TSTP Solution File: NUM528+3 by ET---2.0

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%------------------------------------------------------------------------------
% File     : ET---2.0
% Problem  : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_ET %s %d

% Computer : n007.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 09:33:26 EDT 2022

% Result   : Theorem 0.25s 1.42s
% Output   : CNFRefutation 0.25s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  102 (  29 unt;   0 def)
%            Number of atoms       :  336 ( 130 equ)
%            Maximal formula atoms :   15 (   3 avg)
%            Number of connectives :  382 ( 148   ~; 152   |;  60   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :   98 (   0 sgn  53   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(mLETotal,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETotal) ).

fof(m__,conjecture,
    ( xm != xn
    & ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xm,X1) = xn )
      | sdtlseqdt0(xm,xn) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__) ).

fof(m__2987,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp)
    & xn != sz00
    & xm != sz00
    & xp != sz00 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__2987) ).

fof(mSortsB_02,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => aNaturalNumber0(sdtasdt0(X1,X2)) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsB_02) ).

fof(m__3152,hypothesis,
    ( ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xn,X1) = xm )
      | sdtlseqdt0(xn,xm) )
   => ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(sdtasdt0(xn,xn),X1) = sdtasdt0(xm,xm) )
      & sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3152) ).

fof(m_AddZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtpldt0(X1,sz00) = X1
        & X1 = sdtpldt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_AddZero) ).

fof(m__3082,hypothesis,
    sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3082) ).

fof(m__3046,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xn) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xn))
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xn = sdtasdt0(xp,X1) )
    & doDivides0(xp,xn) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3046) ).

fof(mSortsC,axiom,
    aNaturalNumber0(sz00),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC) ).

fof(mZeroMul,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtasdt0(X1,X2) = sz00
       => ( X1 = sz00
          | X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mZeroMul) ).

fof(m__3059,hypothesis,
    ( aNaturalNumber0(xq)
    & xn = sdtasdt0(xp,xq)
    & xq = sdtsldt0(xn,xp) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3059) ).

fof(mAddComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mAddComm) ).

fof(m__3014,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3014) ).

fof(mZeroAdd,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtpldt0(X1,X2) = sz00
       => ( X1 = sz00
          & X2 = sz00 ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mZeroAdd) ).

fof(mLETran,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X3) )
       => sdtlseqdt0(X1,X3) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLETran) ).

fof(mMulCanc,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( X1 != sz00
       => ! [X2,X3] :
            ( ( aNaturalNumber0(X2)
              & aNaturalNumber0(X3) )
           => ( ( sdtasdt0(X1,X2) = sdtasdt0(X1,X3)
                | sdtasdt0(X2,X1) = sdtasdt0(X3,X1) )
             => X2 = X3 ) ) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulCanc) ).

fof(m_MulUnit,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz10) = X1
        & X1 = sdtasdt0(sz10,X1) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m_MulUnit) ).

fof(m__3025,hypothesis,
    ( xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',m__3025) ).

fof(mLEAsym,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( ( sdtlseqdt0(X1,X2)
          & sdtlseqdt0(X2,X1) )
       => X1 = X2 ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mLEAsym) ).

fof(mSortsC_01,axiom,
    ( aNaturalNumber0(sz10)
    & sz10 != sz00 ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mSortsC_01) ).

fof(mMonMul2,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( X1 != sz00
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMonMul2) ).

fof(mMulComm,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => sdtasdt0(X1,X2) = sdtasdt0(X2,X1) ),
    file('/export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p',mMulComm) ).

fof(c_0_22,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])])]) ).

fof(c_0_23,negated_conjecture,
    ~ ( xm != xn
      & ( ? [X1] :
            ( aNaturalNumber0(X1)
            & sdtpldt0(xm,X1) = xn )
        | sdtlseqdt0(xm,xn) ) ),
    inference(assume_negation,[status(cth)],[m__]) ).

cnf(c_0_24,plain,
    ( sdtlseqdt0(X2,X1)
    | sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_22]) ).

cnf(c_0_25,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_26,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | aNaturalNumber0(sdtasdt0(X3,X4)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])]) ).

fof(c_0_27,negated_conjecture,
    ! [X2] :
      ( ( ~ aNaturalNumber0(X2)
        | sdtpldt0(xm,X2) != xn
        | xm = xn )
      & ( ~ sdtlseqdt0(xm,xn)
        | xm = xn ) ),
    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)],[c_0_23])])])])])]) ).

