TSTP Solution File: NUM506+1 by ET---2.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM506+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n012.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 09:33:11 EDT 2022

% Result   : Theorem 1.16s 158.33s
% Output   : CNFRefutation 1.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   85 (  23 unt;   0 def)
%            Number of atoms       :  352 (  85 equ)
%            Maximal formula atoms :   32 (   4 avg)
%            Number of connectives :  447 ( 180   ~; 194   |;  49   &)
%                                         (   2 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   7 con; 0-2 aty)
%            Number of variables   :  106 (   2 sgn  59   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mDefPrime,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( isPrime0(X1)
      <=> ( X1 != sz00
          & X1 != sz10
          & ! [X2] :
              ( ( aNaturalNumber0(X2)
                & doDivides0(X2,X1) )
             => ( X2 = sz10
                | X2 = X1 ) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefPrime) ).

fof(mDefQuot,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != sz00
          & doDivides0(X1,X2) )
       => ! [X3] :
            ( X3 = sdtsldt0(X2,X1)
          <=> ( aNaturalNumber0(X3)
              & X2 = sdtasdt0(X1,X3) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mDefQuot) ).

fof(m__1860,hypothesis,
    ( isPrime0(xp)
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1860) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1837) ).

fof(m__2306,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2306) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB_02) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMulComm) ).

fof(mLETran,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETran) ).

fof(mIH_03,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != X2
          & sdtlseqdt0(X1,X2) )
       => iLess0(X1,X2) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mIH_03) ).

fof(mMonAdd,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( X1 != X2
          & sdtlseqdt0(X1,X2) )
       => ! [X3] :
            ( aNaturalNumber0(X3)
           => ( sdtpldt0(X3,X1) != sdtpldt0(X3,X2)
              & sdtlseqdt0(sdtpldt0(X3,X1),sdtpldt0(X3,X2))
              & sdtpldt0(X1,X3) != sdtpldt0(X2,X3)
              & sdtlseqdt0(sdtpldt0(X1,X3),sdtpldt0(X2,X3)) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mMonAdd) ).

fof(mSortsB,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtpldt0(X1,X2)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mSortsB) ).

fof(mAddCanc,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtpldt0(X1,X2) = sdtpldt0(X1,X3)
          | sdtpldt0(X2,X1) = sdtpldt0(X3,X1) )
       => X2 = X3 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mAddCanc) ).

fof(m__2377,hypothesis,
    ( xk != xp
    & sdtlseqdt0(xk,xp) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2377) ).

fof(mLEAsym,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLEAsym) ).

fof(m__1799,hypothesis,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( isPrime0(X3)
          & doDivides0(X3,sdtasdt0(X1,X2)) )
       => ( iLess0(sdtpldt0(sdtpldt0(X1,X2),X3),sdtpldt0(sdtpldt0(xn,xm),xp))
         => ( doDivides0(X3,X1)
            | doDivides0(X3,X2) ) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__1799) ).

fof(m__2362,hypothesis,
    ( sdtlseqdt0(xr,xk)
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2362) ).

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & doDivides0(xr,xk)
    & isPrime0(xr) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__2342) ).

fof(m__,conjecture,
    ( doDivides0(xr,xn)
    | doDivides0(xr,xm) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',m__) ).

fof(mLETotal,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in',mLETotal) ).

fof(c_0_19,plain,
    ! [X3,X4] :
      ( ( X3 != sz00
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( X3 != sz10
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( ~ aNaturalNumber0(X4)
        | ~ doDivides0(X4,X3)
        | X4 = sz10
        | X4 = X3
        | ~ isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( aNaturalNumber0(esk3_1(X3))
        | X3 = sz00
        | X3 = sz10
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( doDivides0(esk3_1(X3),X3)
        | X3 = sz00
        | X3 = sz10
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( esk3_1(X3) != sz10
        | X3 = sz00
        | X3 = sz10
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) )
      & ( esk3_1(X3) != X3
        | X3 = sz00
        | X3 = sz10
        | isPrime0(X3)
        | ~ aNaturalNumber0(X3) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefPrime])])])])])])]) ).

