TSTP Solution File: NUM503+3 by E---3.1.00

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%------------------------------------------------------------------------------
% File     : E---3.1.00
% Problem  : NUM503+3 : TPTP v8.2.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_E %s %d THM

% Computer : n003.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  : 300s
% DateTime : Tue May 21 01:14:21 EDT 2024

% Result   : ContradictoryAxioms 6.13s 1.27s
% Output   : CNFRefutation 6.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   23
% Syntax   : Number of formulae    :  138 (  44 unt;   0 def)
%            Number of atoms       :  517 ( 174 equ)
%            Maximal formula atoms :   28 (   3 avg)
%            Number of connectives :  596 ( 217   ~; 212   |; 134   &)
%                                         (   1 <=>;  32  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   18 (  18 usr;  14 con; 0-2 aty)
%            Number of variables   :  156 (   0 sgn  75   !;  18   ?)

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

fof(mDefLE,axiom,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
      <=> ? [X3] :
            ( aNaturalNumber0(X3)
            & sdtpldt0(X1,X3) = X2 ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefLE) ).

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

fof(m__2342,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2342) ).

fof(m__2287,hypothesis,
    ( xn != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xn,X1) = xp )
    & sdtlseqdt0(xn,xp)
    & xm != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xm,X1) = xp )
    & sdtlseqdt0(xm,xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2287) ).

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

fof(m__2362,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xr,X1) = xk )
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xr,X1) )
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2362) ).

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/benchmark/theBenchmark.p',mLETran) ).

fof(m__2306,hypothesis,
    ( aNaturalNumber0(xk)
    & sdtasdt0(xn,xm) = sdtasdt0(xp,xk)
    & xk = sdtsldt0(sdtasdt0(xn,xm),xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2306) ).

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

fof(m__1860,hypothesis,
    ( xp != sz00
    & xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1860) ).

fof(m__1837,hypothesis,
    ( aNaturalNumber0(xn)
    & aNaturalNumber0(xm)
    & aNaturalNumber0(xp) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1837) ).

fof(m_MulZero,axiom,
    ! [X1] :
      ( aNaturalNumber0(X1)
     => ( sdtasdt0(X1,sz00) = sz00
        & sz00 = sdtasdt0(sz00,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m_MulZero) ).

fof(mMulAsso,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMulAsso) ).

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

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

fof(m__2389,hypothesis,
    ( ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xp,X1) = xk )
    & sdtlseqdt0(xp,xk) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2389) ).

fof(m__1870,hypothesis,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xp,X1) = xn )
      | sdtlseqdt0(xp,xn) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1870) ).

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

fof(m__2315,hypothesis,
    ~ ( xk = sz00
      | xk = sz10 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2315) ).

fof(mMonMul,axiom,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( X1 != sz00
          & X2 != X3
          & sdtlseqdt0(X2,X3) )
       => ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mMonMul) ).

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/benchmark/theBenchmark.p',mMulCanc) ).

fof(m__2075,hypothesis,
    ~ ( ? [X1] :
          ( aNaturalNumber0(X1)
          & sdtpldt0(xp,X1) = xm )
      | sdtlseqdt0(xp,xm) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2075) ).

fof(c_0_23,plain,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( sdtlseqdt0(X1,X2)
        | ( X2 != X1
          & sdtlseqdt0(X2,X1) ) ) ),
    inference(fof_simplification,[status(thm)],[mLETotal]) ).

fof(c_0_24,plain,
    ! [X37,X38,X40] :
      ( ( aNaturalNumber0(esk1_2(X37,X38))
        | ~ sdtlseqdt0(X37,X38)
        | ~ aNaturalNumber0(X37)
        | ~ aNaturalNumber0(X38) )
      & ( sdtpldt0(X37,esk1_2(X37,X38)) = X38
        | ~ sdtlseqdt0(X37,X38)
        | ~ aNaturalNumber0(X37)
        | ~ aNaturalNumber0(X38) )
      & ( ~ aNaturalNumber0(X40)
        | sdtpldt0(X37,X40) != X38
        | sdtlseqdt0(X37,X38)
        | ~ aNaturalNumber0(X37)
        | ~ aNaturalNumber0(X38) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mDefLE])])])])])]) ).