cnf(c_0_28,hypothesis,
    ( sdtlseqdt0(xm,X1)
    | sdtlseqdt0(X1,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_30,hypothesis,
    ! [X2] :
      ( ( aNaturalNumber0(esk9_0)
        | ~ aNaturalNumber0(X2)
        | sdtpldt0(xn,X2) != xm )
      & ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
        | ~ aNaturalNumber0(X2)
        | sdtpldt0(xn,X2) != xm )
      & ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
        | ~ aNaturalNumber0(X2)
        | sdtpldt0(xn,X2) != xm )
      & ( aNaturalNumber0(esk9_0)
        | ~ sdtlseqdt0(xn,xm) )
      & ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
        | ~ sdtlseqdt0(xn,xm) )
      & ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
        | ~ sdtlseqdt0(xn,xm) ) ),
    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)],[m__3152])])])])])])]) ).

fof(c_0_31,plain,
    ! [X2] :
      ( ( sdtpldt0(X2,sz00) = X2
        | ~ aNaturalNumber0(X2) )
      & ( X2 = sdtpldt0(sz00,X2)
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_AddZero])])]) ).

cnf(c_0_32,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,hypothesis,
    sdtasdt0(xm,xm) = sdtasdt0(xp,sdtasdt0(xq,xq)),
    inference(split_conjunct,[status(thm)],[m__3082]) ).

cnf(c_0_34,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_35,hypothesis,
    ( aNaturalNumber0(esk7_0)
    & sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0)
    & doDivides0(xp,sdtasdt0(xn,xn))
    & aNaturalNumber0(esk8_0)
    & xn = sdtasdt0(xp,esk8_0)
    & doDivides0(xp,xn) ),
    inference(skolemize,[status(esa)],[inference(shift_quantors,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[m__3046])])])]) ).

cnf(c_0_36,negated_conjecture,
    ( xm = xn
    | ~ sdtlseqdt0(xm,xn) ),
    inference(split_conjunct,[status(thm)],[c_0_27]) ).

cnf(c_0_37,hypothesis,
    ( sdtlseqdt0(xn,xm)
    | sdtlseqdt0(xm,xn) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_38,hypothesis,
    ( aNaturalNumber0(esk9_0)
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_39,plain,
    ( sdtpldt0(X1,sz00) = X1
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_40,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

fof(c_0_41,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | sdtasdt0(X3,X4) != sz00
      | X3 = sz00
      | X4 = sz00 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroMul])]) ).

cnf(c_0_42,hypothesis,
    ( aNaturalNumber0(sdtasdt0(xm,xm))
    | ~ aNaturalNumber0(sdtasdt0(xq,xq)) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).

cnf(c_0_43,hypothesis,
    aNaturalNumber0(xq),
    inference(split_conjunct,[status(thm)],[m__3059]) ).

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

cnf(c_0_45,hypothesis,
    sdtasdt0(xn,xn) = sdtasdt0(xp,esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_46,hypothesis,
    aNaturalNumber0(esk7_0),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,hypothesis,
    ( aNaturalNumber0(esk9_0)
    | ~ sdtlseqdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_48,negated_conjecture,
    ( xm = xn
    | sdtlseqdt0(xn,xm) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_49,hypothesis,
    ( aNaturalNumber0(esk9_0)
    | xm != xn ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_29])]) ).

cnf(c_0_50,plain,
    ( X1 = sz00
    | X2 = sz00
    | sdtasdt0(X2,X1) != sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_41]) ).

cnf(c_0_51,hypothesis,
    sdtasdt0(xp,sdtasdt0(xm,xm)) = sdtasdt0(xn,xn),
    inference(split_conjunct,[status(thm)],[m__3014]) ).

cnf(c_0_52,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[m__2987]) ).

cnf(c_0_53,hypothesis,
    aNaturalNumber0(sdtasdt0(xm,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_32]),c_0_43])]) ).

fof(c_0_54,plain,
    ! [X3,X4] :
      ( ( X3 = sz00
        | sdtpldt0(X3,X4) != sz00
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) )
      & ( X4 = sz00
        | sdtpldt0(X3,X4) != sz00
        | ~ aNaturalNumber0(X3)
        | ~ aNaturalNumber0(X4) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroAdd])])]) ).

cnf(c_0_55,hypothesis,
    ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
    | ~ sdtlseqdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_56,plain,
    ( sdtpldt0(X1,X2) = sdtpldt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_57,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xn)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_45]),c_0_46]),c_0_34])]) ).