fof(c_0_20,plain,
    ! [X4,X5,X6,X6] :
      ( ( aNaturalNumber0(X6)
        | X6 != sdtsldt0(X5,X4)
        | X4 = sz00
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( X5 = sdtasdt0(X4,X6)
        | X6 != sdtsldt0(X5,X4)
        | X4 = sz00
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( ~ aNaturalNumber0(X6)
        | X5 != sdtasdt0(X4,X6)
        | X6 = sdtsldt0(X5,X4)
        | X4 = sz00
        | ~ doDivides0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefQuot])])])])])]) ).

cnf(c_0_21,plain,
    ( ~ aNaturalNumber0(X1)
    | ~ isPrime0(X1)
    | X1 != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_22,hypothesis,
    isPrime0(xp),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_23,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_24,plain,
    ( X2 = sz00
    | X1 = sdtasdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1)
    | X3 != sdtsldt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_25,hypothesis,
    xk = sdtsldt0(sdtasdt0(xn,xm),xp),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_26,hypothesis,
    doDivides0(xp,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[m__1860]) ).

cnf(c_0_27,hypothesis,
    sz00 != xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23])]) ).

fof(c_0_28,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

cnf(c_0_29,plain,
    ( X2 = sz00
    | aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ doDivides0(X2,X1)
    | X3 != sdtsldt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

fof(c_0_30,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtasdt0(X3,X4) = sdtasdt0(X4,X3) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])]) ).

cnf(c_0_31,hypothesis,
    ( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
    | X1 != xk
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_23])]),c_0_27]) ).

cnf(c_0_32,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_33,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_34,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_35,hypothesis,
    ( aNaturalNumber0(X1)
    | X1 != xk
    | ~ aNaturalNumber0(sdtasdt0(xn,xm)) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_26]),c_0_23])]),c_0_27]) ).

cnf(c_0_36,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_37,hypothesis,
    ( sdtasdt0(xp,X1) = sdtasdt0(xn,xm)
    | X1 != xk ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_33]),c_0_34])]) ).

cnf(c_0_38,hypothesis,
    ( aNaturalNumber0(X1)
    | X1 != xk ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_32]),c_0_33]),c_0_34])]) ).

cnf(c_0_39,hypothesis,
    ( sdtasdt0(xn,xm) = sdtasdt0(X1,xp)
    | X1 != xk ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_23])]),c_0_38]) ).

fof(c_0_40,plain,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ sdtlseqdt0(X4,X5)
      | ~ sdtlseqdt0(X5,X6)
      | sdtlseqdt0(X4,X6) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])]) ).

cnf(c_0_41,hypothesis,
    ( aNaturalNumber0(sdtasdt0(X1,xp))
    | X1 != xk ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_39]),c_0_33]),c_0_34])]) ).

fof(c_0_42,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | X3 = X4
      | ~ sdtlseqdt0(X3,X4)
      | iLess0(X3,X4) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIH_03])]) ).

fof(c_0_43,plain,
    ! [X4,X5,X6] :
      ( ( sdtpldt0(X6,X4) != sdtpldt0(X6,X5)
        | ~ aNaturalNumber0(X6)
        | X4 = X5
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( sdtlseqdt0(sdtpldt0(X6,X4),sdtpldt0(X6,X5))
        | ~ aNaturalNumber0(X6)
        | X4 = X5
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( sdtpldt0(X4,X6) != sdtpldt0(X5,X6)
        | ~ aNaturalNumber0(X6)
        | X4 = X5
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) )
      & ( sdtlseqdt0(sdtpldt0(X4,X6),sdtpldt0(X5,X6))
        | ~ aNaturalNumber0(X6)
        | X4 = X5
        | ~ sdtlseqdt0(X4,X5)
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5) ) ),
    inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonAdd])])])])])]) ).

fof(c_0_44,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtpldt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])]) ).