fof(c_0_25,plain,
    ! [X7,X8] :
      ( ~ aNaturalNumber0(X7)
      | ~ aNaturalNumber0(X8)
      | aNaturalNumber0(sdtpldt0(X7,X8)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB])])]) ).

fof(c_0_26,hypothesis,
    ( aNaturalNumber0(xr)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & xk = sdtasdt0(xr,X1) )
    & doDivides0(xr,xk)
    & xr != sz00
    & xr != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xr = sdtasdt0(X1,X2) )
            | doDivides0(X1,xr) ) )
       => ( X1 = sz10
          | X1 = xr ) )
    & isPrime0(xr) ),
    inference(fof_simplification,[status(thm)],[m__2342]) ).

fof(c_0_27,hypothesis,
    ( xn != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xn,X1) = xp )
    & sdtlseqdt0(xn,xp)
    & xm != xp
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtpldt0(xm,X1) = xp )
    & sdtlseqdt0(xm,xp) ),
    inference(fof_simplification,[status(thm)],[m__2287]) ).

fof(c_0_28,plain,
    ! [X50,X51] :
      ( ( X51 != X50
        | sdtlseqdt0(X50,X51)
        | ~ aNaturalNumber0(X50)
        | ~ aNaturalNumber0(X51) )
      & ( sdtlseqdt0(X51,X50)
        | sdtlseqdt0(X50,X51)
        | ~ aNaturalNumber0(X50)
        | ~ aNaturalNumber0(X51) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_23])])])]) ).

fof(c_0_29,plain,
    ! [X1,X2] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2) )
     => ( X1 != sz00
       => sdtlseqdt0(X2,sdtasdt0(X2,X1)) ) ),
    inference(fof_simplification,[status(thm)],[mMonMul2]) ).

cnf(c_0_30,plain,
    ( sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | sdtpldt0(X2,X1) != X3
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    ( aNaturalNumber0(sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

fof(c_0_32,hypothesis,
    ( aNaturalNumber0(esk13_0)
    & sdtpldt0(xr,esk13_0) = xk
    & aNaturalNumber0(esk14_0)
    & sdtasdt0(xn,xm) = sdtasdt0(xr,esk14_0)
    & doDivides0(xr,sdtasdt0(xn,xm)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2362])]) ).

fof(c_0_33,hypothesis,
    ! [X107,X108] :
      ( aNaturalNumber0(xr)
      & aNaturalNumber0(esk12_0)
      & xk = sdtasdt0(xr,esk12_0)
      & doDivides0(xr,xk)
      & xr != sz00
      & xr != sz10
      & ( ~ aNaturalNumber0(X108)
        | xr != sdtasdt0(X107,X108)
        | ~ aNaturalNumber0(X107)
        | X107 = sz10
        | X107 = xr )
      & ( ~ doDivides0(X107,xr)
        | ~ aNaturalNumber0(X107)
        | X107 = sz10
        | X107 = xr )
      & isPrime0(xr) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])])])])]) ).

fof(c_0_34,plain,
    ! [X47,X48,X49] :
      ( ~ aNaturalNumber0(X47)
      | ~ aNaturalNumber0(X48)
      | ~ aNaturalNumber0(X49)
      | ~ sdtlseqdt0(X47,X48)
      | ~ sdtlseqdt0(X48,X49)
      | sdtlseqdt0(X47,X49) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLETran])])]) ).

fof(c_0_35,hypothesis,
    ( xn != xp
    & aNaturalNumber0(esk10_0)
    & sdtpldt0(xn,esk10_0) = xp
    & sdtlseqdt0(xn,xp)
    & xm != xp
    & aNaturalNumber0(esk11_0)
    & sdtpldt0(xm,esk11_0) = xp
    & sdtlseqdt0(xm,xp) ),
    inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_27])])]) ).

cnf(c_0_36,plain,
    ( sdtlseqdt0(X1,X2)
    | sdtlseqdt0(X2,X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_28]) ).

cnf(c_0_37,hypothesis,
    aNaturalNumber0(xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

fof(c_0_38,plain,
    ! [X59,X60] :
      ( ~ aNaturalNumber0(X59)
      | ~ aNaturalNumber0(X60)
      | X59 = sz00
      | sdtlseqdt0(X60,sdtasdt0(X60,X59)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_29])])]) ).