cnf(c_0_58,hypothesis,
    aNaturalNumber0(esk9_0),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_49]) ).

cnf(c_0_59,hypothesis,
    ( sdtasdt0(xm,xm) = sz00
    | sdtasdt0(xn,xn) != sz00 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_34])]),c_0_52]),c_0_53])]) ).

cnf(c_0_60,hypothesis,
    xm != sz00,
    inference(split_conjunct,[status(thm)],[m__2987]) ).

fof(c_0_61,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_62,plain,
    ( X1 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X1) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_63,hypothesis,
    ( sdtpldt0(esk9_0,sdtasdt0(xn,xn)) = sdtasdt0(xm,xm)
    | ~ sdtlseqdt0(xn,xm) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_58])]) ).

cnf(c_0_64,hypothesis,
    sdtasdt0(xn,xn) != sz00,
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_59]),c_0_25])]),c_0_60]) ).

cnf(c_0_65,plain,
    ( sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X3,X2)
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_61]) ).

cnf(c_0_66,hypothesis,
    ( sdtlseqdt0(xn,X1)
    | sdtlseqdt0(X1,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_29]) ).

cnf(c_0_67,hypothesis,
    ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
    | sdtpldt0(xn,X1) != xm
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_68,hypothesis,
    ( sdtasdt0(xm,xm) != sz00
    | ~ sdtlseqdt0(xn,xm) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_58]),c_0_57])]),c_0_64]) ).

cnf(c_0_69,negated_conjecture,
    ( xm = xn
    | sdtlseqdt0(X1,xm)
    | ~ sdtlseqdt0(X1,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_48]),c_0_29]),c_0_25])]) ).

cnf(c_0_70,hypothesis,
    sdtlseqdt0(xn,xn),
    inference(spm,[status(thm)],[c_0_66,c_0_29]) ).

fof(c_0_71,plain,
    ! [X4,X5,X6] :
      ( ( sdtasdt0(X4,X5) != sdtasdt0(X4,X6)
        | X5 = X6
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6)
        | X4 = sz00
        | ~ aNaturalNumber0(X4) )
      & ( sdtasdt0(X5,X4) != sdtasdt0(X6,X4)
        | X5 = X6
        | ~ aNaturalNumber0(X5)
        | ~ aNaturalNumber0(X6)
        | X4 = sz00
        | ~ aNaturalNumber0(X4) ) ),
    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)],[mMulCanc])])])])])]) ).

cnf(c_0_72,plain,
    ( X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | sdtpldt0(X2,X1) != sz00 ),
    inference(split_conjunct,[status(thm)],[c_0_54]) ).

cnf(c_0_73,hypothesis,
    ( sdtpldt0(sdtasdt0(xn,xn),esk9_0) = sdtasdt0(xm,xm)
    | xm != xn ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_39]),c_0_40]),c_0_29])]) ).

cnf(c_0_74,negated_conjecture,
    ( xm = xn
    | sdtasdt0(xm,xm) != sz00 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_29])]) ).

cnf(c_0_75,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X3,X1) != sdtasdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

cnf(c_0_76,hypothesis,
    sdtasdt0(xm,xm) != sz00,
    inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_57])]),c_0_58])]),c_0_64]),c_0_74]) ).

fof(c_0_77,plain,
    ! [X2] :
      ( ( sdtasdt0(X2,sz10) = X2
        | ~ aNaturalNumber0(X2) )
      & ( X2 = sdtasdt0(sz10,X2)
        | ~ aNaturalNumber0(X2) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulUnit])])]) ).

fof(c_0_78,hypothesis,
    ! [X3,X4] :
      ( xp != sz10
      & ( ~ aNaturalNumber0(X4)
        | xp != sdtasdt0(X3,X4)
        | ~ aNaturalNumber0(X3)
        | X3 = sz10
        | X3 = xp )
      & ( ~ doDivides0(X3,xp)
        | ~ aNaturalNumber0(X3)
        | X3 = sz10
        | X3 = xp )
      & isPrime0(xp) ),
    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)],[m__3025])])])])])]) ).

cnf(c_0_79,plain,
    ( X1 = sz00
    | X3 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | sdtasdt0(X1,X3) != sdtasdt0(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_71]) ).

fof(c_0_80,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])]) ).

cnf(c_0_81,hypothesis,
    ( X1 = xp
    | sdtasdt0(X1,sdtasdt0(xm,xm)) != sdtasdt0(xn,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_51]),c_0_34])]),c_0_53])]),c_0_76]) ).