fof(c_0_45,plain,
    ! [X4,X5,X6] :
      ( ( sdtpldt0(X4,X5) != sdtpldt0(X4,X6)
        | X5 = X6
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) )
      & ( sdtpldt0(X5,X4) != sdtpldt0(X6,X4)
        | X5 = X6
        | ~ aNaturalNumber0(X4)
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddCanc])])]) ).

cnf(c_0_46,plain,
    ( sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X3,X2)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_40]) ).

cnf(c_0_47,hypothesis,
    sdtlseqdt0(xk,xp),
    inference(split_conjunct,[status(thm)],[m__2377]) ).

cnf(c_0_48,hypothesis,
    ( aNaturalNumber0(sdtasdt0(xn,xm))
    | X1 != xk ),
    inference(spm,[status(thm)],[c_0_41,c_0_39]) ).

fof(c_0_49,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | ~ sdtlseqdt0(X3,X4)
      | ~ sdtlseqdt0(X4,X3)
      | X3 = X4 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])]) ).

fof(c_0_50,hypothesis,
    ! [X4,X5,X6] :
      ( ~ aNaturalNumber0(X4)
      | ~ aNaturalNumber0(X5)
      | ~ aNaturalNumber0(X6)
      | ~ isPrime0(X6)
      | ~ doDivides0(X6,sdtasdt0(X4,X5))
      | ~ iLess0(sdtpldt0(sdtpldt0(X4,X5),X6),sdtpldt0(sdtpldt0(xn,xm),xp))
      | doDivides0(X6,X4)
      | doDivides0(X6,X5) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1799])]) ).

cnf(c_0_51,plain,
    ( iLess0(X1,X2)
    | X1 = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_42]) ).

cnf(c_0_52,plain,
    ( X2 = X1
    | sdtlseqdt0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_43]) ).

cnf(c_0_53,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_54,plain,
    ( X2 = X1
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtpldt0(X3,X2) != sdtpldt0(X3,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_45]) ).

cnf(c_0_55,hypothesis,
    ( sdtlseqdt0(X1,xp)
    | ~ sdtlseqdt0(X1,xk)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_23])]) ).

cnf(c_0_56,hypothesis,
    sdtlseqdt0(xr,xk),
    inference(split_conjunct,[status(thm)],[m__2362]) ).

cnf(c_0_57,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[m__2342]) ).

cnf(c_0_58,plain,
    ( X1 = sz00
    | aNaturalNumber0(sdtsldt0(X2,X1))
    | ~ doDivides0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(er,[status(thm)],[c_0_29]) ).

cnf(c_0_59,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(er,[status(thm)],[c_0_48]) ).

fof(c_0_60,negated_conjecture,
    ~ ( doDivides0(xr,xn)
      | doDivides0(xr,xm) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_61,plain,
    ( X1 = X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_49]) ).

cnf(c_0_62,hypothesis,
    xk != xp,
    inference(split_conjunct,[status(thm)],[m__2377]) ).

cnf(c_0_63,hypothesis,
    ( doDivides0(X1,X2)
    | doDivides0(X1,X3)
    | ~ iLess0(sdtpldt0(sdtpldt0(X3,X2),X1),sdtpldt0(sdtpldt0(xn,xm),xp))
    | ~ doDivides0(X1,sdtasdt0(X3,X2))
    | ~ isPrime0(X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_64,plain,
    ( X1 = X2
    | iLess0(sdtpldt0(X3,X2),sdtpldt0(X3,X1))
    | ~ sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53]),c_0_53]),c_0_54]) ).

cnf(c_0_65,hypothesis,
    ( sdtlseqdt0(xr,xp)
    | ~ aNaturalNumber0(xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57])]) ).

cnf(c_0_66,hypothesis,
    aNaturalNumber0(xk),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_25]),c_0_26]),c_0_23])]),c_0_27]),c_0_59])]) ).

fof(c_0_67,negated_conjecture,
    ( ~ doDivides0(xr,xn)
    & ~ doDivides0(xr,xm) ),
    inference(fof_nnf,[status(thm)],[c_0_60]) ).