fof(c_0_39,plain,
    ! [X17,X18] :
      ( ~ aNaturalNumber0(X17)
      | ~ aNaturalNumber0(X18)
      | sdtasdt0(X17,X18) = sdtasdt0(X18,X17) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulComm])])]) ).

fof(c_0_40,hypothesis,
    ( xp != sz00
    & xp != sz10
    & ! [X1] :
        ( ( aNaturalNumber0(X1)
          & ( ? [X2] :
                ( aNaturalNumber0(X2)
                & xp = sdtasdt0(X1,X2) )
            | doDivides0(X1,xp) ) )
       => ( X1 = sz10
          | X1 = xp ) )
    & isPrime0(xp)
    & ? [X1] :
        ( aNaturalNumber0(X1)
        & sdtasdt0(xn,xm) = sdtasdt0(xp,X1) )
    & doDivides0(xp,sdtasdt0(xn,xm)) ),
    inference(fof_simplification,[status(thm)],[m__1860]) ).

cnf(c_0_41,plain,
    ( sdtlseqdt0(X1,sdtpldt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(csr,[status(thm)],[inference(er,[status(thm)],[c_0_30]),c_0_31]) ).

cnf(c_0_42,hypothesis,
    sdtpldt0(xr,esk13_0) = xk,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_43,hypothesis,
    aNaturalNumber0(xr),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_44,hypothesis,
    aNaturalNumber0(esk13_0),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_45,plain,
    ( sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_34]) ).

cnf(c_0_46,hypothesis,
    sdtlseqdt0(xn,xp),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_47,hypothesis,
    aNaturalNumber0(xp),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_48,hypothesis,
    aNaturalNumber0(xn),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_49,hypothesis,
    ( sdtlseqdt0(xk,X1)
    | sdtlseqdt0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

fof(c_0_50,plain,
    ! [X23] :
      ( ( sdtasdt0(X23,sz00) = sz00
        | ~ aNaturalNumber0(X23) )
      & ( sz00 = sdtasdt0(sz00,X23)
        | ~ aNaturalNumber0(X23) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m_MulZero])])])]) ).

fof(c_0_51,plain,
    ! [X19,X20,X21] :
      ( ~ aNaturalNumber0(X19)
      | ~ aNaturalNumber0(X20)
      | ~ aNaturalNumber0(X21)
      | sdtasdt0(sdtasdt0(X19,X20),X21) = sdtasdt0(X19,sdtasdt0(X20,X21)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mMulAsso])])]) ).

fof(c_0_52,plain,
    ! [X9,X10] :
      ( ~ aNaturalNumber0(X9)
      | ~ aNaturalNumber0(X10)
      | aNaturalNumber0(sdtasdt0(X9,X10)) ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mSortsB_02])])]) ).

cnf(c_0_53,plain,
    ( X1 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X2,X1))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_38]) ).

cnf(c_0_54,plain,
    ( sdtasdt0(X1,X2) = sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

fof(c_0_55,hypothesis,
    ! [X99,X100] :
      ( xp != sz00
      & xp != sz10
      & ( ~ aNaturalNumber0(X100)
        | xp != sdtasdt0(X99,X100)
        | ~ aNaturalNumber0(X99)
        | X99 = sz10
        | X99 = xp )
      & ( ~ doDivides0(X99,xp)
        | ~ aNaturalNumber0(X99)
        | X99 = sz10
        | X99 = xp )
      & isPrime0(xp)
      & aNaturalNumber0(esk9_0)
      & sdtasdt0(xn,xm) = sdtasdt0(xp,esk9_0)
      & doDivides0(xp,sdtasdt0(xn,xm)) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])])])]) ).

cnf(c_0_56,hypothesis,
    sdtlseqdt0(xr,xk),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_44])]) ).

cnf(c_0_57,hypothesis,
    sdtpldt0(xn,esk10_0) = xp,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_58,hypothesis,
    aNaturalNumber0(esk10_0),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

fof(c_0_59,plain,
    ! [X45,X46] :
      ( ~ aNaturalNumber0(X45)
      | ~ aNaturalNumber0(X46)
      | ~ sdtlseqdt0(X45,X46)
      | ~ sdtlseqdt0(X46,X45)
      | X45 = X46 ),
    inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mLEAsym])])]) ).