cnf(c_0_82,plain,
    ( X1 = sdtasdt0(sz10,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_77]) ).

cnf(c_0_83,plain,
    aNaturalNumber0(sz10),
    inference(split_conjunct,[status(thm)],[mSortsC_01]) ).

cnf(c_0_84,hypothesis,
    xp != sz10,
    inference(split_conjunct,[status(thm)],[c_0_78]) ).

cnf(c_0_85,hypothesis,
    ( X1 = esk7_0
    | sdtasdt0(xp,X1) != sdtasdt0(xn,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_45]),c_0_46]),c_0_34])]),c_0_52]) ).

fof(c_0_86,plain,
    ! [X3,X4] :
      ( ~ aNaturalNumber0(X3)
      | ~ aNaturalNumber0(X4)
      | X3 = sz00
      | sdtlseqdt0(X4,sdtasdt0(X4,X3)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMonMul2])]) ).

fof(c_0_87,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_88,plain,
    ( X1 = X2
    | ~ sdtlseqdt0(X2,X1)
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_80]) ).

cnf(c_0_89,hypothesis,
    ( sdtlseqdt0(sdtasdt0(xn,xn),sdtasdt0(xm,xm))
    | ~ sdtlseqdt0(xn,xm) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_90,hypothesis,
    sdtasdt0(xm,xm) != sdtasdt0(xn,xn),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_82]),c_0_83]),c_0_53])]),c_0_84]) ).

cnf(c_0_91,hypothesis,
    sdtasdt0(xm,xm) = esk7_0,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_51]),c_0_53])]) ).

cnf(c_0_92,plain,
    ( sdtlseqdt0(X1,sdtasdt0(X1,X2))
    | X2 = sz00
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_86]) ).

cnf(c_0_93,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_87]) ).

cnf(c_0_94,hypothesis,
    ( sdtasdt0(xm,xm) = sdtasdt0(xn,xn)
    | ~ sdtlseqdt0(sdtasdt0(xm,xm),sdtasdt0(xn,xn))
    | ~ sdtlseqdt0(xn,xm) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_89]),c_0_57]),c_0_53])]) ).

cnf(c_0_95,hypothesis,
    sdtasdt0(xn,xn) != esk7_0,
    inference(rw,[status(thm)],[c_0_90,c_0_91]) ).

cnf(c_0_96,plain,
    ( X1 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(spm,[status(thm)],[c_0_92,c_0_93]) ).

cnf(c_0_97,hypothesis,
    ( ~ sdtlseqdt0(esk7_0,sdtasdt0(xn,xn))
    | ~ sdtlseqdt0(xn,xm) ),
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_94,c_0_91]),c_0_91]),c_0_95]) ).

cnf(c_0_98,hypothesis,
    sdtlseqdt0(esk7_0,sdtasdt0(xn,xn)),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_45]),c_0_34]),c_0_46])]),c_0_52]) ).

cnf(c_0_99,hypothesis,
    ~ sdtlseqdt0(xn,xm),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_97,c_0_98])]) ).

cnf(c_0_100,negated_conjecture,
    xm = xn,
    inference(sr,[status(thm)],[c_0_48,c_0_99]) ).