fof(c_0_68,plain,
    ! [X3,X4] :
      ( ( X4 != X3
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( sdtlseqdt0(X4,X3)
        | sdtlseqdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETotal])])]) ).

cnf(c_0_69,hypothesis,
    ( ~ sdtlseqdt0(xp,xk)
    | ~ aNaturalNumber0(xk) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_47]),c_0_23])]),c_0_62]) ).

cnf(c_0_70,hypothesis,
    ( sdtlseqdt0(X1,xk)
    | ~ sdtlseqdt0(X1,xr)
    | ~ aNaturalNumber0(xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_56]),c_0_57])]) ).

cnf(c_0_71,hypothesis,
    ( xp = X1
    | doDivides0(X1,xn)
    | doDivides0(X1,xm)
    | ~ isPrime0(X1)
    | ~ doDivides0(X1,sdtasdt0(xn,xm))
    | ~ sdtlseqdt0(X1,xp)
    | ~ aNaturalNumber0(sdtpldt0(xn,xm))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_64]),c_0_34]),c_0_33]),c_0_23])]) ).

cnf(c_0_72,hypothesis,
    doDivides0(xr,sdtasdt0(xn,xm)),
    inference(split_conjunct,[status(thm)],[m__2362]) ).

cnf(c_0_73,hypothesis,
    isPrime0(xr),
    inference(split_conjunct,[status(thm)],[m__2342]) ).

cnf(c_0_74,hypothesis,
    sdtlseqdt0(xr,xp),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_65,c_0_66])]) ).

cnf(c_0_75,negated_conjecture,
    ~ doDivides0(xr,xn),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_76,negated_conjecture,
    ~ doDivides0(xr,xm),
    inference(split_conjunct,[status(thm)],[c_0_67]) ).

cnf(c_0_77,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_78,hypothesis,
    ( ~ sdtlseqdt0(xp,xr)
    | ~ aNaturalNumber0(xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_23])]) ).

cnf(c_0_79,hypothesis,
    ( xr = xp
    | ~ aNaturalNumber0(sdtpldt0(xn,xm)) ),
    inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_73]),c_0_74]),c_0_57])]),c_0_75]),c_0_76]) ).

cnf(c_0_80,hypothesis,
    ( sdtlseqdt0(xp,X1)
    | sdtlseqdt0(X1,xp)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_77,c_0_23]) ).

cnf(c_0_81,hypothesis,
    ~ sdtlseqdt0(xp,xr),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_78,c_0_66])]) ).

cnf(c_0_82,hypothesis,
    xr = xp,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_53]),c_0_33]),c_0_34])]) ).

cnf(c_0_83,hypothesis,
    sdtlseqdt0(xp,xp),
    inference(spm,[status(thm)],[c_0_80,c_0_23]) ).