cnf(c_0_60,hypothesis,
    ( sdtlseqdt0(X1,xp)
    | ~ sdtlseqdt0(X1,xn)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]),c_0_48])]) ).

cnf(c_0_61,hypothesis,
    ( sdtlseqdt0(xn,xk)
    | sdtlseqdt0(xk,xn) ),
    inference(spm,[status(thm)],[c_0_49,c_0_48]) ).

fof(c_0_62,hypothesis,
    ( aNaturalNumber0(esk15_0)
    & sdtpldt0(xp,esk15_0) = xk
    & sdtlseqdt0(xp,xk) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[m__2389])]) ).

fof(c_0_63,hypothesis,
    ! [X102] :
      ( ( ~ aNaturalNumber0(X102)
        | sdtpldt0(xp,X102) != xn )
      & ~ sdtlseqdt0(xp,xn) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__1870])])])]) ).

cnf(c_0_64,plain,
    ( sdtasdt0(X1,sz00) = sz00
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_65,plain,
    ( sdtasdt0(sdtasdt0(X1,X2),X3) = sdtasdt0(X1,sdtasdt0(X2,X3))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_51]) ).

cnf(c_0_66,plain,
    aNaturalNumber0(sz00),
    inference(split_conjunct,[status(thm)],[mSortsC]) ).

cnf(c_0_67,plain,
    ( aNaturalNumber0(sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_52]) ).

cnf(c_0_68,hypothesis,
    xk = sdtasdt0(xr,esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_69,hypothesis,
    aNaturalNumber0(esk12_0),
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_70,plain,
    ( X1 = sz00
    | sdtlseqdt0(X2,sdtasdt0(X1,X2))
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_53,c_0_54]) ).

cnf(c_0_71,hypothesis,
    sdtasdt0(xn,xm) = sdtasdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[m__2306]) ).

cnf(c_0_72,hypothesis,
    xp != sz00,
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_73,hypothesis,
    ( sdtlseqdt0(X1,xk)
    | ~ sdtlseqdt0(X1,xr)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_56]),c_0_37]),c_0_43])]) ).

cnf(c_0_74,hypothesis,
    ( sdtlseqdt0(xn,X1)
    | xp != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_57]),c_0_48]),c_0_58])]) ).

cnf(c_0_75,hypothesis,
    ( X2 = sz10
    | X2 = xp
    | ~ aNaturalNumber0(X1)
    | xp != sdtasdt0(X2,X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_55]) ).

cnf(c_0_76,hypothesis,
    xr != sz10,
    inference(split_conjunct,[status(thm)],[c_0_33]) ).

cnf(c_0_77,plain,
    ( X1 = X2
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ sdtlseqdt0(X1,X2)
    | ~ sdtlseqdt0(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_59]) ).

cnf(c_0_78,hypothesis,
    ( sdtlseqdt0(xn,xk)
    | sdtlseqdt0(xk,xp) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_60,c_0_61]),c_0_37])]) ).

cnf(c_0_79,hypothesis,
    sdtlseqdt0(xp,xk),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_80,hypothesis,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xp,X1) != xn ),
    inference(split_conjunct,[status(thm)],[c_0_63]) ).

cnf(c_0_81,plain,
    ( sdtpldt0(X1,esk1_2(X1,X2)) = X2
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

fof(c_0_82,hypothesis,
    ( xk != sz00
    & xk != sz10 ),
    inference(fof_nnf,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2315])]) ).

cnf(c_0_83,hypothesis,
    sdtlseqdt0(xm,xp),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_84,hypothesis,
    aNaturalNumber0(xm),
    inference(split_conjunct,[status(thm)],[m__1837]) ).

cnf(c_0_85,plain,
    ( sdtasdt0(X1,sdtasdt0(X2,sz00)) = sz00
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_64,c_0_65]),c_0_66])]),c_0_67]) ).

cnf(c_0_86,hypothesis,
    ( sdtasdt0(xr,sdtasdt0(esk12_0,X1)) = sdtasdt0(xk,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_68]),c_0_69]),c_0_43])]) ).