cnf(c_0_101,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_99,c_0_100]),c_0_70])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : NUM528+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13  % Command  : run_ET %s %d
% 0.14/0.34  % Computer : n007.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Thu Jul  7 12:17:14 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.25/1.42  # Running protocol protocol_eprover_63dc1b1eb7d762c2f3686774d32795976f981b97 for 23 seconds:
% 0.25/1.42  # Preprocessing time       : 0.020 s
% 0.25/1.42  
% 0.25/1.42  # Proof found!
% 0.25/1.42  # SZS status Theorem
% 0.25/1.42  # SZS output start CNFRefutation
% See solution above
% 0.25/1.42  # Proof object total steps             : 102
% 0.25/1.42  # Proof object clause steps            : 63
% 0.25/1.42  # Proof object formula steps           : 39
% 0.25/1.42  # Proof object conjectures             : 8
% 0.25/1.42  # Proof object clause conjectures      : 5
% 0.25/1.42  # Proof object formula conjectures     : 3
% 0.25/1.42  # Proof object initial clauses used    : 33
% 0.25/1.42  # Proof object initial formulas used   : 22
% 0.25/1.42  # Proof object generating inferences   : 25
% 0.25/1.42  # Proof object simplifying inferences  : 73
% 0.25/1.42  # Training examples: 0 positive, 0 negative
% 0.25/1.42  # Parsed axioms                        : 48
% 0.25/1.42  # Removed by relevancy pruning/SinE    : 0
% 0.25/1.42  # Initial clauses                      : 107
% 0.25/1.42  # Removed in clause preprocessing      : 3
% 0.25/1.42  # Initial clauses in saturation        : 104
% 0.25/1.42  # Processed clauses                    : 1200
% 0.25/1.42  # ...of these trivial                  : 11
% 0.25/1.42  # ...subsumed                          : 620
% 0.25/1.42  # ...remaining for further processing  : 569
% 0.25/1.42  # Other redundant clauses eliminated   : 41
% 0.25/1.42  # Clauses deleted for lack of memory   : 0
% 0.25/1.42  # Backward-subsumed                    : 55
% 0.25/1.42  # Backward-rewritten                   : 204
% 0.25/1.42  # Generated clauses                    : 3874
% 0.25/1.42  # ...of the previous two non-trivial   : 3588
% 0.25/1.42  # Contextual simplify-reflections      : 203
% 0.25/1.42  # Paramodulations                      : 3801
% 0.25/1.42  # Factorizations                       : 1
% 0.25/1.42  # Equation resolutions                 : 69
% 0.25/1.42  # Current number of processed clauses  : 306
% 0.25/1.42  #    Positive orientable unit clauses  : 36
% 0.25/1.42  #    Positive unorientable unit clauses: 0
% 0.25/1.42  #    Negative unit clauses             : 19
% 0.25/1.42  #    Non-unit-clauses                  : 251
% 0.25/1.42  # Current number of unprocessed clauses: 1339
% 0.25/1.42  # ...number of literals in the above   : 8218
% 0.25/1.42  # Current number of archived formulas  : 0
% 0.25/1.42  # Current number of archived clauses   : 262
% 0.25/1.42  # Clause-clause subsumption calls (NU) : 45619
% 0.25/1.42  # Rec. Clause-clause subsumption calls : 14494
% 0.25/1.42  # Non-unit clause-clause subsumptions  : 668
% 0.25/1.42  # Unit Clause-clause subsumption calls : 2041
% 0.25/1.42  # Rewrite failures with RHS unbound    : 0
% 0.25/1.42  # BW rewrite match attempts            : 20
% 0.25/1.42  # BW rewrite match successes           : 20
% 0.25/1.42  # Condensation attempts                : 0
% 0.25/1.42  # Condensation successes               : 0
% 0.25/1.42  # Termbank termtop insertions          : 69556
% 0.25/1.42  
% 0.25/1.42  # -------------------------------------------------
% 0.25/1.42  # User time                : 0.124 s
% 0.25/1.42  # System time              : 0.004 s
% 0.25/1.42  # Total time               : 0.128 s
% 0.25/1.42  # Maximum resident set size: 6036 pages
% 0.25/23.41  eprover: CPU time limit exceeded, terminating
% 0.25/23.42  eprover: CPU time limit exceeded, terminating
% 0.25/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.43  eprover: No such file or directory
% 0.25/23.43  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.43  eprover: No such file or directory
% 0.25/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.44  eprover: No such file or directory
% 0.25/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.44  eprover: No such file or directory
% 0.25/23.44  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.44  eprover: No such file or directory
% 0.25/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.45  eprover: No such file or directory
% 0.25/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45  eprover: No such file or directory
% 0.25/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.45  eprover: No such file or directory
% 0.25/23.45  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.45  eprover: No such file or directory
% 0.25/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.46  eprover: No such file or directory
% 0.25/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.46  eprover: No such file or directory
% 0.25/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.46  eprover: No such file or directory
% 0.25/23.46  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.46  eprover: No such file or directory
% 0.25/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47  eprover: No such file or directory
% 0.25/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.47  eprover: No such file or directory
% 0.25/23.47  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.47  eprover: No such file or directory
% 0.25/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.48  eprover: No such file or directory
% 0.25/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48  eprover: No such file or directory
% 0.25/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48  eprover: No such file or directory
% 0.25/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.48  eprover: No such file or directory
% 0.25/23.48  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p
% 0.25/23.48  eprover: No such file or directory
% 0.25/23.49  eprover: Cannot stat file /export/starexec/sandbox2/solver/bin/../tmp/theBenchmark.p.mepo_128.in
% 0.25/23.49  eprover: No such file or directory
%------------------------------------------------------------------------------