cnf(c_0_84,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_81,c_0_82]),c_0_83])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : NUM506+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : run_ET %s %d
% 0.13/0.34  % Computer : n012.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Wed Jul  6 07:41:00 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.36/23.41  eprover: CPU time limit exceeded, terminating
% 0.36/23.41  eprover: eprover: CPU time limit exceeded, terminatingCPU time limit exceeded, terminating
% 0.36/23.41  
% 0.36/23.42  eprover: CPU time limit exceeded, terminating
% 0.49/46.42  eprover: CPU time limit exceeded, terminating
% 0.49/46.43  eprover: CPU time limit exceeded, terminating
% 0.49/46.43  eprover: CPU time limit exceeded, terminating
% 0.49/46.44  eprover: CPU time limit exceeded, terminating
% 0.63/69.44  eprover: CPU time limit exceeded, terminating
% 0.63/69.45  eprover: CPU time limit exceeded, terminating
% 0.63/69.45  eprover: CPU time limit exceeded, terminating
% 0.63/69.46  eprover: CPU time limit exceeded, terminating
% 0.78/92.45  eprover: CPU time limit exceeded, terminating
% 0.78/92.47  eprover: CPU time limit exceeded, terminating
% 0.78/92.48  eprover: CPU time limit exceeded, terminating
% 0.78/92.49  eprover: CPU time limit exceeded, terminating
% 0.92/115.48  eprover: CPU time limit exceeded, terminating
% 0.92/115.49  eprover: CPU time limit exceeded, terminating
% 0.92/115.49  eprover: CPU time limit exceeded, terminating
% 0.92/115.50  eprover: CPU time limit exceeded, terminating
% 1.04/138.50  eprover: CPU time limit exceeded, terminating
% 1.04/138.51  eprover: CPU time limit exceeded, terminating
% 1.04/138.52  eprover: CPU time limit exceeded, terminating
% 1.04/138.53  eprover: CPU time limit exceeded, terminating
% 1.16/158.33  # Running protocol protocol_eprover_4a02c828a8cc55752123edbcc1ad40e453c11447 for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # SinE strategy is GSinE(CountFormulas,hypos,1.4,,04,100,1.0)
% 1.16/158.33  # Preprocessing time       : 0.019 s
% 1.16/158.33  # Running protocol protocol_eprover_f171197f65f27d1ba69648a20c844832c84a5dd7 for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # Preprocessing time       : 0.009 s
% 1.16/158.33  # Running protocol protocol_eprover_eb48853eb71ccd2a6fdade56c25b63f5692e1a0c for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # Preprocessing time       : 0.010 s
% 1.16/158.33  # Running protocol protocol_eprover_761a0d093d9701c0eed884aebb46468e8d439c31 for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # SinE strategy is GSinE(CountFormulas,hypos,1.2,,,100,1.0)
% 1.16/158.33  # Preprocessing time       : 0.018 s
% 1.16/158.33  # Running protocol protocol_eprover_bb5e3cecdbc7660bd3a6f864cadb7769d8aea26a for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # SinE strategy is GSinE(CountFormulas,hypos,1.1,,,500,1.0)
% 1.16/158.33  # Preprocessing time       : 0.010 s
% 1.16/158.33  # Running protocol protocol_eprover_e252f7803940d118fa0ef69fc2319cb55aee23b9 for 23 seconds:
% 1.16/158.33  
% 1.16/158.33  # Failure: Resource limit exceeded (time)
% 1.16/158.33  # OLD status Res
% 1.16/158.33  # SinE strategy is GSinE(CountFormulas,,1.4,,03,100,1.0)
% 1.16/158.33  # Preprocessing time       : 0.019 s
% 1.16/158.33  # Running protocol protocol_eprover_b1d72019af42f5b571a6c0b233a5b6d1de064075 for 23 seconds:
% 1.16/158.33  # SinE strategy is GSinE(CountFormulas,hypos,1.5,,02,500,1.0)
% 1.16/158.33  # Preprocessing time       : 0.010 s
% 1.16/158.33  
% 1.16/158.33  # Proof found!
% 1.16/158.33  # SZS status Theorem
% 1.16/158.33  # SZS output start CNFRefutation
% See solution above
% 1.16/158.33  # Proof object total steps             : 85
% 1.16/158.33  # Proof object clause steps            : 52
% 1.16/158.33  # Proof object formula steps           : 33
% 1.16/158.33  # Proof object conjectures             : 5
% 1.16/158.33  # Proof object clause conjectures      : 2
% 1.16/158.33  # Proof object formula conjectures     : 3
% 1.16/158.33  # Proof object initial clauses used    : 27
% 1.16/158.33  # Proof object initial formulas used   : 19
% 1.16/158.33  # Proof object generating inferences   : 22
% 1.16/158.33  # Proof object simplifying inferences  : 62
% 1.16/158.33  # Training examples: 0 positive, 0 negative
% 1.16/158.33  # Parsed axioms                        : 51
% 1.16/158.33  # Removed by relevancy pruning/SinE    : 1