cnf(c_0_87,hypothesis,
    sdtlseqdt0(xk,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_70,c_0_71]),c_0_37]),c_0_47])]),c_0_72]) ).

cnf(c_0_88,hypothesis,
    aNaturalNumber0(sdtasdt0(xn,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_71]),c_0_37]),c_0_47])]) ).

cnf(c_0_89,hypothesis,
    ( sdtlseqdt0(xn,xk)
    | xr != xp ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_74]),c_0_48]),c_0_43])]) ).

cnf(c_0_90,hypothesis,
    ( xr = xp
    | xk != xp ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_68]),c_0_43]),c_0_69])]),c_0_76]) ).

cnf(c_0_91,hypothesis,
    ( xk = xp
    | sdtlseqdt0(xn,xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_79]),c_0_37]),c_0_47])]) ).

cnf(c_0_92,hypothesis,
    ( X1 != xn
    | ~ sdtlseqdt0(xp,X1)
    | ~ aNaturalNumber0(esk1_2(xp,X1))
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_47])]) ).

cnf(c_0_93,plain,
    ( aNaturalNumber0(esk1_2(X1,X2))
    | ~ sdtlseqdt0(X1,X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_94,hypothesis,
    xk != sz00,
    inference(split_conjunct,[status(thm)],[c_0_82]) ).

fof(c_0_95,plain,
    ! [X1,X2,X3] :
      ( ( aNaturalNumber0(X1)
        & aNaturalNumber0(X2)
        & aNaturalNumber0(X3) )
     => ( ( X1 != sz00
          & X2 != X3
          & sdtlseqdt0(X2,X3) )
       => ( sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
          & sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
          & sdtasdt0(X2,X1) != sdtasdt0(X3,X1)
          & sdtlseqdt0(sdtasdt0(X2,X1),sdtasdt0(X3,X1)) ) ) ),
    inference(fof_simplification,[status(thm)],[mMonMul]) ).

fof(c_0_96,plain,
    ! [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 ) ) ) ),
    inference(fof_simplification,[status(thm)],[mMulCanc]) ).

cnf(c_0_97,hypothesis,
    sdtpldt0(xm,esk11_0) = xp,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_98,hypothesis,
    aNaturalNumber0(esk11_0),
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_99,hypothesis,
    ( sdtlseqdt0(X1,xp)
    | ~ sdtlseqdt0(X1,xm)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_83]),c_0_47]),c_0_84])]) ).

cnf(c_0_100,hypothesis,
    ( sdtlseqdt0(xm,xk)
    | sdtlseqdt0(xk,xm) ),
    inference(spm,[status(thm)],[c_0_49,c_0_84]) ).

cnf(c_0_101,plain,
    ( sz00 = sdtasdt0(sz00,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_50]) ).

cnf(c_0_102,hypothesis,
    sdtasdt0(xk,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_69]),c_0_43]),c_0_66])]) ).

cnf(c_0_103,hypothesis,
    ( sdtlseqdt0(X1,sdtasdt0(xn,xm))
    | ~ sdtlseqdt0(X1,xk)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_87]),c_0_88]),c_0_37])]) ).

cnf(c_0_104,hypothesis,
    sdtlseqdt0(xn,xk),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).

cnf(c_0_105,hypothesis,
    ( X1 != xn
    | ~ sdtlseqdt0(xp,X1)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_93]),c_0_47])]) ).

cnf(c_0_106,hypothesis,
    sdtlseqdt0(xp,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_53,c_0_71]),c_0_47]),c_0_37])]),c_0_94]) ).

fof(c_0_107,plain,
    ! [X55,X56,X57] :
      ( ( sdtasdt0(X55,X56) != sdtasdt0(X55,X57)
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtlseqdt0(sdtasdt0(X55,X56),sdtasdt0(X55,X57))
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtasdt0(X56,X55) != sdtasdt0(X57,X55)
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) )
      & ( sdtlseqdt0(sdtasdt0(X56,X55),sdtasdt0(X57,X55))
        | X55 = sz00
        | X56 = X57
        | ~ sdtlseqdt0(X56,X57)
        | ~ aNaturalNumber0(X55)
        | ~ aNaturalNumber0(X56)
        | ~ aNaturalNumber0(X57) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_95])])])]) ).

