,3351,theory(equality)]) ).

cnf(90899,plain,
    $false,
    inference(sr,[status(thm)],[90898,235,theory(equality)]) ).

cnf(90900,plain,
    $false,
    90899,
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : NUM483+3 : TPTP v7.0.0. Released v4.0.0.
% 0.00/0.04  % Command  : Source/sine.py -e eprover -t %d %s
% 0.02/0.24  % Computer : n118.star.cs.uiowa.edu
% 0.02/0.24  % Model    : x86_64 x86_64
% 0.02/0.24  % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24  % Memory   : 32218.625MB
% 0.02/0.24  % OS       : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24  % CPULimit : 300
% 0.02/0.24  % DateTime : Fri Jan  5 06:46:30 CST 2018
% 0.02/0.24  % CPUTime  : 
% 0.06/0.28  % SZS status Started for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.28  --creating new selector for []
% 1.85/2.10  -running prover on /export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1 with time limit 29
% 1.85/2.10  -running prover with command ['/export/starexec/sandbox2/solver/bin/Source/./Source/PROVER/eproof.working', '-s', '-tLPO4', '-xAuto', '-tAuto', '--memory-limit=768', '--tptp3-format', '--cpu-limit=29', '/export/starexec/sandbox2/tmp/tmpox5AiH/sel_theBenchmark.p_1']
% 1.85/2.10  -prover status Theorem
% 1.85/2.10  Problem theBenchmark.p solved in phase 0.
% 1.85/2.10  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.85/2.10  % SZS status Ended for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.85/2.10  Solved 1 out of 1.
% 1.85/2.10  # Problem is unsatisfiable (or provable), constructing proof object
% 1.85/2.10  # SZS status Theorem
% 1.85/2.10  # SZS output start CNFRefutation.
% See solution above
% 1.85/2.11  # SZS output end CNFRefutation
%------------------------------------------------------------------------------