% 1.16/158.33  # Initial clauses                      : 93
% 1.16/158.33  # Removed in clause preprocessing      : 3
% 1.16/158.33  # Initial clauses in saturation        : 90
% 1.16/158.33  # Processed clauses                    : 38144
% 1.16/158.33  # ...of these trivial                  : 165
% 1.16/158.33  # ...subsumed                          : 33748
% 1.16/158.33  # ...remaining for further processing  : 4231
% 1.16/158.33  # Other redundant clauses eliminated   : 2782
% 1.16/158.33  # Clauses deleted for lack of memory   : 850544
% 1.16/158.33  # Backward-subsumed                    : 359
% 1.16/158.33  # Backward-rewritten                   : 675
% 1.16/158.33  # Generated clauses                    : 1036813
% 1.16/158.33  # ...of the previous two non-trivial   : 1007756
% 1.16/158.33  # Contextual simplify-reflections      : 16094
% 1.16/158.33  # Paramodulations                      : 1033587
% 1.16/158.33  # Factorizations                       : 3
% 1.16/158.33  # Equation resolutions                 : 3105
% 1.16/158.33  # Current number of processed clauses  : 3129
% 1.16/158.33  #    Positive orientable unit clauses  : 123
% 1.16/158.33  #    Positive unorientable unit clauses: 0
% 1.16/158.33  #    Negative unit clauses             : 246
% 1.16/158.33  #    Non-unit-clauses                  : 2760
% 1.16/158.33  # Current number of unprocessed clauses: 100655
% 1.16/158.33  # ...number of literals in the above   : 625723
% 1.16/158.33  # Current number of archived formulas  : 0
% 1.16/158.33  # Current number of archived clauses   : 1071
% 1.16/158.33  # Clause-clause subsumption calls (NU) : 6096793
% 1.16/158.33  # Rec. Clause-clause subsumption calls : 1936886
% 1.16/158.33  # Non-unit clause-clause subsumptions  : 27409
% 1.16/158.33  # Unit Clause-clause subsumption calls : 200563
% 1.16/158.33  # Rewrite failures with RHS unbound    : 0
% 1.16/158.33  # BW rewrite match attempts            : 69
% 1.16/158.33  # BW rewrite match successes           : 69
% 1.16/158.33  # Condensation attempts                : 0
% 1.16/158.33  # Condensation successes               : 0
% 1.16/158.33  # Termbank termtop insertions          : 23639942
% 1.16/158.33  
% 1.16/158.33  # -------------------------------------------------
% 1.16/158.33  # User time                : 18.980 s
% 1.16/158.33  # System time              : 0.122 s
% 1.16/158.33  # Total time               : 19.102 s
% 1.16/158.33  # Maximum resident set size: 139404 pages
% 1.16/161.51  eprover: CPU time limit exceeded, terminating
% 1.16/161.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53  eprover: No such file or directory
% 1.16/161.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53  eprover: No such file or directory
% 1.16/161.53  eprover: CPU time limit exceeded, terminating
% 1.16/161.53  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.53  eprover: No such file or directory
% 1.16/161.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.54  eprover: No such file or directory
% 1.16/161.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 1.16/161.54  eprover: No such file or directory
% 1.16/161.54  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.54  eprover: No such file or directory
% 1.16/161.55  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55  eprover: No such file or directory
% 1.16/161.55  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55  eprover: No such file or directory
% 1.16/161.55  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.55  eprover: No such file or directory
% 1.16/161.56  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.56  eprover: No such file or directory
% 1.16/161.56  eprover: CPU time limit exceeded, terminating
% 1.16/161.57  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.57  eprover: No such file or directory
% 1.16/161.57  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.57  eprover: No such file or directory
% 1.16/161.58  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58  eprover: No such file or directory
% 1.16/161.58  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58  eprover: No such file or directory
% 1.16/161.58  eprover: Cannot stat file /export/starexec/sandbox/solver/bin/../tmp/theBenchmark.p
% 1.16/161.58  eprover: No such file or directory
%------------------------------------------------------------------------------