fof(c_0_108,plain,
    ! [X30,X31,X32] :
      ( ( sdtasdt0(X30,X31) != sdtasdt0(X30,X32)
        | X31 = X32
        | ~ aNaturalNumber0(X31)
        | ~ aNaturalNumber0(X32)
        | X30 = sz00
        | ~ aNaturalNumber0(X30) )
      & ( sdtasdt0(X31,X30) != sdtasdt0(X32,X30)
        | X31 = X32
        | ~ aNaturalNumber0(X31)
        | ~ aNaturalNumber0(X32)
        | X30 = sz00
        | ~ aNaturalNumber0(X30) ) ),
    inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_96])])])])]) ).

cnf(c_0_109,hypothesis,
    ( sdtlseqdt0(xm,X1)
    | xp != X1
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_97]),c_0_84]),c_0_98])]) ).

cnf(c_0_110,hypothesis,
    ( sdtlseqdt0(xm,xk)
    | sdtlseqdt0(xk,xp) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_37])]) ).

fof(c_0_111,hypothesis,
    ! [X103] :
      ( ( ~ aNaturalNumber0(X103)
        | sdtpldt0(xp,X103) != xm )
      & ~ sdtlseqdt0(xp,xm) ),
    inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[m__2075])])])]) ).

cnf(c_0_112,plain,
    ( sdtasdt0(sz00,sdtasdt0(X1,X2)) = sdtasdt0(sz00,X2)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_101]),c_0_66])]) ).

cnf(c_0_113,hypothesis,
    sdtasdt0(sz00,xk) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_102]),c_0_66]),c_0_37])]) ).

cnf(c_0_114,hypothesis,
    sdtlseqdt0(xn,sdtasdt0(xn,xm)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_48])]) ).

cnf(c_0_115,hypothesis,
    sdtasdt0(xn,xm) != xn,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_88])]) ).

cnf(c_0_116,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X1,X3))
    | X1 = sz00
    | X2 = X3
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_107]) ).

cnf(c_0_117,plain,
    ( X2 = X3
    | X1 = sz00
    | sdtasdt0(X1,X2) != sdtasdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_108]) ).

cnf(c_0_118,plain,
    ( sdtlseqdt0(sdtasdt0(X1,X2),sdtasdt0(X3,X2))
    | X2 = sz00
    | X1 = X3
    | ~ sdtlseqdt0(X1,X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1)
    | ~ aNaturalNumber0(X3) ),
    inference(split_conjunct,[status(thm)],[c_0_107]) ).

cnf(c_0_119,hypothesis,
    ( sdtlseqdt0(xm,xk)
    | xr != xp ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_109]),c_0_84]),c_0_43])]) ).

cnf(c_0_120,hypothesis,
    ( xk = xp
    | sdtlseqdt0(xm,xk) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_110]),c_0_79]),c_0_37]),c_0_47])]) ).

cnf(c_0_121,hypothesis,
    ( ~ aNaturalNumber0(X1)
    | sdtpldt0(xp,X1) != xm ),
    inference(split_conjunct,[status(thm)],[c_0_111]) ).

cnf(c_0_122,hypothesis,
    sdtpldt0(xp,esk15_0) = xk,
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_123,hypothesis,
    aNaturalNumber0(esk15_0),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_124,hypothesis,
    sdtasdt0(sz00,sdtasdt0(xn,xm)) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_71]),c_0_113]),c_0_37]),c_0_47])]) ).

cnf(c_0_125,hypothesis,
    ~ sdtlseqdt0(sdtasdt0(xn,xm),xn),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_114]),c_0_48]),c_0_88])]),c_0_115]) ).

cnf(c_0_126,plain,
    ( X1 = sz00
    | X2 = X3
    | ~ sdtlseqdt0(sdtasdt0(X1,X3),sdtasdt0(X1,X2))
    | ~ sdtlseqdt0(X2,X3)
    | ~ aNaturalNumber0(X3)
    | ~ aNaturalNumber0(X2)
    | ~ aNaturalNumber0(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_116]),c_0_67]),c_0_67]),c_0_117]) ).

cnf(c_0_127,hypothesis,
    ( X1 = xp
    | sdtlseqdt0(sdtasdt0(X1,xk),sdtasdt0(xn,xm))
    | ~ sdtlseqdt0(X1,xp)
    | ~ aNaturalNumber0(X1) ),
    inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_71]),c_0_47]),c_0_37])]),c_0_94]) ).

cnf(c_0_128,hypothesis,
    sdtlseqdt0(xm,xk),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_119,c_0_90]),c_0_120]) ).

cnf(c_0_129,hypothesis,
    xk != xm,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123])]) ).

cnf(c_0_130,hypothesis,
    xn != xp,
    inference(split_conjunct,[status(thm)],[c_0_35]) ).

cnf(c_0_131,hypothesis,
    sdtasdt0(sz00,xm) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_124]),c_0_84]),c_0_48])]) ).

cnf(c_0_132,plain,
    ( sdtlseqdt0(sz00,X1)
    | sdtlseqdt0(X1,sz00)
    | ~ aNaturalNumber0(X1) ),
    inference(spm,[status(thm)],[c_0_36,c_0_66]) ).

cnf(c_0_133,hypothesis,
    ~ sdtlseqdt0(sdtasdt0(xm,xn),xn),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_54]),c_0_84]),c_0_48])]) ).

cnf(c_0_134,hypothesis,
    xn = sz00,
    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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_126,c_0_127]),c_0_128]),c_0_37]),c_0_84]),c_0_48]),c_0_46])]),c_0_129]),c_0_130]) ).

cnf(c_0_135,hypothesis,
    sdtasdt0(xm,sz00) = sz00,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_131]),c_0_84]),c_0_66])]) ).

cnf(c_0_136,plain,
    sdtlseqdt0(sz00,sz00),
    inference(spm,[status(thm)],[c_0_132,c_0_66]) ).

cnf(c_0_137,hypothesis,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_134]),c_0_136])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : NUM503+3 : TPTP v8.2.0. Released v4.0.0.
% 0.07/0.13  % Command    : run_E %s %d THM
% 0.13/0.35  % Computer : n003.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon May 20 04:40:53 EDT 2024
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  Running first-order theorem proving
% 0.20/0.48  Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.13/1.27  # Version: 3.1.0
% 6.13/1.27  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.27  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.27  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.27  # Starting new_bool_3 with 300s (1) cores
% 6.13/1.27  # Starting new_bool_1 with 300s (1) cores
% 6.13/1.27  # Starting sh5l with 300s (1) cores
% 6.13/1.27  # G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 5460 completed with status 0
% 6.13/1.27  # Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 6.13/1.27  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.27  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.27  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.27  # No SInE strategy applied
% 6.13/1.27  # Search class: FGHSF-FSLM32-SFFFFFNN
% 6.13/1.27  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.13/1.27  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 811s (1) cores
% 6.13/1.27  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.13/1.27  # Starting new_bool_3 with 136s (1) cores
% 6.13/1.27  # Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 6.13/1.27  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y1 with 136s (1) cores
% 6.13/1.27  # G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y1 with pid 5470 completed with status 0
% 6.13/1.27  # Result found by G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y1
% 6.13/1.27  # Preprocessing class: FSLSSMSSSSSNFFN.
% 6.13/1.27  # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 6.13/1.27  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 6.13/1.27  # No SInE strategy applied
% 6.13/1.27  # Search class: FGHSF-FSLM32-SFFFFFNN
% 6.13/1.27  # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 6.13/1.27  # Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 811s (1) cores
% 6.13/1.27  # Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 6.13/1.27  # Starting new_bool_3 with 136s (1) cores
% 6.13/1.27  # Starting U----_116_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN1 with 136s (1) cores
% 6.13/1.27  # Starting G-N--_023_B07_F1_SP_PI_Q7_CS_SP_CO_S5PRR_S0Y1 with 136s (1) cores
% 6.13/1.27  # Preprocessing time       : 0.004 s
% 6.13/1.27  
% 6.13/1.27  # Proof found!
% 6.13/1.27  # SZS status ContradictoryAxioms
% 6.13/1.27  # SZS output start CNFRefutation
% See solution above
% 6.13/1.27  # Parsed axioms                        : 51
% 6.13/1.27  # Removed by relevancy pruning/SinE    : 0
% 6.13/1.27  # Initial clauses                      : 247
% 6.13/1.27  # Removed in clause preprocessing      : 3
% 6.13/1.27  # Initial clauses in saturation        : 244
% 6.13/1.27  # Processed clauses                    : 4473
% 6.13/1.27  # ...of these trivial                  : 308
% 6.13/1.27  # ...subsumed                          : 2331
% 6.13/1.27  # ...remaining for further processing  : 1834
% 6.13/1.27  # Other redundant clauses eliminated   : 0
% 6.13/1.27  # Clauses deleted for lack of memory   : 0
% 6.13/1.27  # Backward-subsumed                    : 139
% 6.13/1.27  # Backward-rewritten                   : 498
% 6.13/1.27  # Generated clauses                    : 54902
% 6.13/1.27  # ...of the previous two non-redundant : 49092
% 6.13/1.27  # ...aggressively subsumed             : 0
% 6.13/1.27  # Contextual simplify-reflections      : 200
% 6.13/1.27  # Paramodulations                      : 54762
% 6.13/1.27  # Factorizations                       : 3
% 6.13/1.27  # NegExts                              : 0
% 6.13/1.27  # Equation resolutions                 : 129
% 6.13/1.27  # Disequality decompositions           : 0
% 6.13/1.27  # Total rewrite steps                  : 48616
% 6.13/1.27  # ...of those cached                   : 48264
% 6.13/1.27  # Propositional unsat checks           : 0
% 6.13/1.27  #    Propositional check models        : 0
% 6.13/1.27  #    Propositional check unsatisfiable : 0
% 6.13/1.27  #    Propositional clauses             : 0
% 6.13/1.27  #    Propositional clauses after purity: 0
% 6.13/1.27  #    Propositional unsat core size     : 0
% 6.13/1.27  #    Propositional preprocessing time  : 0.000
% 6.13/1.27  #    Propositional encoding time       : 0.000
% 6.13/1.27  #    Propositional solver time         : 0.000
% 6.13/1.27  #    Success case prop preproc time    : 0.000
% 6.13/1.27  #    Success case prop encoding time   : 0.000
% 6.13/1.27  #    Success case prop solver time     : 0.000
% 6.13/1.27  # Current number of processed clauses  : 1191
% 6.13/1.27  #    Positive orientable unit clauses  : 295
% 6.13/1.27  #    Positive unorientable unit clauses: 0
% 6.13/1.27  #    Negative unit clauses             : 63
% 6.13/1.27  #    Non-unit-clauses                  : 833
% 6.13/1.27  # Current number of unprocessed clauses: 44662
% 6.13/1.27  # ...number of literals in the above   : 338247
% 6.13/1.27  # Current number of archived formulas  : 0
% 6.13/1.27  # Current number of archived clauses   : 642
% 6.13/1.27  # Clause-clause subsumption calls (NU) : 305762
% 6.13/1.27  # Rec. Clause-clause subsumption calls : 103785
% 6.13/1.27  # Non-unit clause-clause subsumptions  : 1566
% 6.13/1.27  # Unit Clause-clause subsumption calls : 40515
% 6.13/1.27  # Rewrite failures with RHS unbound    : 0
% 6.13/1.27  # BW rewrite match attempts            : 258
% 6.13/1.27  # BW rewrite match successes           : 60
% 6.13/1.27  # Condensation attempts                : 4473
% 6.13/1.27  # Condensation successes               : 13
% 6.13/1.27  # Termbank termtop insertions          : 1263079
% 6.13/1.27  # Search garbage collected termcells   : 2480
% 6.13/1.27  
% 6.13/1.27  # -------------------------------------------------
% 6.13/1.27  # User time                : 0.726 s
% 6.13/1.27  # System time              : 0.029 s
% 6.13/1.27  # Total time               : 0.755 s
% 6.13/1.27  # Maximum resident set size: 2396 pages
% 6.13/1.27  
% 6.13/1.27  # -------------------------------------------------
% 6.13/1.27  # User time                : 3.617 s
% 6.13/1.27  # System time              : 0.094 s
% 6.13/1.27  # Total time               : 3.711 s
% 6.13/1.27  # Maximum resident set size: 1760 pages
% 6.13/1.27  % E---3.1 exiting
% 6.13/1.27  % E exiting
%------------------------------------------------------------------------------